Polarized Absorption Spectra of Purines and Pyrimidines Citation Stewart, Robert Farrell (1963) Polarized Absorption Spectra of Purines and Pyrimidines. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/Y85T-DN22. https://resolver.caltech.edu/CaltechTHESIS:10302012-085345824 Abstract The polarized absorption spectra for single crystals of 1-methylthymine and 9-methyladenine and hydrogen-bonded complex of the two have been determined. A microspectro-photometer was constructed to carry out these measurements. A technique for preparing thin sections of the single crystals with thicknesses down to 10^(-5) cm has been developed. Special attention has been given to intensity determinations for the several ultraviolet absorption spectra. Item Type: Thesis (Dissertation (Ph.D.)) Subject Keywords: (Chemistry) Degree Grantor: California Institute of Technology Division: Chemistry and Chemical Engineering Major Option: Chemistry Thesis Availability: Public (worldwide access) Research Advisor(s): Davidson, Norman R. Thesis Committee: Unknown, Unknown Defense Date: 1 January 1963 Record Number: CaltechTHESIS:10302012-085345824 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:10302012-085345824 DOI: 10.7907/Y85T-DN22 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 7249 Collection: CaltechTHESIS Deposited By: Benjamin Perez Deposited On: 30 Oct 2012 16:15 Last Modified: 09 Jan 2024 00:44 Thesis Files Preview PDF - Final Version See Usage Policy. 36MB Repository Staff Only: item control page

POL A R I ZED ABSORP TION SPECTRA OF PURINES AND PYR IMIDINES Thesis by Robert Far rell S tewart I n Partial Fulfillment of the Requirement s For th e D egree o f Doc tor of P hilosophy California.lnsti tute of Technolog y Pasadena . California • 1963 ~a-Cwc; l;;r]T'1'//J- a TOVTlJ \· J ! AC KNOWLEDGMENTS 1 am gra teful to Professor N orman Davidson for his c ounsel and guidance during my graduate s tudies here at the Institute. gratitude cannot be ove r stated . Tlu s I wish to thank Dr. Kar st H oogs teen for his coopera tion a nd advice i n the cry s tal work; 1 am i n debted to Dr . Walter Huber for hi s many helpful suggestions concerning the vari ous mathematical deri vations t hrou g hout thi s investigation. The cooperation of the Geology Departm ent i n th e optical mea surements of t-"11e cry s tals is apprecia ted . Mr. William Schuelke's a dvice made the cry stal grinding and m icro s pectrophotometer possible, I am thankful to Dr . P hilip S eeger and to M r. Robert Deverill for their hel p i n writing compute r p r ogr ams . M y general educ a tion at the I ns ti tut e has been an invaluable experience. I am particularly g r a teful for the association with and advice from Profe ssors Hammond and Robin s on, a nd Dr. Vinograd. The Na tional In s tit;ute of Health predoctoral fellowship and I ns titute S chola r ship, which suppor t ed me i n thi s work and g eneral studies, a r e appr e ciate d . My wife' s love and encouragement during my graduate studie s have been i nvaluable; p r ogress could not have been made without her. ABS TRACT The polarized ab s orption spectra for s ingle crystals of 1 ~methyl thymine and 9-methyladenine and a hydrogen-bonded complex of the two have been dete rmined. A microspectro- photometer was constructed to carry out these measurements. A technique for preparing thin sections of the single crystals wi th thick nesse s down to 10 -5 em has been developed. S pecial attention ha s been given to intensity determinations for the s everal ultraviolet absorption spectra. T ABLE OF CONTENTS S ection I ntroduction 1 The M icros pectrophotometer 6 Gen eral Description Component s and C ons tr u ction Operational Features Retardation Measurements The P repa r atio n of C rystals Crystal Growth . The Technique for Preparing Thin Sections 6 8 16 25 33 33 34 O ptic a l Propertie s of Crystals and Crystallographic Data • .52 S olu tion S pectra and Oscillator S trengths 55 P olarized Ab sorption Spec tra of the Singl e Crystals 58 1-Methylthymine • 9 - Methyladenine • H oogsteen D i mer Discussion T r ansiti on Moment Dir e ction s and Wa velength Shifts • 1-Methyl thy mine 9 - Me thylade nine and the Hoogstecn D i mer I n ten sities and Compari son of Molec ul a r Spectra 58 66 70 84 84 88 104 A ppendi x A 11 9 i\ ppendix B 128 Appenclix C 148 R eferenc es 15 3 P ropositions 156 INTRODUCTION Polarized absorption spectra of single cry stals of purin e s and p yrimidine s are of intere s t for the understanding o f absorption spectra , exciton phenomena and other electronic properties of nucleic acids ( 27, 5, 24). With favor able c rystal s ymm etries, dichroism measure- ments are useful for resolving absorption bands and f or assigning transition dipole moment directions to electron ically allowed tran s itions. To da t e ultr a violet dichroism measurements of purines and p yrimidines h ave been sparse . Lyon s ( 14) measured the polarization of the first three ultraviolet tr ansitions of 2 - amino-4 -ch l o ro- 6 methylpyrimidine and of 2 -chloro - 4 , 6 -dirnethylpyrimidine . c hroic ratio s N o di - were r e ported, but the polari za tions we re used for tentative assi gnments of the transitions . Seed s ( 25) has r e p o rted that the fir s t near ultraviolet absorption band for 2-hydroxy-4, 6 dimethylpyrimidine is i n the p l ane of the pyrimidine rin g . The experi- ment s described in this research a r e p ola riza tion s tudie s of single cry s tals of 1 - rnethylthymine, 9 - me thyladenine, a nd a hydrogen bonded complex of 1-methylthymine and 9 -meth yladenine. The major difficulty in p olarization experiments of this nature lie s in the preparation of thin , s ingle crystals wi th cr oss - sectional dim~nsions of between 10 -4 s everal h undr ed m icron s and a con trolled thickness and 10 -5 em. l n the past the tec hnical problem has 2 been overcome by selecting thin sublimation flake s , by crystallizing between two clo sely spaced plates, or by doping a transparent crystal with a chromophore which has a fixed orientation. These technique s have limitation s; sublimation and cry stallization usually result in only one predominant form and doping is restricted to special cases. one can prepare thin sections (~10· 5 When em) of single crystal s in an arbitrary crystallographic plane, then thi s technical problem in cry stal absorption is solved. Thi s research has attempted to solve the problem by optically polishing tractable crystals to thicknesses of 10 -5 em. The techniq u.e has n ot been perfected for the general problem, but a major development i n this direction has been made . Microtornes, developed for thin sec tioning i n electron microscopy, have made this advance poss ible. A crystal was optically polished by slicing small sections of£ of it with a diamond knife; the small increment of advancement for the microtome arm allowed grinding of the cry stals down to a thickness of 10- 5 em without destroying it. The faces of the cry stal were kept p arallel by observing interference color s of the crystal between crossed polaroids. One cry s t a l, the hydrogen bonded d.imer, was successfully polished in a direction perpendicular to the molecular layers. The method employed i n thi s wor k c an probably be extended to the polishing of soft organic crystals in a direction of choice. 3 In the past the accuracy of intensity measurements from absorption has been difficult to estimate due to thickness uncertainty and reflections off the crystal face. special attention in this work. Both p roblems hav e been given Thicknesses were determined by measuring the retardation of the crystal under crossed Nicols with a quartz wedge and monochromator. The relati vely high birefringences of the crystals made thickness measurements possible with the retardation technique. The reflection coefficients of the crystal can be calculated by the well k nown Fresnel formulae if the refractive indices and the absorption coefficients at the wavelengths ·of intere s t are known. The refractive indice s in an absorption band of interest for the research presented here were calculated from a two term Drude di spersion expression with the help of a K ramers- K ronig transformation. A more accurate method of determining crystal thickness has recently been applied in the field o£ crystal spectroscopy (1). By means of d ouble beam i nterferometry B ree and Thirllnamachanbran were able to determine the thickness of single naphthalene cry stals w ithin 5o/o to lOo/o. The interfe rometer technique made it possible, moreover. for the se workers to determine refractive indices up to the edge of the absorption band. Recent theories on the molecular interactions i n crystal s ( 4), 4 " aggregates'' (15), and polymers ( 27 , 24) have led to the concern for a ccurate intensity measurementG. In particular, the nucleic a cid polymers have interesting intensity behavior when compared to the nucleo tide monomers. For DNA the observed absorptivity per nucleotide is 0. 6 of the sum of the molar absorptivities of the i ndi vidual n ucleotides in solution. The decrease i n intensity (hypochromism) i s uniform over the first ultraviolet absorption band of the polymer and shows no apparent wavelength shift from the overall absorption band due to the several nucleotide monomers. The phenomenon of hypo- chromism in the nucleic a cids has been a subject of theoretical interest for the last few years. Tinoco and, i ndependently , Rhodes have pre sen ted a fir at order dispersion theory to a ccount for the intensity behavior of polynucleotide a. I n the absence of exchange, the per - turbation interaction is coulombic; the potential energy opera tor has been expanded to g ive the first non -zero matrix elements. These elements are of a transition d ipole-dipole interaction type. There - fore the geometry of the several , ordered nucleotides in the polymer is an i mportant factor for determining the intensity behavior. There is a remote possibility that a good theory will make it possible to draw some conclusions about the base sequence in a nucleic acid fro m its hypochromism . The crystalline purine and pyrimidine derivatives studied i n this re search a re approximations to polynucleotide s and are expected s to have similar interactions between chromophore s . By determining transition dipole moment directions for the various absorption band s and by knowing the cry stal s tr u cture one can test the Tinoco or Rhodes theory for intensity behavior in polymers. I n practice, how- ever, thi s wo rk did not realize a rigorous te s t of the theory. Several source s of error led to intensity uncertainties of from lOo/o to 40o/o. Furthermore, only the tran ::3ition dipole moment directions for the fir3t ultraviolet absorption bands could be determined. As a result the experiments were limited to a qualit..1. tive compa rison with the theory. • 6 THE M ICR 0.3 PEC TROPHOTOMETER General Description. The m icrospectr ophotometer con sist s of a magne tically stabilized, high pressu1·e xenon a rc, two monochromator o i n tandem, a modified polarizing micro s c ope, and a photomultiplier tube, the voltage of which i s amplified b y a n A. C. coupled amplifier. A schematic drawing o f the optical sys t em is shown i n Figure 1. The light source is continuous w ith an ultra violet output, which i s rela tively f lat f rom 4 00 m~ to 300 m !J. . Below 300 m~ the output inten s ity falls off; at 2 25 m!J. the i nten ::lity is too low to be of pra ctical use . The instrument is ordina rily opera ted w ith a half-band width of 3.3 miJ.. The spec tral purity of the m o nochroma tic light i s s ufficiently g ood to measure transmi s sio n s o f one part in 10 5 at 270 m~ . T he m ono- chromatic light, reflected onto an ayerture with a front Sllrface alum inurn mirror, has a t otal convergence a ngle of 13°. B ecause of the relatively high dielectric constant <:: of the cry s tals, the incident light is essentially parallel to the normal of the crystal face. A Glan- Thompson polarizing pri sm is between the m irr o r and the aperture. The crystal is mounted over a selected, movable aperture (llsually 50 p. in diameter); a s econd a perture of the s ame diam eter ser ves as a refe rence. . (The apertures move across a r otatable s tag e.) The light s ign al, detected with a photomultiplier tube, i s chopped every two s econds with a s l ow t u rnin g , saw toothed wheel. The one-ha lf ?a F igure 1. S chematic optical diagram of the microspectrophotometer. XA Xenon a!"c light source H S tainless steel housing EM S tabilizing electromagnet L Collimating lens 1 ,:.;;:p Dispersive quartz prisms L Focusing lens 2 W Light chopping wheel 3 Entrance slit o ~ g ratin g monochromator 1 1 lv~ .M M 2 3 Front surface, plane mirrors Focusing mirror G Grating s2 Exit slit of gr ating monochromato r L 1: 1 imaging l ens 3 P Polarizing prism A Aperture 7 a.. <( 8 cycle A. C. signal allow s the filtering out of the higher frequency noise for high gain amplification and , moreover, eliminate s the problem of D. C. drift. The A. C. signal i s read on an oscilloscope grid; the smallest detectable absorbance is • 02 units. The gain of the amplifier limit s the high absorbance measurements to Sat 270 m iJ. and to 3 at 230 m~J.. A detailed discussion of the construction and operational features of the in s trument is given below. Components and Construction. The microspectrophotometer was constructed with two monochromator s in tandem w ith near matched £-numbers in the ultraviolet. The premonochromator is a B ausch and Lomb quartz prism monochromator, Catalog No. 232. The instrument ha s two 30- 60 quartz pri sms which are symmetrically pl a ced on a variable drum. A s shown in the figure, the prism s h a ve corresponding faces which are nearly perpendicular to the optic axis of the instrument. The two focusing lenses, which are crystalline qua rtz cut perpendicular to the optic axis, are mounted on racks and pinion gear s , which have calibrated drums to correct for the chromatic aberration of the lense s . The focal lengths and diameter of the lenses are matched; the se leng ths were measured with a 436 m~J. mercury arc line. They agree within 0. 1 mm. The calculated linear dispersion, as s uming near perpendicular incidence at 250 m~J. is 4 m !l/mm. The focal lengths and £-number s in the ultraviolet re gion 9 a re li s t ed in Table I. The vah1es were c a lc ulated from the indice s of refr a ction of quartz {9 ) a nd the diam ete r of the lenses. wh ich are the entrance and exit pupils of the optical sys te m . The device i :;; mounted on a c as t iron b ase which ha s three feet for vertical adju ~J t ment. The light s ource· stand s at the focal point o{ the entrance len s . Tl•e e ntrance slit of a se c o nd monochro mator i. s placed a t the fo cal p oint of the exit le ns in the premonochromator. TABLE I --- ----- \ =436 ID!J. f :: 150 . 8 mn• \ ( m!J.) N •t' f( mm ) f / nc . 36 1 l. 5 6 3 ~ l l- 8 .3 •L 8 2 330 1. 5 j · '17 146 • .! -::- . 7 8 303 1. 577 0 144 .8 4 .72 2.75 l. 5 875 14::: . 2. 4.6 3 257 1. 5962 14 0.2 4. 5 7 2 45 1. 6 047 138. 2 4 .50 231 l. 6140 13 6 . l ~ . 43 ..J ,< The sec ond mono chroma tor i s a Bausc h a nd Lornb 500 mm foc a l l ength grating monoch r omator . Catalog Number 33-8 6 - 4 5 - 58. The grating i s 10 0 rom X 100 mm grazed i n the fir s t ord er ultr a vio let w i th 600 groove :.:; / mm . The monochroma tor ha s a di spersi on of 3. 3 m 11/ mm and an equivalent aper tur e r a tio of f/ 4 . 4 . ment was operat ed w i th the s litg set at 1 m m . The i nstru - The wavelength drUin 10 readings w ere c a librated with a l ow pressure mercury a rc. s trong line s f rom 4 3 58 A to 2537 A• d:s:-u.m i s accurate to with i n . 5 m~-t . were s elected. Se ver a l T h e calib ra ted R e e k i ng the p rernon o c hro ma t o r back and f o rth 5 mi..L about a mercury line, while the g ratin g w as fi x ed, a tten uated the s ignal by a factor of about a h l1 ndred. The light source i s a 500 watt Osram xenon ar c which approxi ma t e!:> a point s ource. The arc is pow ered w ith a D . C. generator a t 2 1 amps and 2 0 volts acro ss t he pole s . To remove fluctua t ion s in the D . C . generator seven 12 volt batterie s are in pa r a llel w i th the circuit, in a trickle charge c onfigura tion. The lamp i s mounted on a } -inch transite block and housed i n stainless s teel s he e t metal. T he transite base i s perforated with 7 I 16-inch hole s to a llow cooling of t he l amp w i th a blower. A 5 mm hole in the me tal housi ng i s centered about the o ptic axis of the in strument; the point source was as s umed t o be 1 mm above the c a thode pole tip. ing s to p for an f/ 4 instr um ent. The 5 mm ape rture is a li m i t - ;3o that a magnified image of the .;;ource c an be p r ojected onto a wall, a second aperture i s s ituated at right angles to the light path. A low fre q uency jumping of the plasma about the burr s on the cathode pole crea t ed a se rio u s difficulty with the a rc. The p robl em wa s s olved by placing nea r the cathode a weak magne ti c field, which force s the p l asma to s it on a pa rticular burr at a m ini m u m potential. T he ma gnet i s c ompos ed of two sof t iron tip s , held by an iron cor e , which i s wound ZOO ti mes w ith 30 ga uge .enam elled copper 11 wire. The magnet draw s severa l milia mps from t w o 1;\ - volt dry c e lls in s erie s . resistor. The field strength i s contr o lled by a 100 ohm var i a ble When one edge of the parabolic image of the plasma i s aligned along the axi s of the poles . the arc is generally s table. In orde r to find the mo t:l t s\:a.ble c onfi gt1rati on it i s nece~:>sary to rotate the arc about it s pole axis in the pre s ence of the magnetic field. The arc usually has to b e re a djusted after s everal hundred hours of u s e. The i mage of the s ource on the exit s lit of the monochroma tor is focu s ed by a s tationary , fused quartz lens onto a s mall aperture. The lens. designed to m inimize spherical aberration for one t o one imaging, has a f o c a l length of 9 em for 260 miJ. light. An iris i s placed over the lens so that the angle of convergence c an be varied. aperture the lens i s f/ 4 . 4 and can be reduced t o f 135. At full For normal operati on s the total angle of convergence i s 13°. I n cident light thu s enter s the cry s t a l a t a maxi mum angle of (:.. 5 • w ith re s pect to the normal . The rela tively high dielectric c o n s ta nts of the crysta l ':! bend the r a y s to a ngles of a pproxima tely 3. s• w ith respect to the norma l . For the u s u a l c ases s tu d i ed the lig ht m ay be considered to have perpend icular i nci d ence u pon the cry s tal f a c e . For m ore critical mea sure - ments the i ris c a n be re d uced , but w ith so m e l o s s of intensity. Figure 2 i s a photog r aph of the rnicro s pectrophotometer; it exclude s t h e light so urc e a nd monochr o m a tor s . A front s urfa ce a lum - inum m irror reflects th e incident li ght onto a s mall a pertur e . The 12 Figure 2. The microspectrophotometer. The premonochromator and light source are not visible. A panel on the grating monochromator is seen on the extreme right. See text for details. 13 m irr or i 3 a ttached to a n adju s ta ble yoke by two i nse t p in s whose axis r uns parall el to the plane of the mi rr o r. F ine adj:.1s tment o f t he m i r - ror a bo ut thi s axis i s a ccompli sh ed w ith a th:.1mb s crew a nd sp rin g fixed t o t h e yoke. The yoke ' s a xi s , wh ich run s perpendicular to the i nset pin s , i s atta c hed to a fixed pos t wi t h a flat - hea d p i n . A ::;mall se t s crew a nd s pring attached to the post permits a fine adjustmen t of the m ir ror a b out the yoke ' s axi s . A used , modifi ed Leitz polarizing m icro s cope c omple tes the in s tru men t. The N ic ol pola rizer and c o no s c o pe w ere re moved , a nd a Glan - Thom pson polari zing p ri sm moun t ed i n plac e of the Ni c o l. The tr ansm i ssi o n of th e pri sm compared t o a ir was recorded on a C a ry Model 14 spectrophotometer from 3 6 0 mj..l. t o 220 mj..l.. At 300 m~-~o the transmi ssi o n i s 17 . 5% and monotonica lly decrease s t o 2. . 5% a t 22. 0 m~-~o . The Glan - Thomp s on pri sm was rotated un ti l i t cro s sed the a nalyzer of t he Leitz m icrosco pe . Thi s rotati on places t he e lectric vector in a north - s o uth po sition. The directi on o f v i b r ati on of the pola ri zer was a l s o det e r m ined by extingui s h i ng reflecte d light from a glass plate near B rew s ter ' s a n g l e . T h e eccentricity of the pol ariz e d lig ht was neve r determined , but a l ower li m it was esta bli s hed f r orn transmi ssi on measurements of a crystal who;:J e dichroic ratio i s at least 38:1. An ampli tude ratio of 2 8:1 wa s c omputed; thus the out of plane comp o n ent, f r om a n i ntensity point of v i ew , i s probably no m ore than o n e par t in 8 00. 14 The base of the microscope was rotated to a 90 • position with respect to the body tube and bolted to a mounting block, to whi ch i s attached a pinion gear box. Two fixed posts, one of which has a r a c k , provi de support for the m icro scope. The mounting block is held to one post by a tight spring and to the other post through the gear box, which has a brake (S ee Fig. 2). The rac k and pinion allows one to correct fer the chromatic aberration of the 1: 1 imaging len s. Thi s correction i s made by movi ng the microscope along the po!Jts t o a region of maximum s ignal for a particular wavelength. The t wo sup - porting post s and the m irr.o r pos t are bolted to a rectangular s tand which i s supported by three adjustable feet. The rotatable s tage on the microscope is calibr a ted in one degree units. The center p iece i s fitted w ith a new disc which has a 1/ 16-inch hole in the middle. Mounted on the stage is an American O ptical mechanical stage w ith latera l and to and fro motion; re.spec tive vernier scales read to the neare Gt 0. 1 mm . The bulk of the mechanical s tage allows r otation of the main stage only thr ough 210 •. The mechanical s tage accommoda tes 3 1 ' X 1" X 1/8" anodized brass blocks which have two 1/16''-holes drilled in them. The two holes, a ligned with the long axi s of the rectangular block~ are separated by 6 mm , each 3 mrn off the short axis of the block. are cemented over the s e holes. P latinum apertures The seve r al pair s include aperture diameters of 25 1J., 50 IJ,, 85 1J. , and 100 \.lo• The se , w ith the exception of the 85 1-L aper t ure , are standard apertu re s used on electron microscopes. 15 The 85 1.1. apertures were punched o ut of 50 1-1 aperture s with a shar p tung s ten pick . All pair s o f apertures are aligned a lon g t.loe long axe s of the bras s blocks within 50 1-1· Thus for the tran s mission measure - m e nts , it is only nece s sary to move the aperture s laterally with a fi x ed to and fro po s ition. O n e of the aperture s s erves as a reference; the other has a cry s tal over it. be described later. The preparation of the crystals w ill The cry s tal s are m ounted on the nipple end of a cylindrical, fused quartz block. The block is supported by a s mall, brass sleeve with the nipple end over the aperture. A copper spring holds the bra s s sleeve onto the pla tinum disc. A light-tight horn fit s s n u gly over the a nodized brass block s. The horn allows free mo vem e nt along the long axi s of the block s . The circular collar of the horn, one inch in diameter, i s coupled to a photomultiplier housing with a tight fitting, felt rin g. re s tricts movement in the to and fro direction . The felt ring T he body tt1be of the m icroscope may be removed; a hou sing f o r a n RC A l P - 28 pho t o multiplier tube fit s in its p l a ce. A 7 I 16" h ole at the b o ttom of the h o u s ing provide s an ade q ua te opening into the photo m ultiplier tube. Voltage i s applied to the dynodes of the photomultiplier by mean s of a voltage divider c o n s i s ting of 80 K ohm resistors betwe e n each stage. The loa d re si s tor can be switched f rom 10 M eg ohms , which i s built into the A. C. coupled amplifier, to 100 K ohm s in para llel with the 10 Meg ohm resistor . The photomultiplier is driven 16 w i th negative voltage fr om a Keithley Model 240 power s upply. The outp ut s i gnal i s amplified by an A . C. co upled h i gh g a in amplifier. A Type E plug -i n unit for the Type 53 5 Tektroni x oscillo s c ope i s an adequate amplifier; its linearity c overs a r ange from 10 MY I em to 0. 05 MV I em. At the entrance s lit of the sec o nd monoc hromator a slow turning, saw-tooth frequency. wheel chop s the light s igna l at one - half cycle The signal , d i spl ayed on a c a thode ray tube, i s a near square wave curve . The peak hei ghts read to the nea re st m illimeter on a centimeter s cale. A set of ca pacito r !'> , i n parallel with the load re s i s tor of the photomultiplier t ube , c a n be s elected t o filter out h i g h fre q uenc y noi se. T he s et r a nges from 1 1-1f to • 00 5 !J.f . Operationa l E'0atur es. O ne major feature of the microspectrophotorn eter i B a half cycle s i gnal , which i s u s ed t o enable filtering out the noise fr om high gain mea s urements . Mo st of the noi se from the power sup - ply a nd photomultiplier tube ha s frequencie s larger t..h.an one hundred cycle s . A c apacitor which provides a re s p o nse time of 0 . 1 s econd s wa s s elected for all mea ::; ur e ments . H ence , even s ixty c ycle pic kup was attenuated for the high gain measur ements. The A. C. s i gnal , with u half cyc le , d ark current refer,~nce, i s advantageou s ; it eli m i n a teo the p r o blem of D . C . drift , which i s often enc o unter ed with D. circtlit, h i gh gain 5pectrophotome ter s . C. 17 There is essentially no problem of stray light with the two monochromators in t andem . The in strun:.ent was first compared to the Cary Model 14 spectrophotometer. The absorption spectrum of a l mm pyrex filter was measured from 390 nlfli to 270 mp. on the Cary. At 270 m!J, the abso rbance was 4 . 9 2 . By placing the filter over the exit s lit of the second monochr oma tor the transmission was then measured with the microspectrophotometer and the computed absorbance compared to the C ar y measurement. From 340 rn~ to Z70 mp., the absorb- ance measllred with the two instrllments agreed w ith in 0. OZ . The signal on the oscilloscope can be read to w ithin two percent at best. Thus absorbances less than . 02 cannot be measllred. (F or cry sta.l absorption the error i s ± • 0 4 absorbance units due to the c orrecti on for the quartz block.) A more critical stray light test was conducted with a 1-methylthymine crystal. A sufficiently thick section trans- mitted one part in ten tl1ollsand of the reference signal at 275 m~J,. P utting the pyrex filter into the light path attenuated the signal beyond detection. Thus any light of wavelengths greater than 300 rntJ. must be . 5 less than one part tn 10 • The transmission of a Hoogsteen dimer crystal at 230 miJ. wa s similarly t ested. The tr ansmittance was 0. 01; the pyrex filter attenuated the s i gnal beyond detection. Since the abs orption of the cry stal itself was an adequate filter for wavelengths from 2 80 mtJ. down to 235 m~-t , s tray light o f wav elength greate r than 3 . 240 m~ mus t be les s than one part in 10 • These stray light studie s 18 indicate that absorbance s a s high as 5. 0 at 270 rnt-1 can be mea s ured w ith confidence. It is important in the de sign of this s y s tem that the rated equivalent aperture of th e grating monochromator not be exceeded. In our preliminary studie s Btray light was a major problem, becau se the grating was overfilled. Vignetting the grating monochromator r educed the stray light a ppreciably, but it was necessary to use a premonoc_hromator in order to measure tran s missions of the order of one The in s trument was usually operated with a full scale signal . on the oscilloscope for the reference aperture. The image of the source at the exit s lit of the s econd monochromator was focused o nto the reference aperture. Wit..~ the 100 K o hm load resistor in parallel with the 10 1tleg ohm resistor, the power supply was increased llntil a 6 0 millivolt signal appea red. By switching out the 100 K ohms resi s t o r a gain of 101 i s introduced; a further gain of ZOO c a n be a chi e ved w ith the amplifier. ( When changing the load re s istor, it is necessary to reduce the capacitor in order to maintain a constant re s ponse time.) Even higher gains can be accomplished by increasing the voltage on the power supply. but this i s usually impractical. Hence, the p:ractical llp per limit for transmission detection is one part in 10 leng ths above 240 ml-!-. 5 to 10 l~ at wave- Due to the relatively low intensity output of the xenon arc in the 2 4 0 m~ to 230 m~ region, and due also to the 19 absorption of the polarizer, the reference signal fro m the apertures used was too weak to measure transmi s sions le ss than one part in a thousand. The maximum voltage from the power supply is 1000 volts; the limit for the photomultiplier i s about 100 volts per stage. At thi s level of gain signals were too noisy to read below o. 01 millivolts. Reference signals were about 10 millivolts. Below 230 m~ reference signals were not within a practical limit of detection. The uncertainty of an intensity measurement is determined essentially by the smaller.t absolute reading on the grid over the oscilloscope tube. Gains were increased so that the largest po ssible reading was displayed. approximately constant. In this way the relative error was kept Every transmi ssion measurement has a cor- responding, constant absorbance error of ± • 02 units. For quartz blank transmissions the crysta l was dissolved of£ with water. absorbances have an error of ±. 0 4 units. Crystal Intensity readings are reproducible when the a per t ure s a re moved to a position of maximum signal. The field seems to be uniform over a region 75 1J. in diameter. The vernier scale on the mechanical stage i s not adequate for repr oducible settings. With c a re the apertures can be aligned so that their rotation does not change the signal. The major limiting feature of the instrument i s probably the polarizer. As mentioned earlier, the out of plane component is be- lieved to be one part in 800 of the in plane energy. For transmissions 20 in the direction of wea k absorption, the out o f plane component is uni mportant , because , a t worst, only one part in eight hundred of the reference s ignal i s removed by the principal direction of s trong absorption. But for transmi ssi ons in the direction of strong absorption , the out of plane component is critical. The analysis presented i m medi£. , ately below show s that in the c a s e of very large dichroic ratio s , a tran s m i s sion of aboat one part i n a hundred i s the limit of confidence. The error in the meas ured absorbanc e i3 1 6A = A (l --D)+ log 10 { I 10-A + lO·A/D ) lO·A +I 10 - A /D where D is the dichroic ratio, A is the true absorbance in the direction o f s trong absorption , and I is th e ratio of the in plane i ntensity t o the o u t of plane intensity. F i gure 3 is a plot of the error as a function of A for different dichroic ratios and for I = 800. From the functional behavior of the absorbance error, it is concluded , in general , that absorbances le s s than 2 are reliable for measurements i n the principal direction of strong ab s orption. For crystals with a dichroic ratio of 2 or less, absorbance s up to 4 can be n"leasured within the error of ±. 04 absorban c e units. The sitaation could be improved by placing a second Glan-Tho mpson polari zer in series with the first. The limit of confidence is thus raised up to absorbances of about 4. However, the loss of intensity near the l o w wavelength region is an undesi r able feature. 21 0.50 0.40 LA 0.30 0.20 0 .1 0 0 0.50 1.00 Figure 3. Absorbance error due to eccentricity of polarized li g ht. See text for discussion. 22 Because c f t h e l m m s lit w i d t h s etti ngs for t h e gra tin g mo nochr c-ma t o r, the width of the wa velength b a nd of the ou t p u t light i s r a ther l arge , a b out 3. 3 ml-k . T h ere i s , therefore , an err o r i n the absorbance mea~urem ents in a wave l ength re g i on where the a b s o r p ti on coefficients v ary ma r kedly with wavelength i n tha t for a thick crystal the average wavelength o f the tr a n ;;mitted light will be diff e r en t fro m that of t he i n cident lig ht. way. Thi s p r o b l em can be tre a ted in th e following The tran ::;m i ::~s ion mea s -...1red i s : ~ r 1/I 2 e \i = 0 - e {\ ) K I {X.)d\ 0 },2 rI I {\ )d \ 0 \1 w here I{ \ )= P {\ ) S( \ ). 0 P (\ ) i s t he inte nsity output functi o n o f the xenon arc p lu s the polari zer . s(q i s t he s lit f un ctio n of th e monochromat o r. as sumed t o be triangular. + 1 f o r A. 1 ~ A. ~ >.. 0 + 1 for A. S (\ ) =0 X s: \ 1 0 ~ X s: \ z The slit fun cti on i s 23 /J.\ i s the half-band w idth of the monoc hroma tor. about X 0 We expand~ ( \) and F (X) about X • 0 Ca se I. P (\) = P a con s tant from >. , 0 1 to \ 2 s (\) = e (A. 0 ) + (\ - \ 0 ) e (X 0 ) 1 T h en . h2 ( - 8 ~X ) s 1n 2 = 10-ak 1/1 0 or i h z. sn whe re dA F = 2. 303 d\ (R ~\ ) 2 (\ ) 0 F igure 4 i s a pl o t of the c o rrectio n term as a f tl n ctio n o f dA I dX (\ ) l 0 for a band width of 3. 3 m~. T h e cry s tal' s ab s orbance slope m1~st h a ·.; e an absol:.1te val ue o f abO ilt 0. 15 m~ reliable transmi ssi on rneas ,lrement . -1 or less f o r a For mo s t ca s e s of i n tere s t t-he cry s tal had to be about .1 IJ. thin in order to de t ermine meaningful toe abso rption . C a s e II. P (\ ) = P 0 e (q = € {\ + (\ - \ ) P ' (\ ) 0 0 ) 0 + (\ - \ 0 ) e'(x0 ) 1.00 2.00 3.0 0 4 .00 5.00 lot,o dA 1.20 ·IdA dAI~ Absor b ance c orrection fo r non-monochromicity. (~~b)~ sinh2.t~) Figur e 4. j ' i9 = 2.3 03 QA. AA=3.3mf- 1.60 2 .00 .t.>- N 25 Then 1/ I ::: 10 - ak + 0 F· '(\ ) 0 s i nh 2. ( 8t.'!2X. ) 2~ P (\ ) 0 r.-..-,---, - .:. L --~'- s i nh ._ ( (Q~).) ): 0 1\\ •.. U fl. "' T he outpLlt function of the xeno n arc i s shown on a logari thm plot in F igur e 5. T he pola rizer d oes not affect the contour · d o wn to a wavelength of abo u t 300 m~. A round 300 m~ . is .-... 3 x 1 0 - 2 m!J. - 1 Thi s i s a small c or rection which justifie s the s impler the o r y of C as e I for e :3 tabli shi ng c onfide :·:c e limit s . l:-1 summary, the rna Jor adv a ntage s of th e 1nicrospectrophoton1 eter are the slow .A .C. signal , whi ch makes h igh gai n m ea surements po s 5 s ible, and the abs e n ce of s tr ay light to within on e part i n 10 . The eccentricity of the p olarized ligh t li mi t s tra :.1 smi ssi on meas;J.r eme nt s in the directi on of stron g a bsorption , for dic hroic r a tio s larger t han five, to o ne part in several h u n dr ed . T he non-mono c h r ornici ty of th e incident li ght li m it s ab s o r pti on measur e m e n t ::> t o a crystal which has an a b s orbance cha nge no more tha n 0. 1 5 absorbanc e u nit s p er m illir:r1icron . Retardation Mea s urements. The general princi pl es for retardation meas ur e me n t s are outli ned below. When a crystal i s fixed w ith on e of it s extinc tio n d ir e ctio n s at an angl e of 4 5 • with re s pect t o the electric vecto r of pla ne polarized , parallel light, the electric vector __j 26 Figure 5. I ntensity output of the xenon a rc with the polari ze r removedA INTENSITY ARB. UNITS 1.0 0.1'=""'="--~~~--~~--~-±--:---_._---400 350 300 250 200 A(m}A) 27 projects its amplitude equally onto the two extinction directions. AG the ray proceeds through the transparent cry stal , one c omponent l ags behind the o ther due to the different refr a ctive indice s along each extinction direction. ally polarized. The emerging light w ill, in gene r al , be elliptic - If quartz , or a ny other b ir efri ngent material , i s placed over the crystal wi th extinction directions a ligned, the retarda tion· produced by the crystal w ill be e ither advanced or retarded depending on the a lig nment of the refr a ctive indice s of the two b ir e fringent materials. If the high refractive index ( s low ray direction) of quartz i s colinea r w ith the low refractive index (fast r ay direction) of the cry stal, then the quartz re t ards the phase difference introduced by the cry stal. By using a wedge of quartz, a ma terial of c onstant birefringence w ith varying thicknesses, it i s possible to va ry the advancement or retardation of the two components of the elliptically polarized light. When the total retardation of the light i s some i n tegral rr1ultiple of the w avelength for the light incident on t he crystal, then the light emerge s from the q u artz as plane polarized ligh t which i s parallel to the plane of polarization of the polar i zer. Thus the final emergent light ha s a plan e of polarization at right angle s to the vibr a ti on directi o n of the analyzer. A d a r k fringe will appea r a c ross the field of view because no light i s transmitted by the analyzer. If the crystal i s rem oved a nd the quartz wedge i s kept fixed, then the light pa ssing through the wedg e -.v ill be elliptically polarized 28 with c omponents which w ill project themselves onto the vibration direc tion of the analyzer a nd w ill add to g i ve a non - zero value. light will appear across t he field of view. Thua The wavelength c an be changed until a dark frin ge appears again; at this point the r etardation of the quartz i s an integral m~ltipl e of the new wavele ng th. Figure 6 i s a two dime ns ional representation illustrating the retardation phenomenon discussed above. The dashed -line waves are vibrating at right angles to the plane of the paper. for cases A and B is 589 m~.~o. The wavelength The qua rtz wedge has its fa s t ray com- ponent over the fast ray component of the cry s tal. The quartz wedge advanc es the fast component from the cry stal to one full wavel ength ahead of the slow component of the crystal. For ca se B the resultant wave , not shown, i s elliptically polarized . I n case C the wavelength is 393 miJ. , where the slow ray of the qua rtz is reta rded one full waveleng t h behind the fast ray of the q u a rtz. For c ase A the retardation of the c rystal plus the quartz w edge iS 589 m11; that i s , 6n t c c where 6 n c + ~n t q q = 589 rnj.l. ( I) = the difference of r efractive i ndice s in a principal plane of th e cry s tal; t c = the physical thic kness of the cry stal; t:, n q = the birefri ngence of the quartz; t q at the po s ition of interfe r ence . = the physic al thickness of the qua rtz 29 plane polarized elliptically polarized plane polarized ...... / f). n t c c + f). t Q Q = 5 89 mi-L /. . = 589 mi-L Figure 6. c B A /). n t QQ A. < 589 m!J. = 589 mi-L f).n 0 A. t _ = 393 m!J. u = 393 m!J. Two dimensional representation of retardation produced by quartz wedge and crystal. 30 For case C the crystal h as been removed and the wavelength changed (the w edge was n ot moved) so that /j, n t qq = 3 9 3 rniJ. (2) This met hod o f measurement i s somewha t s i mplified becaus e !::. n q does not change w ith wavelen g th . From equation 2 w e can deter- mine !::. n t , a nd then from equation 1, solve for the retarda ti on of the q q cry stal , t:, n t • c c In this example, !:. n t c c = 196 m!J. . If the cry s tal has a birefringence of 6 n c 0. l, then it s physica l thicknes s is _ R t - _ 196 m !J. 6n - o. 1 _ l - • 96 ~ The birefringence of t he cry s tal is measured independently; e . g. , oil i mmer sion determination of t h e refractive i ndic e s . If the w edge h a s a thickne ss such th at for 393 m(Jo light the s low ray i s retarded tw o full waveleng t hs , then th e t otal retarda tion i s 7 86 m!J. . I n this c ase if the wavelength we r e fixed at 393 miJ. , one could see that the dark fri n ge i s a second order fringe by withdrawing the wedge and observing a s e c ond d a r k fr i nge when l:he thickn e s s c o rre sponding to the fir s t order is i n the field o f view . Or t hoscopic o b se rvati ons with the m icro spec t ropho to m eter were used to orient a ll cry stal s for retar dati on mea s ur e m entG and i n s pectrophotom etry. A cry stal could be o ri ent ed to w ithin o n e degree between cr ossed polarizers. Retardations o f th e cry stal we r e measured with a quartz wedge in the manner d escribed above . A wavelength of 31 589 mt-L was selected. The crystal wa s rotated 4 5• with respect to the extinction direction. A quartz wedge was inserted into t..he body tube at an angle of 45 • with respect to the vibration direction of the analyzer. With the ocular removed so that the eye could foc\IS on an inte rference fringe, the wedge was pu ,3hecl in until an interference fringe bisected the image of the field. With the wedge fixed, the ocular was put in and the crystal was moved off the field of view. The refer- ence aperture was brought into view and centered with the help of the ocular cross-hairs. The ocular was again removed and t he wavelength was varied until the interference fringe bisected tbe field. Care was tak en to know the order of the fringe; this was done by counting fringes as the wedge was s lowly pulled out. Since the birefringence of quartz is constant over the vi s ible re gion, the reading on the monochromator drum ti m es the order is the retardation of the quartz wedge. Depend- ing o n the position of the slow and fa st rays of the crystal, the retardation of the quartz plu s or minu.s the reta r da tion of the crystal i s some integral multiple of 589 rnt-L. For mo s t retardation measurement s the fir s t order was an adequate rang e. In some ca ses cry stal retardations were larger than 100 m~ it was then nece ssary to use the s econd or third order fringe of the quartz wedge. If the crystal retardation was larger than 589 m!J., its order was easily determined up to about fourth order. The crysta l was oriented s o that its fa s t c omponent was co- incident with the slow component of the quartz wedge. The quartz 32 wedge wa s pushed in until the zeroth order interference fringe appea red. One could recogniz e the zeroth o rder by noting tha t the fringe did not 1nove when the wavelength drum w as mov e d. When the zeroth order w as found, the order of the wedge w a s mea s ured. the wedge is the order of the cry s ta.l. 589 m!Jo. T he order of The wedge ha s four orders for For first order work the retardation of the quartz was re- produced within 2 t o 3 rrw. • Ten meas urements w er e usu a lly made; five with added retardation s and five w ith subtracted retarda tion s . From an independent birefringence deter m ina tion of the cry s tal s a t 589 m~Jo , and from the retarda d o n m e a surem e n ts. the physica l thickn e s s was computed. 33 THE P REP ARATION OF CRYSTALS Crystal Growth. Three different cry s tal s were s tudied in this work . l · M ethylthymine, Lot No . 1074 , and 9 - methyladenine, Lot No. 1075 , were purchased from the Cyclo Chemical C ur poration . The compounds were , separately , onc e recrystallized from water and dried at room temperature under vacuum. lvlonoclinic crystal s of each compo und were grown by evaporation of aqueous solutions at room temper atur e. 1-M ethylthymine usually had { 111} forms and was prismatic i n shape . ( 102 ). and {100} as the predominant A les s predominant face i s the The w ell-developed edges we re 0. •l mm t o 0. 7 mm. By spreading a hot solution, saturated in l·methylthymine onto a q ua rtz coverslip, very thin plates were obtained. ated. T he (10 2) face predomin- S ome plates were as thin as 0. 7 1.1. w ith a cros s section of 0. 2 mm X 0. 1 mm. 9 - Methyladenine cry s tals appe a red as needles with the c -axi s parallel to the needle axi a a nd with form s { 001\ well d ev(;l,loped. The { 0 10} { 110~ and was a less prominent form. The crystal s were 2 m m to 3 mm long and 0. 2 mm to 0. 4 mm along the edges of the i 00 1} face . In order to grow a h ydrogen bonded p a ir of 1-me thylthy m ine and 9 - methyladeni ne , hereafter c a lled the Hoogsteen dimer , equitnolar quantitie s of the t wo compounds were dissolved i n water. Upon 34 evaporation to dryness at room temperature well formed , monoclinic needles were obtained. Forms {100\ , fool} The b - axi s lie s parallel to the needle axi s . and {o1ol predominated. Typic al dimension s were 1 em X • 4 mm X 0. 2 mm . T h e Techni que for P reparing Thin Sec tions. The major problem in obtaining ultraviolet absorption spectra of single organi c crystals lies in the preparation of thi n sections. The compounds are typically 10 M in the crystalline state and have molar abso r p tivities of the order of 4 -1 -1 10 .t. mole em • I n order to obtain measurable ab s orbances , the crystal s must have a thickness of the order of 10 -5 em . I n the past inve sti gators have had to sublime thin plates or to crystallize com pounds between clo sely spa ced , quartz plates . Up to the present , there seemed to be n o satisfac tory, general technique for m aking thi n sections of s ingle crystals w ith cro ss secti ons as large as 0 . 2 mm X 0 . 2 mm. However , a gene r al technique for p reparing thin section s of tra ctable cry s tals ha s been developed. We first attempted to prepare a thin s ection. by conventional slicing techni ques us i ng an ultramicrotome of the type u s ed fo r pre paring electron microscope s pecimens. This method , w hich i s described i n detail in the next paragraph , failed because the cry stal , when c u t , shattered i n.to a mosaic of microcrystal s . 35 The actual proc edur e was as foll ow s . A uracil cry stal , whic h is a layer s tr uc ture ( 20), was coa t e d w ith polyvinyl alcohol a nd then i m bedded in a methacrylate block by polymerizing a m ixture of methyl m ethacrylate and n - butylmethacrylate monomers a round it. A t thi s stage the crystal extinguished well under cro ss ed pol a rizer s . Th e block wa s oriented so that the ( 001) face (the plane o f the molec u l ar laye rs) was i n the plane of the c u tting edge. The block was waxed onto a rod which fits into a standard chuc k fo r the S e rvall Porte r - B l um m icrotome. N ith the m icr otorne set at ?; IJ. i n crernents the cry stal w a s cut w ith a diamond knife. The sections we re flo a ted on a wate r- acetone solution saturated in uracil. The polyvinyl a lcohol prevented the u racil from falling out of the methacrylate section . The sections were recov e red by catch i ng them on a q uartz cov er s lip. C ut o f a t."'Lousand s lices fo u r were rec over e d . they were cut . The s ections often w rinkled as Under orthoscopic observation the recovered section s exti n g uished, b u t not sharply, and appe a red to hav e grainy 3urfa ce s . The retardation of o ne section was 26 mi.J.. F rom the birefringence (8), the calculated thic kne ss was 0. 15 IJ. . The absorb ance at 290 mp, was 1. 8Z for E ll b a nd 1. 00 for E_L b. From 290m~ down to 2.4 0 m\.1. t he apparent absorbance rose smoothly to 3 and 2 , re s pectively. r e s ults see med su spi cious for two rea s on s . The s e In the first place the abs orban ce at all wavelengths i s too high a s c ompared w ith the solution 36 spectrllrn. In the second place the solution spectrum shows a maxi- mum at 258 m~ and a minimum at 229 rn).J.. A conoscopic observation ravealed that the Bxa figure was a supe rposition of many little Bxa figures; the i sogyres were h ighly distorted. It was concluded that the crystal was s hattered during the cutting and that a mosaic of microcrystalline regions remained. Therefore, the birefringence was low and the calculated thickness too small. The same experience was encountered for a 1-methylthymine cry stal. While repeating the same experiment with 1-methylthymine. it was observed that the crystal face remaining on the methacrylate block a fter sectioning seemed to be optically polished. It was rea3oned that one could cut the crystal down to a very thin s ection on the me thacrylate block by taking advantage of the microtome's small advance increments. The smallest setting on the microtome is • 025 ~-~< · After some practice and adaptations the following technique was found adeqllate for cutting crystals to s ections as thin as 0. 1 1-L· For a cry stal with a thicknes s of 5 X 10-S em and cros·s- . sec tiona1 dimens1ons o f 10parallel within 2 . 1s . necessary t h at th e two f'ace s b e em, 1t 0. 001 radian s (4' of an arc) for the thickness to be con stant within 20o/o a cro ss the crystal. of satisfying these tolerances. The technique used was capable It is described schematically by the following steps and accompanying figure s. 37 Step L Carve a small nipple out of a methacrylate block with a sharp 0 A nipple ~ mm in razor blade. diameter is adequate. Step II. THIN PlASTIC Mount the methacrylate block into an adjustable chuck (to be de s cribed below; see Figure 7) which fits the microtome. Shave off 10 to 20 1-L of the plastic with a diamond knife to make an optica lly polished face parallel to the cutting plane .. Step III. Remove the chuck from the microtome. CRYSTAL I ETHYLENE 'OICI-lLO~IOE ~~ Glue the desired, natural, developed face onto the optically polished nipple face by applying a few microliters of ethylene dichloride. It is possible to do this and maintain the crystal face parallel within I o of the meth- acrylate face. Step IV. Remount the chuck onto the microtome. The crystal face is now parallel to the cutting edge. Shave off 10 to 20 1-L of the crystal; this leaves an optically polished face on the crystal. 38 Step V. RAZOR BLADE J Remove the chuck and carefully cut the crystal loo se from the methacrylate block with a sharp razor blade. Cover the crystal with the polished face up. should be -.- 7 5 1-l. The cry s tal thick at thi s stage in order to avoid s training the polished face while removing it from the methacrylate block. SOLUTION Step VI. Insert a stainless .steel-methacrylate ~ MfTHAC.RYLATE ~ rod into the chuck, which has a quartz ~(J ~~UA'RTZ METHACRYLATE block mounted on it. The nipple end of the quartz block is covered with a 5 1-J. layer of ultraviolet "transparent" +----"' methacrylate by pipetting several STAINLESS STEEL microliters of a dilute solution of the ~ CHUCK polymethacrylate. ~ Step VII. Shave 1 to 2 1-l. off the 5 1-l. plastic film with the microtome in order to define a plane on the film which is par a llel to the cutting plane. QUI\RTZ Care must be taken to align the quartz block in o rder to avoid grinding the quartz while polishing the thin methacrylate film. 39 Step VIII. Mount the previously polished CRYSTAL _/ C2 H Cl2. 4 ~THIN ~ METHACRYLATE .______ FILM crystal face onto the polished thin film of methacrylate by applying a microliter of ethylene dichloride at the interface of the crystal and plastic. QUA~TZ Step IX. I Grind the crystal down to the de sired thicknes s with the micro- CRYSTAL tome . For the highly birefringent materials used in this work, interPLAIII£" POLARIZ.ED ference colors appear when the LI~J.{T <i}UARTZ 1 ~ KNIFE }' crystal i s 10 iJ. thick. Keep these colors uniform while grinding by adjusting the cutting angle with the chuck. 40 P lane polarized, white light i s reflected off the face of the stainless steel-methacrylate r o d which holds the quartz block. The light b ecomes elliptically polarized i n passing th rough the crystal. T he plane of polarization i s perpendicular t o the rod axi s . With a cro ssed polaroid th e i nter fe rence colo r s of the crystal are obser ved. illu strate s the optical s ystem. F i gur e 7 These interferen ce color s a re observed during the process of g rind ;.ng (:3tep IX) in s itus w ith the apparatu s depicted i n Figure 8. An adjustable chuck was built t o m ov e t he block thr ough sma ll angle s . Figure 7 i s a sketch o f the ch•.1ck . A collar attac h e s the main axis of the chuck to the ball joint of the m icroto me arm. collar cin che s the cutting bloc k i n t o the chu c k . fit 9 0• apart on the sec ond collar . A second Two, large-head screws The out e r perimeters o f the scre w heads are ma r ked off every 3. 6 degrees. The p itch of the s crew s is 32 turns/inch; the s crews are s et 1-7 /3 2 inche s out from t he center of t.~e chuck. The se s crews work again st two other screws ( s prings were unsuccessful) to adjust the inclination o£ the cutting block with respect to th e cutting edge o f the knife . I n p rinciple , a disp lace ment as small as 26 11 of an arc can be resolved, but due to backlash, a practical limit is about 1' of an a rc. The entire asse mbly of the grindin g apparatus is shown in the photograph in Figure 8. The m icrotom e a dvancement i s con trolled m anually by the handle to the right of the gear box. The mounting plate 41 Front View Side View Figure 7. Chuck us e d for orientin g cry s tals with re s pect to the cutting k n ife . 42 Figure 8. The total assembly of the apparatus used for grinding crystals. The diamond, not visible here, is mounted in the trough directly below the quartz block attached to the adjustable chuck. See text on pages 40 and 43 for general description. 43 for the k nife holder is fi x ed w hile the microtome a r m is advanced. The adjustable chuck i s mounted on the microtome arm. The stainle ss steel - m ethacrylate-q•J.artz cuttin g bloc k i s mounted i n the chuck . The light sollrce above the cutting rod i s c overed with a polaroid filter. A 2. . 5X powe r binocular was used to observe the cry s tal and the inter - ference color s ; t he analyzer was usually held just in fron t of the binoculars . A detailed discus s ion of the various steps carried out i n th e p reparation of these thin crystal sections i s found below . Following this discu ssion the re appear s ome commentg on the limitation of the proced ure and a derivation of the absorption behavio r for an o ptical wed ge . A methacrylate block is glued to a bra s s rod by wetting the block w ith l • 2 - dichloroethane . With a sharp razor blade a small nipple of about 0. 5 mm in diameter is carved at the end of the block . A face is developed on the nipple by cutti ng off 10 ~ to 2 0 p. o f the p l as ti c w ith the microtome. A particular cr y stal face is then placed onto the polished face of the meth a crylate . A few microliters of ethylene di - chloride is added by touching the plastic edge with a small capilla ry. The solvent flows around the crystal an d dries within a n1inute. In this manner th e cry stal is fixed to the pla:Jti.c block w i th the crystal face paralle l to the polished plastic face. crystal is c u t off with 1- ~to A bou t 10 }.1 to 2 0 l-1 o f the ~ sections per s lic e in order to i nsure an optically poli s hed fa ce free of f rac t ure s or cleavages . A trough. 44 to which the diamond knife is attached, i s filled w ith w a ter up to the c u tting edge of the knife. The section s wh ich are taken off of the cry stal float onto the water and d i s s olv e . crystal face is left clean . With each s lic e then , the It is i mportant , however, that the knife edge be cleaned ·with a soft, wooden s tic k about every twenty s ections , fo r crystal grains will pile ap on the k nife edge and leave a scratched face on the cr ys tal. The knife must a l so be free of srn.all dirt particle s which can mar the face with fine streaks. When a n optical polish on one face has been achieved , the crystal is then carefully cut of£ the methacryl ate block by stroki ng along the poli shed , plastic face with a sharp razor blade . In order to avoid s train or damage to the crystal ' s p o lished fa ce, the cry Gtal should be a t leas t 7 5 1.1 thick . The crys tal i s transferred to a dirt free micro s c ope slide w ith a t u ngsten pic k . The j)Olished face i s placed '.lpward s and the c rystal is covered. A s tainless steel rod w ith its end c u t 4 5 ° with respect to the rod axi s i s fixed to a methacrylate cylinder. O ne fa ce of the meth - ac rylate i s ground to an angle of 1~5 · wi th re spect to its rod axis by a sander. The pla s tic is glued to the steel rod by wetting the plastic fa ce with ethylene dichloride . T h e front face of the pl as tic i s san ded to a flat surface near perpendicular to th e rod axis . A cylindrical, brass block with a hole machined to clear the plz.5tic by a few thousandths of an inch is used for gri nding a flat surface on the front face of the p l a stic. The methac rylate - s tainless steel rod i s s lipped into the 45 brass block to maintain a fixed orientation while grinding the plastic o n an optically flat piece of g l a s s with levigated alumina. The method insures a flat surface perpendicular to the rod axi s . A fused quar tz block, with an optically poli sh ed face, i s then mounted onto the flat surface of the t"!lethacrylate with a small am ount of ethylene dichloride . detectable strains . at the base. Under crossed polarizers the quartz has no The cylindri cal q u a rtz block L ; 4 mm in diameter The front face, a Grna ll nipple 0. 5 rom in diameter, i s parallel to the base and has a grainy poli sh of s everal m icrons . block i s 3 rom thic k . The The total assembly is shown in the s ide view in Figure 7 . l',. thin film of methacr yla t e coats the f r ont face of the quartz. Thi s film i e a specially prepared, ul t raviolet transparent polymer. lv1 et..lLylmethacrylate and n - butylmethacrylate m onomers were di!>tilled at about 4 0°C under reduced pressure. A 7. 2 mol ar r atio of methyl - methacrylate to n - butylmethacrylate was heat polymerized for 2<1 hours at 6 5 ° after i n itiation with an H85 A 3 G. E. mercury ar c . The ab s ence of an a ro mati c cataly s t such as benzoyl peroxide is necessary . wise the plastic w ill have i n t olerabl e u ltr aviol et absorption . O ther- 30. 4 mg of the polymer w ere di 3solved in 10 ml of 1, 2 - dic hloroe t hane , s pectra g rade Lot No . 3 4 from Eastman Organic Chemi cal s . A uniform layer of the solution was spread on a qua rtz cover ::3lip to g i ve a p l as tic film of about 10 IJ.• The solution evaporated and the fil m was pumped on w ith 46 a fore•pump for an hour. The absorption s pectra of the film was recorded with a Cary Model 14: S pectrophotometer. An absorption maximum at 215 mp. with an absorbance 0. 71 was obtained. mf,!. the absorbance fell below • 04 unit s . the literature value ( 29). Lm its at 230 m!J.. Above 240 The spectrum agreed well w ith A 5 f.l. l a yer contribute s about 0. 2 absorbance 1. 5 microliters of the methacrylate solution pipetted onto the nipple of the quartz block for ms a 5 1-.1. layer i n good optical contact with the quartz. The refractive indice s are close matching in the vi s ible. but in the ultraviolet, undoubtedly , f.l ome reflecti ons occur A reasonable estimate i s a 1. 5o/o at the interface of the t wo materials . loss i n the intens ity of a ray traveling from pla s tic into quartz . When the m ethacrylate l ayer has dried , the asse mbly is mounted on the m icrotome and aligned by eye w ith r espect to the knife edge. The diamond knife is set near the front face of the quartz . A t 0. 1 1-1. intervals the qaartz assernbly i s slowly adva nced until the first segment of plastic comes off the quartz nipple. are taken. U s ually another 5 to 10 sections Sometimes the alignment is so poor that an edge of the quartz nipple is ground. Wi th angular adjustments fixed, the chuck is removed from the m icrotome arm. The optically polished face of the crystal is pla ced on the polished methacryla t e film . C are was taken to set an extinc tion direction of the crystal at approximately 45 • w ith respect to a line colinear with the stainle ss s teel face. The cry:5tal 47 was fixed to the quartz block with a small drop of s pectre quality 1, 2 - dichlorocthane • .l. fter d r yi ng , th e cry s tal wa s s ectioned every l/ ·1, ~ to l / 8 1-b per s lice. With polari zed ligh t o ptica l wed ge effects can be r eadily seen and p r ogressively cor rec ted w ith the ad j ustabl e chuck. As the crystal becomes thinner , the microtome intervals are reduced to 1 I 4 0 iJ. incre ment s . The thickne ~ s c an be followed down to a corre s pondi ng r etarda tio n of about 25 mj..b . Below that, one must s i m ply c ount the number of s ection s taken. 'Nhen the cr ystal i s abo ut 1 l.l. thick , section i ng is very critical. By this time it i s very i mportant tha t t..he c r ystal i s ali gned and tha t the sectioning i s done at a constant rate . If a rhythm i s not establi shed, back-lash in the ge ar s of the m icr o to me w ill c ause the arm to advanc e too far, and this w ill des troy the cry stal . One must l earn to observe the i nterference color s while th e crystal m o ves across the field of v ie w . When the c rysta.l h as been g r ound to a desirabl e thickness , the quartz blo c k i s remov e d from the methacrylate rod with a razor blade . It is often helpful to soft en the rnethac ryl ate block w ith ethylene dichloride . The soften i ng rnust b e done w i th c aution; e thylene d ic h l oride vapors can soft en the thin methacry l ate film on the n i ppl e a nd thu s s h atter the c rysta l. T he thick qua rtz base prov-ides abso r p tion for any shoc k or strain which the cry stal would otherwise suffer in its removal from the cutting bloc k . A tight-fi tting , brass sleeve p rovides support for the qua rtz block whe n placed over an aper t ure. 48 The larger the birefringence of t he c rystal, the rnore a ccurately one can cut the cry s tal to a desired thic knes s . If t he b i re - fr ingenc e i s le ss than • 02 the techniq:..xe i s o f margi nal .1.1se for thick ne ss es l es s than 0. ·; 1.1 . O n e would probably h ave t o set up an elaborate opti!=al systen> and foll ow reflected interfere nce fringe s in order to take the cry stal to thinner sections w ith confidence. Ultraviolet abs orb - ing crystal s whic h have interesting d ic hroism , ho w ever , usually ha ve a birefri n gence larger th an • 02. problem . A l ow biref ring enc e pose s anoth er O ptical wedge s can then only be ob s erved for rel ative ly large angle s . For a typical cro ss - section of 0. 15 mm· the s malles t angl e which can be observed for a birefringence of • 02 i s • 007 radian g . The p r oblem of abs orption for an opti c al wedge over a circula r aperture i B treated i n the followi ng way. The crystal is oriented s o that the plane of pol arization i s coincident with a principal direction . The angle of the wedge i s o· and the thi c kne ss t = t . + et r c os €: whe re . t . 0 is the c rystal thicknes s at t he center of the aper t ure. 0 a r =o 1/I 0 -K{ t Zrr r e 0 + r::x r cos C) -------------------~2~.------------------- na where a i s the radius of the a per t ur e. Then I / 1 =e 0 • -Kt 0 rd 0 dr 0 = Areal - loglO t 1 21 ( KCY a ) 1 Kr' a i s an i magina r y B e 3s el fun ction of the fir s t kind . tivi ty constan t in e m -1 K( ~ ) i s an absorp - One c a n approximate K f rom th e absorba nce mea s urement and th en c a lc ul a te the c o1·rection t e r m . The angle CY ma y be determin ed by m ea suring retardation s at two different place s 2! ( Kc'Ya) 1 on the cry s t al. Figure 9 i s a plot of log 10 Krv a as a f un ction of K CY a . F e r K ry a absorbanc e units . le ss than unity , the correction i s le ss tha n. 05 K i s usually no mo re than 5 X 10 aperture radi us is 2 . 5 X 10 radians i s tolerable. -3 em. 5 a nd a typical T h us an a ngle les s t han 0. 001 For s trong a b s orpti on, ther e fore , the cry s tal faces s hould be pa r a llel to within 4 ' of ar c. A ll three cry s tals studied in t h i s work a re layer s tructure s . The cleavage planes are alway s w ell-defined and cutting alon g the cleavage face po ses no proble n1 . 1-Methylthymine h as no natu r a l fa ce per pendicula r to the cleavage plane . .Since the dia mond knife in its pre s ent m ounting i s s tatio nary , it w as not pos s ible to c ut 1 - methylthymine perpendic ular to the (10 2 ) pla ne . molecule <> a re coplanar w ith (00 1), but the The 9-methyladenine tolo! form was oo poorly d evelo ped that the cry s tal could no t be mounted on the ( 010) fa ce. The Hoog s teen dimer, however , does have well de vel ope d {10o} l<;l-yers. { 001\ and forms , b o th of which are perpendic ular to the plane of molecular The cry stal could be cut along the (100) to a section as .th i n Figure 9 . I og 10 kao 21, ( kaa) ka a A bsorbance error due to an optical wedg e over a circular a per tur e. .02 .04 .06 .08 .10 .12 K: ~bsorptivity in ern -l for base e c:v: wedge angle a: aperture. radiu s in ern 1.60 0 U1 51 a s 1 1.1. w ithout cl eavi ng. T h i!:; thickne s s wa s sufficient for the tipectra rep ortod he re. The crystal sectioning technique described above take s iLlll advantage of the high birefringen ce which the :3 e purine s and py ri m idine s ha v e. For the general proble m of sectioning s oft o r ganic crystals, t b e optical sys t~m would have to be improved . Reflecte d light from the dia m ond knife and from t he cry s t a l fac e c an p r ovide for l ong , optic a l lever a rm s which are needed for a ccura te c u tting orientations. A rotatable knife would e li m i nate t h e pre s ent nec e ..;sity of ha ving to poli sh a nattlral cr y ;,tal face. I do feel, however, that w ith a s harp diamond k nife and a m icro tome whic h ha s a st-r1all advanc e incre ment, one c an cut soft organic cry!:l tal s to thicknesse s of the order of 0. 1 IJ.• 52 OPTICAL P ROPER TIES OF CRY STAL S AND CRY '3TALLOGRA PHIC DATA The refractive ind ic es of the cry s t als we r e deterrr,ined by o il i mme r s io n . A student model L eitz polarizi ng m icr-oscope was u sed for the rr1easure ments . A sodi ur:n D line source was s i mul ated with a 589 mi-L inte r feren ce fil te r a n d a C o rning glass filter, No . 3480 , placed together i n front o f a t tmgsten li ght source . c a librate d with an Ab be refr a ctomet6r. T h e i mmersi on o ils wer e The i ndic es fo r h i gh refrac - ti ve index oils w er e determined by the metho d of minimum d eviation . ZV measurements were rnade w ith a Leitz uni versal s tage . I n t he c as e of 9 - methyladenine the 2 V angle was esti mated from c ono s copic o b ser vation of a Bxa fi gu r e. For the Hoog steen dh~n er, a s signn>ent of the i ndi catrix t o the cr ystallographic axes was ma de with a N ei sa enberg photograph . 1-m ethylthymi ne the b - axis assi gnmen t wa s verifi ed w ith a berg photograph. Fo r W eisse:-~ ­ The b-axis o f 9 - metbyladenine was assigned from mor phology and from th e pronounc ed horizontal di sper s ion . The optic a l properties of the three cr ystals a r c li sted below. A. 1 - m e thyl thy m in e NY = l. 6 60 + • 00 2 NZ = l. 762 + • 002 zv = 59. o• + o. 2 • NX = 1. 428 {c a lc ll.lated) y =b D i sper s ion Opt(-) r < v , i n clined 53 B. 9 - methyladenine NZ = 1. 880 + • 00 2 z =b NY = 1. 7 83 + • 002 Dis persio n r < v , s tron g , horizontal Cpt( - ) NX ~ 1 . 53 ( calc ulated) c. Hoo g s teen D imer NX = 1. 4·18 + . 001 X = b NY = l. ·;: L!:E: + • 00 1 Disper s ion r < v , cro ss ed O pt(- ) NZ = 1 . 783 + • 00 l z~ a 2V = 3 '-1 . o• + o. (;• B = 106 ° + 1• = 25 . 4 + 0. 4 The crystal structure s of 1 - methyl thymi ne and the Hoogsteen d i mer have been determined ( 10). The space group and unit-c ell dimen s i ons for '1 - m ethyladenin e have been reported ( 11), but the crystal structure has not been determined . Crystallographic data of the three c r y s tals are tabulated below . 1- me thy1thy m ine ( 1 0) 9 - :rrlethylade n ine (11) a = ·1. 3 51 + . 00 4 a = 7. 67 + • 03 b = 1 2 .091 + .00 6 b c :: 7 . 602 + • 004 c ::::! 8 . 47 + • 03 e : 89 ° 58 + 3 e = 1 2. 3 • 2 6 1 + 10 I I = 12 . 2.4 + .04 1 Space group: P2 p=l.3 8l g / cm z =4 3 p = 1. -171 g/ e m 3 z = 4 1 /c 54 Hoo g stee n d i m er ( 10) a = 8. 30 4 + • 002 b = 6. 55 2 + . 00 2 = 1 2 . 8 3 7 + .003 2 ;: 10 t 50 + 3 c 0 I I .Spac e g roup : Pc. p=l. 4 33g/c m 3 1 o r P2. / m 55 S OLUTION SPEC TRA AND OSCILLATOR :-3TRENGTHS The solution spectra of l-met1<ylthymine and 9 -methyladenine w ere recorded on a Cr-:ry Model 14 spe ctr ophotometer. Both compounds , once recry stallized frorn water and dried u nde r vacuum , we re assutned to be pure and dry. The molar absorp ti vities we r e calculated; the re sult s a re shown in Figure 10. A n equimolar mixture of the purine and pyrimidine were also recorded. This spectr um , als o shown in Figure 10 , i 3 the sum of the corre sponding ab sorptivities of 1-methylthymine a nd 9-methylade:Une. For all solutions the pH was about 6 . For both 1-methylthymine and 9 - rnethyladenine the respective spectra appear to con s i st of two bands. band has>.. nJa.x = 2 73 mp,, the second b ?. nd has A. minimum occurs at\ band has 'A 1nax For 1-methylthymine the fir s t = 238 mp. . . rrll r. rnax • m tn and the Fo r 9 -methyladenin e the first = 261 m!.L , t he second band has A t he rninirnu o ccur s at A. = 20 "i m~J. max = ;;05 nJ~ and = 228 l"Y•IJ. . The oscillator s trength s £o r t'be seve ral absorption band s were determined by the for m u la f = 11. 33 X 10 - where a i s in 1 · rnole and "is in ern -1 • em -1 9 J ad u ( 22 ) :or ba s e 10 units -1 For the second absorption bands, the area '.mder th e red side was detern'1ined and then doubled . The oscillator strengths a re li s ted below. Figure 10. 3.20 3.60 260 3.80 270 Solution spectra. 3.40 a( l·mole-'· cm-1·16.q) A 1-methylthymine B 9 -methy1adenine C 1: 1 molar mixture of A & B ,310 300 290 280 4.20 240 A(mf') v{cm-'·to"'"~) 4.00 250 4.40 230 4.60 220 4.80 210 5.00 200 U1 0' 57 1-methyl thymi ne ~ f max 9 - methyla d eni ne 27 3 mf.l. 207 m11 261 m11 2 0 5 mj.J. o. 19 0 . 28 o. zs 0 . 52 58 P OLARI ZED AB SORPTI ON 3FECTR A OF THE SINGLE C RYS TJ\ L S The cry stal ab t> orption spectra a re p re s ented in thi s secti o n . F o r each sub ::; t a nce the final re sults w er e ob tained by a veraging of data fr om s everal speci mens of d ifferent thicknes s e s . It is i mportant to record the detail s of t he exper i men t s :,; o that the critical reader c an e vah.tate th eir reliability and o verall con s i s t ency. C orre cti on s f o r refle ctions , eccen t r ici ty of the p ola rized light , convergence of t he li ght beam , and photodamage to the cry s t al must Qe c on sidered . I n the inte re st o f clarity , for e a c h substance b elo w , O l1 r fi nal c oncl uai ons a s to the ab so rpti on spe ctr a o f the cry :~ta l are fir s t pres ented . This i s follow ed by a discl\ ssi o n of t he e xperi mental detail <3 an d the correction s . 1-Methylthy m ine. T h e crystal a b s orption s pectra in th e ( 102) pla ne of 1-me t h ylthym ine are show n in F i gllre 11 ; the molar a b s orptivi tie s are listed i n Tabl e II. O ne recall s that ( 102) i s the p l ane of the molec- ul a r layer s . The fir s t tran s mi ssion data for 1 - m ethylthy m i ne w ere obtai ned from a natur ally grown , thi n pla te . a ~~ T he prominen t face was the ( 102) d etern1i ned fr o:cn a conosc opi c observation . c oplanar t o one anothe r in the ( 10 2) plan e . The molecule s lie T h e cr os s - sectional 3-40 cm-'·1o"1 3.60 _, l)(cm ·10 3.80 ) --+ 4.00 o-~ 4.20 Absorption spectra in ( 102} of 1-methylthymine. a(l·mole-'· Figure 11. 0.20 0.60 1.00 1.40 I. 80 2.20 ;\(my) 4.40 U1 -a 60 TABLE II. M o lar Abso rptivitie s o f 1-Methylthymi ne i n the ( 102) Plane a!b _ _ _ _ _ _(::...l_·_n_l_o_ le a -1 -1 -3 • ~~- ) !! b D ichroic Ratio -1 - 1 -3 (1• mole · e m · 10___...._)- - - - 305 2. 2 + 0. 8 0. 1 + • 09 2 2 + 28 300 6 .7 + 1. 7 o. 2 7 +. 10 2.5 + 16 9 . 8 + 2. 4 0. 6 2 +. 12 15 . 8 + 6.9 290 1 2 . 9 + 3.0 1.0 5 +.1 6 12. 3 + 4 . 7 285 1 1,;; . 9 + 3. 4 1. 3 + • 2 11 . 5 + 4 . 4 280 l i .l+3 .8 1.6+ . 2 10. 7 +3. 7 17 . "; + 4 .0 1.7 +. 2 10. 4 + 3. 6 2.70 1 i ' . •! + 3. 9 1.6 +. 2 10. 9 + 4 . 1 26 5 1·4. 8 + 3.4 1. ~-! +. l 10. 6 + 3. 9 2 60 11. 8 + .~. 8 1.3+. 2 .::.ss 9 . 0 + 2. 2 1.3+. 2 ~ 50 ·i· . 2 + 1. 245 5 . 8 + 1. 6 L. l + • 2 3. 4 + .3 240 235 :Cav. a 3.0 + 1.6 7 .3+ 2 .0 = 11 . 2 + 1.0 61 dimen sions of th e cr y ~;tal w ere 0. 2 m m X 0. 2 rnm. U n f o rtuna tely, t h e retar da ti on wa s n o t m e a s u r e d until a fter t h e tr a n <:> rni ssion rn e a :~ ur e rnen ts were m a de . D uring the cour s e of the m ea s urement o c o n Bi d er- a ble photoda rnage of t h e cry s t a l t o ok place. Th e d am a ge w a s d etected w hen the cr y t> tal w a s o b s erved under cr o~ s ed p o l a rizer s w ith white light. A da rk region , the s i ze of the a pertur e , of muc h lo'.;v er re ta rda - tion than the rest of the cry s tal wa s evi dent. The r etardation m ea s ure - rn ents , therefore, w ere n o t characteri s tic for a. cry s tal o f ! - m ethyl thy m i ne . T h e physic a l t h ic k ness of the crystal was rega rded a s t o o un c ertai n f o r mola r a b s o r p tivi ty calculatio n s . T h e nature o f the photoda mage i s pr o bably t he for m ati o n o f 1-m ethylthy m ine di m e r s ( 30). It ha s been :>u g g ested that Llle s. 6 double bon d o pen s a nd f o r m s a cyclo buta ne double bond ( 31) . ring w ith a near n eighbor 5 , 6 The m o lecQ].ar orienta tion s a re favora ble f o r the diG1eriza tio n rea ctio n. (S ee Fig . 18, m o lecule s No s . 1 and 3.) The effect of satur n tin g the 5 , 6 doubl e bond i s to remove the fir s t u ltr a violet a b s orption band from thymine. Hence , p h o todam a g e w ill caus e an i n crea s e in t r a n sr.ni ssi o n of th e cry s tal over t h e fir s t u ltr c:vi o le t b a nd. To the extent that there L• p h o tod i m er i z a ti on taking pla ce dur i n g a m e a s urement, calcula te d mola r abs o rptivi ties w ill be lo w . The gene r al fea tur es of the s p ectra were us eful . T h e weak a b sorpti o n i s alo ng t h e b-axi s an d it r eached a max imuin a t 2 7 5m~ t o 270 m~J.. Perpend ic ular to t h e b·a xi G the a b sor p tion r o s e very r api d ly from 305 rnt.l down to 295 mt.l. From 295 rnu. to 255 m!-1 the absorbance flattened Ol.lt to a plateau o£ about 5 absorbG.nce unitG. tv,o directions crossed. At 240 rm.J. the The dichroic r atio at 295 m!-1 was about ten. The section was evidently too thick for absorption in the strong direction. 1v1ore quantitative spectra were obtained from ground sec ti ons of 1-methylthymine. For the absorption perpendicular to the b-axis in the (102) l3lane , a cry stal was cut toO. 1 OJ. • The retardation wa :-J Inea sured before transmission measurements we re G1ade. calculated thickness was 0. 10 !_ 0. 02 !-1. 1. 72 absorbance units. The The maximum at 275 m:.,~. was Along the b-axis the abso rbance was too w e ak for reliable measurements (0. 15 at 270 m iJ.). of the two directions cro ss . tion had fallen about 30o/o. At 241 rn~. the absorbances After tran s missions were made the r etarda - Although care was taken to make the trans- m ission n1easurement an rapidly as possible, some photodamage had evidently occurred . Thui3 some uncerta inty is introduced into t h e absorption spectrum; the magnitude of the error i s hard to assess. Another 1-methylthymine crystal wa s cut in the ( l OZ) plane to a thickness of 0. 5;;.. From the retardation measurement, the thickness was c alculated t o be 0.49 + .03>J. • The transmission was measured along the b-axi s , but not in the direction perpendic ular to the b- axis. The maximum of the first absorption band was at 275 mi-1; the abso r p ti on sta rted ri s i ng s trongly into a second band a t 240 m t.l . 63 A t the.concl usion of the expe ri m ent there was no meas ur able decrease in retarda tion. The raw a b s orbance s for the t wo different s ections are li s t ed in Table III. The se data are un c orrected for r eflectio n 3 off the cry s t al f a ce, but a base corr e ction from t he edge of t he a b;;;orpti on c u4ve was made. The r e po rted e r ro r ·; are based on the a ccur acy of t..lJ. c i ntensity meas urements. The refle ction coe fficients for 1 - m ethylthyrnine in the region of the mea~ur ed a b so rptio n wer e c o.lcula ted by an I BM 7 0 90 c omputer. T he D rude the or y for a n optice>.l electron w as assume d . The full di s per sion fo r mula wa s app r oxi mated w ith t wo ter m s . For the fir s t ter m the measur ed a b sor ption band was used; t he oscillator s tr eng t h and position of the sec o nd ultravi o let ab:'.lorpti on b a nd were taken frorn solution . B y fitting t he c a lcula ted refractive i ndex to the measured v a lue a t 589 m!J., a reiterative p roc edure wa s u s ed until a c onsi s t ent set of l"efrac tive indic e s was c omputed . The general theo r y and d e ta il s of the c alculation a re found i n App e ndi x}'. . Th e c a lculate d r e fl o ction spectra a l ong t he b-axi s a nd pe r p endicul2.r to th e b - a xi G oft the ( 102) face a r e shown in F i gur e 1 2 . T he c o rDputed refractive i ndic e s a n d reflection coeffici e nt.:; are follnd i n Appendi x A . T he i nput d ata are a l so li.:: t cd i n P.ppendix A . For refle ction corrections of the raw ab so rbance data , it was assume d that the back cry :3t&.l fa c e was in good optic a l c ontac t w ith the m e t hacrylate fil m . Refle ctions off th e fil m ar e amall c omp a r ed Fig ure 12. 4.0 %R 16.0 3 .4 0 .... 3.60 El..b 280 260 4.00 250 4 v (cm-'·10- ) 3 .80 A(mfl) 270 4.20 240 4.40 230 Calculated reflection spe ctra off the ( 102} of 1-methylthymine. 3.20 320 310 300 290 *"" 0' 65 TAB L E III. R aw A b sorbance Da ta for 1 - Me thylthymine - ). , ( rnp,) t = O.l 0 + . 0i i.J. A 3 20 0 31 5 0 A 'b t =o. 4 9 .:!:. • 0 3 IJ. I! b A li b -0 0 0 295 o. 05 + • 0 4 o. 2.3 + . 0 ·4 o. 6 8 + • 0 4 o. 9 8 + . 0 4 29 0 1. 28 + • O<'l: 285 1. 47 + • 04 280 1. 68 + • 0 4 275 l. 7 2 + • 0 4 270 1. 68 + • 0 4 0.1 5 + .04 o. 77 + . 0 4 265 1. 4 1 + • 0 4 o. 13 + . 0 £1 0.73 + .0·1 260 1. 11 + • 04 0. 09 + • 0 1 o. 64 + • 04: 255 Oo 84 + • 0 4 o. 08 + 04 o. 64 + . 04 25 0 o. 6 6 + • 0 Ll o. 07 + • 0 4 o. 6 8 + • 0 4 24 5 o. 5 2 + • 04 o. 38 + • 0 ·~ o. 24 + • 0 6 . . . o. 7 0.15+.04 1.0 2 + .04 0.51 +. 0 4 1. 66 + • 0 5 3 10 30 5 300 240 235 2 30 0 0 o. 0 8 + • 0 4 o. 05 + • 0 4 o. 13 + • 04 o. 30 + • 0 <1 0. 1 2 + • 0 ·1 0 . 5 1+.04 0. 6 5 + . 0 4 0 . 13 + • 0 4 o. 77 + • 0 4 0 . 84 + • 04 o. 7 2 + > 1. 6 0 0 06 > z. 5 66 to the e :3tabli shed error of • 04 a b so rbanc e unitq. T hus only r efle ctions o££ t he fr ont face of the cry s ta.l w ere c onsidered . A l ong t he b - axis the co r re c tion wa s negligible; pe r pendic ular to the b - axi s the correction an1o-.1n.ted to • 0 5 absor bance units nt the most. N i th the ra "" absorbance corrected for reflections , molar a b sorptivities were calculated. The density of 1-xr.ethylthymine i s reported w ith th e cry sta.l s tructu r e dete r mina tio n ( 10) . Table U is a tab u l a tion of the c a lc :Jla tcd val ues w ith e rr ors based on . t he a cc u r a cy o f inten s ity mea s uren1ents, on the birefri ngenc e unc er ta inty, a n d on the repro ducibility of retardati on measurements . The weak abso r p - ti on values we r e c a lc llla t ed f rom the th ic ke r of the tw o section3. Figure 11 i s a plc-,t of the absorptivitieB as a function of wa velength and wave number . The error s are not shown . T h e s li gh tly saw - too thed shape of the str on g absorption curve may reflect the photo cl.arnage which took p l a ce dllri ng the measur e!nent s . 9 - Me thy l adenin~. The c rystal absorpti on spectr a of 9 - methyladenine i n the {00 1) plane a re shown i n F i gure 13 and Table IV. Al though the cr ystal structure o f 9 - methyladenine has not been determi ned , its unit cell d i mens i ons have b een repo rte d (11). The x -ray d iff r a ction d a ta a l so s uggest t ha t the c ry stal i s a lay e r s tr u c ture w i th the molecule s l ying in the (00 1) plane (1 2). age plane ( 001 ). The crystals do have a pronounced cleav - -Figure 13. 3 .40 29o 3.60 2ao 2so 250 3.80 4.00 V (em_, ·16 4 ) A(mf) 210 4.20 240 Absorption spectra in (001) of 9 - methyladenine. 3.20 1.20I-a(l·mole-1 ·cm-1 ·IO-~) 3ao 310 3oo 4.40 230 -..] 0' 68 TABLE IV. Mola r Absorptivitie s for 9 - Me thyladenine in the (001 ) P lane a ~~ b .\ ( m p. ) {!· mole -1 ·e m a lb -1 ·10 -3 ) D ic hroic (l·mole-l·crr--1·10-3) Rati o 300 0 295 0. 9 + • 4 o. 20 + .08 4 .9+3. 9 29 0 7 . 0 + 1.3 1. 2 + o. 2 5. 7 + 1.3 285 14 . 9 + 2.. 5 2. 9 + o. 3 5. 0 + o. 5 280 18. 5 + 3. 1 3. 6 + o. 4 5. 1 + o. 4 275 2 1.0+3. 4 4 . 7 + o. 5 4.5 + 0. 3 2 '70 19 . 8 + 3.3 4 . 9 + o. 6 265 l'l. 1 + 2. 8 4. 7 + 0. 5 260 14 . 8 + ?. . 4 4. 5 + o. 5 255 11. 7 + 2 . 1 4 . 1 + o. 6 2.50 8. 8 + 1.6 3. 8 + 0.5 245 E. . 5 + 1.3 3.9 + 0.5 240 'L 5 + 1.3 Ll o 2 + 0 . 9 23 5 3 . 2 +0.7 5 . 0 + 1.0 23 0 3.2+0. 7 7 . 6 + 1. 4 Dav. 0 =5 . 1 + 0 . 5 A 9 - methyladenin e crystal was ground to a thin s ection in the ( 00 1) plane. The thic k ness , de t ermine d from t h e retardation mea s llre - ments , was 0. 1 6 + • 03 1.1. . There wa s no e videnc e of photodamage during the transmission me as urement::~. The direction of s tron g ab - sorption wa s along the b - axis w ith a maximllm a t 2 75 m1.1.. A long the a - axis_ the absorption reached a rr;aximllm at a bout 270 m~-L an.d remained rela tiv ely flat to 240m~. Below 240 m!J. the a - a x i s become s t he direc tion 69 of strong ab~orption . At 240 m!J. the two ab s orption curve s cros s . I n order t o measure the absorption along the a - axi s with greater accuracy , a thick er c ection of the (001 ) plane was prepared. s econd sam ple had a thickne ss of 0. 6 1,:!:.. OS 1). . the thinner sec tion was :;.·ea sonable . Table V The The ag reement with i s a tabula tion of the raw absorbance d ata unc orrected fo r refl e ctions . TABLE V. Raw Absorbance D a ta for 9 - M ethyladenine t = 0.1 6 ,:!:. . 03 p. A '! b A I b t =o. 6 1 + • 0 5 IJ. A II b !b A 3 ::: 0 0 31 5 0 310 0 0 305 0 0 . - 300 .03 + ;.:95 • 18 + • 04 ~90 1. 17 + .0 4 • 2.0 + • 04 . . : 85 2 . 45 + • 04 . 1 8 + .04 l. 90 + • 0 4· ;~. 80 3.03 + • 0 4: • S9 + . 0 4 c.. 15 + .0 4 .~7 5 3 . 11 + • 0 ·1 . ?. . 85 + • 0 .J: ,:.'( 0 3. 2 1 + • 0 4 • 7'-! + .04 z. <:6 5 2.. . 6 + . 0 4 . '73 + .O J 2.90 + .04 2 G0 ,:,: . 37 + • 0 4 • 7 1 + • 04 2 . 78 + • 0 4 255 l. 85 + .OL'. . 59 + • 0 4· 2 . 61 + • 0 4 250 l. 39 + 0 . 4 • 50 + • 0 4 2 .50 + . 0 4 ~4 5 l. 01 + . 04 • 54 + .04 2 . 6 3 + .04 2AO 0. 69 + • 04 • 68 + .04 235 0 • .1.~ 'I' + • 04 • 80 + • 0 4 2 30 0 . 4 8 + • 04 1. 22 + .04 Q :\ ~ 0 o. 8 2 + 0 .( !~ . fJ 8 + .04 • / ; C· + . 04 ' "% • 12 + • 0 ,1 I .. ~ • v! 9 ~, ~3 . 0 + • Q <l + . 04 70 Reflection s pectra of£ the tool} face were calculated in the same manner for 9 - methyladenine as for 1-methylthymine. The i nput data and c omputed refractive indices and reflection coefficient s are listed i n. Appendix A. Tr.1e calculated reflection spectra are shown in Figure 1~. The appropriate reflection corrections were n1ade in the ~arne manner as for 1-methylthymine. puted. Molar absor p tivitie s were then c om - The density of the crystal i G reported with the unit cell dimen - sions (11). Table rv i s a tabulation of the results . The errors are based on the thickness uncertainty and on ·the limited accuracy of intensity m easurements. The absorbanceo near the maxirnum of the strong a bsorption band may have been low due to th e small out of plane com: oncnt of the polarized light. At the worst they are low by 0 . 2 absorbance units. (See section on the m icro s pectrophoto met er .) The weak absorption band was averaged from the absorption measurements of the two different thicknesses . Figure 13 is a plot of the molar absorptivities as a function of wavelength and of wavenumber . Hoogsteen Dimer. The hydrogen bonded complex of 1 - methylthyrnine and 9 - methyladenine lies in the (010) plane. Therefore. the symmetry (b ) axi s of the monoclinic crystal is pe rpendicular to the molecular planes. The ai:H;or ption spectrum for the light polarized along the b · axis is recorded on page 80a. /oR Figure 14 . 0 3.40 290 3.60 280 A(mf) 260 V(cm- 1·10--4) 270 Calc ula ted reflec tion s pectra off the (001) of 9 - methyla deni ne. 3.20 320 310 300 --J ..... 72 The spec tral data for li ght pola rized i n t h e molecula r pla n e are necessarily more c omplicated than was t h e ca s e for 1-methylthy mine or 9 -methyladenine cry stal s . B oth 1-methylthymine and 9 - methyladenine ar e monoclinic , but in each c ase the b - axis lie s i n the plane of the molecules. Therefore , for 1 - methylthym i ne and 9 - methyladenine , for light polari zed in the plane of the molecule s , the b - axis iB a principal dir ection and the ab sor p tivity ellipsoid has its p rin cipal dir e ctions par allel and perpendicular to b. H o wever, for the H oogs t een d i mer t he orientation of the a b sor p tivity ellipsoi d i s no t fixed by cr ystallog rap hic symmetry and i n fc.ct can and doe s vary w ith -wa vel cngt.~ . The experi mente r m ust dete r m i n e b oth t he orientation of the pr inci pal axe s with r espec t to a cry s tal face and the magnitude s of the absorbanc es a long th e p rin cipal axe s . If C;'i i s the angl e b etween a c ry s tal face and t he e lectric vector of the incident light a n d 8 i s the angle bet;.x; een the same cr y stal f ac e and a principal a xi s , then th e transmis s ion i s 1/l where A 1 0 and A cipal axes. titie s A 1 =co s , A 2 2 ( <F - " ) 10 -A2 + si n 2 are the absorbance s along the two respectiv e p rin- From measurements of 1/I 2 - Al (<:!· - '=' ) 10 , and as a function o f c:-·., th e quan - " as a function of wav e length have b een d e ter.m ined by a leas t squa r es a nalysi s . sented i n Table VI. o (:5 e e i\ ppendix B .) The results are pre - 73 TABLE VI. Mol ar A b s orptivitie s o f P rinci pal D irections and Position Angles for t he Hoog s teen Dimer t = 0 . 22 + . o·; tJ. A. ( m~) amax • lo-3 -1 (l· mole-l ·c m ) a :mi n • 10-3 (1· rnole- 1. cm-1) ( d egrees) D ichroic Rati os 230 11. 6 + 4 . 5 3. 6 +1.5 91.9+1.1 3.2 235 9.3 + 5. 2 3. 9 + 2. 5 92 . 2 + 5. 2 2. 4 240 7.6+3.0 4. 8 + 2. 0 83 . 4 + 2..9 1. 6 245 7. 4 + 2. 6 5. 9 + 2. 2 28 . 8 + ·1. 0 1. z5 250 9 . 4 +3. 2 5 . 5 + l. 8 14 . 2 + 0 .. 6 1. 7 255 12 .0 + 4·.3 5. 7 + 2. 2 10. ~.!: + 1.1 2. 1 26 0 13. 4 + 4 . 6 6 . 1 + 2. 2. 12.2+1.1 2. 2 265 1'L 6 + 4 . 9 7 .2.+2.. 5 11. 0 + o. 6 2.0 2."i 0 15 . 9 + 5. 8 8 . 8+3.3 9 . 1 + 1.7 1. 8 275 15. 4 + 5 . 1 9. 9 + 3. 2 7 . 3+0 . 6 1. ss 280 14 . 2 + t.J:. 8 9 . 6 + 3. 2 6 .0+1.1 1. 4g 23 5 11. 6 + 4 . 0 8 . 4: + 2 . 9 6 . 2 + 1. 7 l. 3 7 290 10 . 0 + 3. 5 7. 5 + 2. 8 4. 1 + 2. 9 1. 33 295 8. l + 2 . 8 5. 9 + 2 . 0 7.8+1.1 1. 3-, 300 4 . 0 + 1. 6 3.2+ 1. 4 -29. 4 +9. 4 1. zs 305 2 . 1 + 0. 8 1.2+0.5 - 12. 6 + 2. 3 1. 7 I} = t 0. 49 ±. . 0 5 !.1 -------------------------------~~--~----------------------------10. 8 + 1. 4 96. 9 + 5. 0 1.1 11.9+1.6 240 295 7.9+0. 8 7.6+0.8 16 . 6 + 6 . 0 300 3.0 + 0. 6 2 . 2 + o. 4 -54 . 7 + 5 . 2 NOTA BENE: The data for 2AO m\J; wa s in very poor agreement for the two sections analyzed. It is hard to under s tand why the dichroism for the thic k section i s rm .tch smaller than for the thin section. The transmis s ion near the directi on for strong absorption may have been too high for the thick section, a lthou gh this seems unlikely. These data represent the large s t discr epancy e ncountered in all th e crystal :measur en>ents presented in this work. 74 TABLE VI (continued) NOTA BENE (c ontinued): The data for 2 4 0 m~ from the 0. 49 p, section were scaled down to fit smoothly into the three dimensional model. Values cho s en were: a max 3 = 7.6xl0 , a min 3 = 6 . 9 x 10 • 8 = 96 + 5 Com pared to 1-m ethylthymine and 9 - m ethyladenine, the Hoog s teen dimer is not very dichroic in the molecular plane. It should be realized that the more isotropic the absorption (that i s , the closer Az'A e. 1 i s to unity), the less accura te is the determination of the angle A sketch of a three dimen!jional model representing the absorption surface is shown in Figure 15. The structure was built around a cylindrical coordinate system . Each plate, perpendicular to t he cylindrica l axis , corre s ponds to a different wavelength . The wave - length, in 5 mtJ. increments, runs from 300 m~ to 230 m~ down the cylindrical axis. The radial coordina te represents absorption and the angular coordina te is defined in the manner described below. The struts , running down the s ide s of the m odel, follow the principal directions; one p a ir correspond s to the large r axi s and the other pai r to the smaller axi s . The preparation of a thin cry s tal i n the (010) plane was a di f ficult task because the birefringence i s only • 03 7 . When the cry stal 75 Figure 15. Three dimensional model of polarized absorption in the t010) of the Hoogsteen dimer. 76 was less than 1 !Jo , the i nterferenc e colors could no l onger be detected . Of several sections prepar ed only one w as t'hin enough ( 0 . 22 ~-t ) for a complete dete r m i nation of the absorption. Two other section s of thick ne sses 0. ,4:9 1.1> and 0. 55 1-1. were usef ul i n confirming the toe absorpti on , near 300 mt1 ami the a b s orption near 240 ml). . There was no eviden c e of photodamage d u ring the cour se of the tran srni ssion measureme nts. The ( 010) plane , pe r pendicular to the b - axis , h as no p ri ndpal d i rections fixed by cry stc'1.llographic symmetry. Hence , the t ransmis si ons were measured by rotatin g the cry stal at increments of 30° w it!>. re spect to the electric ,rector of the polariz ed light. The c rystal was rotated through a total angle of 240 ° for each wavelength . The angula r depe n d ence of th e tr ans mis s i on i s understood i£ one c on s ide r s the absorption of lig h t a ri s ing fr om tw o i n dependent r a y s polar ized along the two principal d ir e ction s . The electric vec tor p rojects i ts ampli tude a long the two pri n cipa l d irectio n s , wr...ich h av e c h a racteri s tic cro ss - sections. The ampli t ude co mponents a re then a ttenuated exponentia lly as the r ays p r oc e ed thr ough the crystal. If '!•· i s the angle bet ween an a rbitrary li ne on the crystal and the electric vector . t h en the angular dependence of th e ab:::oorption i s A = - l og 10 ( P. cos 2•r + y s in z,r·+ 6 ) fo r v.1hich the three par ameters , ~, y and 6 , deter n·1ine the r espective cr o s s - s ections of the two pri n cipal d i r e ctions c. nd the position o f the principa l directicns in the crystal. ·n y/ 8 =tan 2° wh ere '"' is the angle be t-w een a line on the cry stal and one of the prin cipa l direction s . principal direction P 1 principal d irection, P is A 2 , A 1 2 The absorbance A os 2~ - B \ = -log 10 ( c ccos .. 1 2:= -log 10 ( ~s zn + e\ c o::; t.e 7. 1 along the a nd :or the other (See Appe : dix B .) The dichroisrn for the fi r s t absorption ban d was never tnore th an two . The r e£lec t i ons off the {OlOJ face , therefore , a r e i sotropic w ithin the a cc uracy of a transmissi on measurement. To the extent that reflections are the same for all dir e ctions , t he above angul ar dependence of a b sor b anc e is independent of r efl ectio!"ls . The r aw abso rbance data were fitted t o the a bove equation by a lea s t squares analysis. 7 0 9 0 computer was used for th e computati ons. An I BM The general theor y and de ri va tions for t he analysis a 1:e in Appendix B . The i sotr opic absor p ti on of the {010) face was deter m i ned by re moving the polari ze r. transrnitted signa l . Rotation of the crystal did not change t he F r om the i sotropic abs o r ption a s et of "m ean" r eflection coeffici e nts for t he (010) fa c e were c omputed . dichr oism is small , such a t r eatment i s justified. .Since the Neve rth ele ss , there i s a slight wei ghting towa r ds the smaller absorption of the t wo princi pal = direction <> . For the r efractive index a t 589 m~.L . the value l. 764 "VNxNy was used . Tbe input d ata , c omput ed refractive i ndice s . and reflection c o efficients ar e Hated in Appendix A . A plot of the i sotropic absorption i n the {010) pl ane is shown in F igure 16 . T he abso rbance .::; at 24 0 mj.l. and 2.45 m~-~o a r e we i ghted Fi gure 16. 1.20·- 1.40 3.40 270 3.60 260 3.80 v(cm-1·10- 4 ) A<mf) 280 4 .00 250 4.20 240 4.40 230 I sotropi c a b sorption i n (010) of Hoog steen dimer . Smooth cur ve is measured a b s o rpti on·. Cir cles are calc ula t e d fr om p r incipal axes i n l east squares anal ys i s. 3.20 ABSORBANCE 320 -.I (X) 79 with t h e dat.-'3. fr om a section 0. 49 p. thic k . The points on t he c u rve a r e calculate d fro!n c orrec ted absorbance s of the pr incipal direction s , which we re obtained from t.~e least squares anal ysi s . T h e agreement for all wavelengtb r~ i s '>:Vithin the s tanda rd a b s orbance error of . 0 4 . The small p eak at 240 m~ , evide;1t i n th e i so tropic absorption spectr um , m ay be syr.:1 ptornatic of a new ba n d. however. It i s by no means conclusive, The c ontour o f the i sotr opic a b sorption c u rve i s very s en s i- tive to t he polari zati on p roperties of the v a r i ouo transitio ns. The polarized s pectr a mus t be analyzed i n order to unde r s tand the isotropic ab sorption. T he i s otropic absorption c u rve does provide a useful confirmation of th e absorbanc e v a l ues c al cula t e d f or the principal axes . The raw a bsorbanc e data for t he polariza ti on s tudie s were correc ted fo r refl e ctionB in th e usua l way . at m ost to • 0 3 a b s orban c e units . d irections wer e co n1pute d. The corrections amo unte d Mol ar absorptivi tie s for t he p ri n cipal The calculated lea st sq:.1are curve s were plotted on pol a r c oordi na tes i n molar absorptivity ·em its . The angular variable i s defi ned as ze:..·o a l ong the c - axi s of t he crystal and inc rea ses i n a ri ght handed sense t oward s the a c ute angle of the (01 0 ) plane . The curves fo r 300 rnJ.J. and 240 m;.L a r e b as ed on measur ements f rom a thicker s ection ( 0 . 49 !.L) . These c urves , w i th the expe ri m ental points , are found in Appendix B . The a - c p l an e is dr awn on a pol a r coo rdi nate graph for conveni ence . The molar absorptiv i tie s of the p rincipal directions with c o rre sponding e rror s and the positio n a n g l es , P, w ith 80 their calc ulated standard deviatio:1 s a r e tabulate d i n Table VI. angle ., The i s from the c-axis to the smaller of t he two p r incipal axes . The abso r p tio n spec trum a l ong the b - axi::i ( perpendic u la r to t he molecular p l anes ) of the Hoogs te en d i mer i s shown i n F igure 17. The molar ab s orptivitie s are f o und i n Table VII. TABLE VII. Mol ar Absorptivi ties a l ong t h e b-Axis of the Hoog s tee n Dimer t= 6 .1 0 .:!:..051.1. a ( 1· mole -1 •cm t -1 • 10 -2 ) = 1. 9 + . 02 p. j a ( 1 • n:lOl e -1 •cm 230 l o. 3 + 0. {, 235 10 .0+ 0.7 10 9 . 0 + 0 . () 9 .1+0. 4 8 . 3 + o. 5 2 50 ,.• 7 + 0 . 2 ·r . ; + o. 5 255 6 . 7 + o. 2. 7.5 + 0 . 5 260 6. 0 + o. z G. 9 + 0. 5 265 5 . 6 + o. 2 {-.. 2 + 0.5 270 5 . 4 + o. 2 275 5 . 0 + o. 2. s. 5 + o. 5 4 . 6 + o. 5 280 4 . 1 + o. z 4 . 0 + 0.4 285 3. 4 + o. 2. 3. 3 + o. 4, 290 3. 0 + 0. 1 2 . 7 + o. ~ 295 1. 6 + o. 2 1. 8 + 0. 4 300 o. 5 + o. 1 0 . 7 + 0. 5 ~ 305 - 1 • 10 -2 ) 2 290 F i gure 17. 2 .0 4 .0 3.40 3 .60 280 4 4 .00 250 V(cm-'·t6 ) 3 .80 270 260 A{m~) 4 .20 240 Spec tr um parall e l t o the b-axi s i n the Hoogs teen dime r. 3.20 6.0~ a(l ·mole·'·cm-'·to ) 8.0 10.0 320 310 300 4 .40 230 00 0 Ill 81 For trans rni. ssi o n measure rnents alo n g the b - axi s , that i ::: , perpe n dicular t o the molecula r planes , a var i ety of different th ic kness e s were used . A natural cry stal of the Hoog s tee r~ di n> er with a thick n ess of 9 6 !. 2 1-1 w as placed over a 100 l.l aperture with the incident to t he ligh t bearn . { 100} face A re s idual absorbance o f • 05 at 4:00 n•~ i ncreased li n early to 0. 11 at 310 ml).. • The va lue ~ are a little h igh for t.."he expected reflections and p r obably indicate a small arnount of impur ity i n t h e crystal. The thick c ry st<-"'ll mea .:> uremen ts , however , did establish an u pper li mit of 1 to 2 mola r abs orptivity unitG for absorp ti on between the molecula r layer s from 4 00 m!Jo to 31 0 r:n~ • A t 310 m~ the absorbanc e perpendicular to the b - axis \"vas 0. 76 and rose to --...3 . 5 at 305 rn!J. . T h e ab s orption parallel to t he b-axis did n ot rise !Jharply until t h e exciting light reached 3JO m~. It is clear fro m the s e s tuciie s that any n - •'* tran s ition which i s polarized perpendicular to the purine rL1g is well i n::lide th e tr - "' * absor ption bands . Anothe r Hoogsteen dimer was ground to a section "'"' 11 ~ thick b the (100) plane. The dichroism i s extremely l arge (alb/a!lb = 6 0 to 4 0 ) in the wavelength region 300 m!J. to 280 m~~ . In determini ng the absorpti on s pectr u m for light polarized perpendicula r to the molecular plane (( 010)), the possibility of an absorption contributi on from com pone nts in the r-:1olecular planes must be con s idered. Cne such contri - bution occur s because the incident light is conve r g ing a nd not perfectly parallel. For the wavelengths from 295 m ~ to 280 miJ. the aperture on the 82 1: 1 ima ging le ns was varied. The absorbance values w ere independent of t h e solid angle, whi ch varied f rom 6. 29 x 10 l. 1 x 10 -3 . sterad1ans . ·3 steradians d own to The theory for the interaction of plane pola r- ized light w ith an ar1i sotropic absorbi ng plane is fO ltnd i n }', ppendix C . · The transn1i ssi on depen dence on the angl e of c onvergence , where thi s anglt! i s small , so that tan T) = oin T) = 'T'~ i s expre ssed as a s erie s . I t i s 00 1/l :: e -A y 0 \ 2 ~1 i (Az 1'1 )' n=o whe re 1l.y and Az a r e t he weak a nd strong abso1·bances, resp ectively, and n is the ang le of conver g ence . The s eries converges absolutely , and indep endently of the argument. To my knowledge the s erie s i s not a tabula ted fu nction . I n or der to have a measw.·a.ble s olid angle de- 2 pe ndence , however , Az:n nmat be about unity. I n base 10 units Az would have to be aboat 100, w hic h is far too l arg e for C)e thickness s t udied . From this argum ent i t is c onclJ.ded that the observed absorbance perpendic ular to the rnolec•.llar l aycr s is bonafide absorptio n a nd not sor-.G~ artifact due to t h e geometry of t.~e system . The a b so rption spectr um p erpendic ular to the molecular p l an e s was sa ti sfactor ily determir:.ed fro rn two sectio:-Hs g r ound in the ( 100) pla n e . One section was 6 . 10 +. 05 iJ. and th e other <:vas 1. 91 ,:!:.. 02 j.!> . T he thi c ker section had a we d ge angle of • 003 6 r~dians . but for the 5 0 \.!· aperture used , the u.bsorbance error was not m e asurable. ( 3 ee 83 the sectio n o n crystal prep ar2.tion .) Reflection s o ff t h e a lon g th e b-axi s a r e negligible. i ioo} f a ce T h e calc ulate d ab so rpti v ide ~ for t h e t-wo sample s are li sted in Tabl e VII. F i gu re 17 i ..; a plot o f the abs o rb- tivitie s as a flln c tion of wavenun1ber a ad wavelength . c urve is a wei ghted average of the two sample s . The absorption 84 D IS CUSSI ON Transition Moment Directions and ~V avelength 3hifts. 1 - Me thylthymi ne. in F igure 18. The cry stal structure in the ( 102) plane is shown For convenience the absorption spectra from page 59 are repeated here in Figure 19. There appears to be a s ingle band from 305 rniJ. to 265 m~J. polarized mainly along the pseudo - axis p (perpendi cular to b in the ( 102)) with a dich:coic ra ti o of 11 . 2.:!: 1. 0 whi ch i ·s constant within the rather large experi mental error. A second band with the opposite polarization behavior begins at perhaps 265 m!J. and is dominant bel ow 240 miJ.. S uppose that at any one wavelength there is a unique direction of absorption ( the direction of the transition moment) for a given 1 rnethy1thyrnine molecule. We also as s ume there is zero absorption i n the perpendicular direction . I nformation abo ut thi s direction can be obtained from the polarized , crystal absorption spectra . Molecules ( 1) and ( 2) ( see Fig. 18) are a h ydrogen bonded pair which are related to each other by a center of symmetry . Therefore , the t r ansition moment directions of these rnolec ules are the sa me • The orientation of the hydrogen bonded pair, molecule s (3 ) and ( 4), is obtained from (1) and ( 2) by a reflec tion in a plane perpendicular to the b - axis. Let Figure 18. ............ ' I ',q~c CH 3 / __, N I "' ~/ 3 CH31 CH 3 I CH 3 ~ I 4 __,"'"/ ___ b-+ ,o I "-cH c~ 3 The (102) plane of 1-methylthymine sh owing the four molecules per unit cell. Molecules 3 and 4 (in light type ) are in a lay er below the plane of the paper. Th e si gnificance of the arrows is de scribed in the text. o /c'-.......N/ I I // / / ~c/ I C"'-. j O-' I 3 CH 0~ / N~ c c c'--* / c . . . . . . . N/ C ~ N/ ~0 l t p {102) CP \J1 86 0 0 0 .,j- - Cf' •o 0 - a> li') :l. E --- -< 0 U) rQ - ""'o 'E u "jQ) 0 ~ 0 0 (\J (\J Figure 19 . 0 (J) 0 ~ 0 0 0 0 c.D ('\j 0 0 Absorption spectra in ( 10 2) of 1-methy1thymine . 'E (.) ~ 87 (,? be the angle which the transition moments of the 1 - 2 pair make w i th the pseudo axi s p; then - rp is the angle made by the transition moment of the 3-4 pair. 2 The dichroic ratio, {alb / a \! b), would then beD= cot q:. The absolute angle , calculated from the weighted average of the dichroic ratios over the first band i s q; = 16 . s•.:!:., 0 . a•. ratios from 305 m~o~o to 2 65 m!J. are listed in Table U. The dichroic The full error i m plied from t..l,.e tabulated dichroic ratios places the transition dipole moment from 21 • to i z• on e~ther side of the p - axis. By Tinoco's convention { 5') the transition dipole moment direction i s a~ s i gned to eith er an angle of 1 4• .:!:.. z• or an angle of 161° .:!:.. z•. T h e c orresponding direction s are shown on molecule 2 i n Figure 18. The above calculation a3sume s t hat for any one m olecule there is a unique direction of absorption with a n infinite dichroi c ratio . Thi s is expected theoretically for a s ingle allowed electronic tran s ition in the absence of vibronic or other perturbations. The oscillator s trength of the first a b s orption band i s 0. 19, corre s ponding to a traneition dipole moment of 3. 3 Debyes. This i s intermediate between an allowed electronic dipole transition a nd a forbidden transition { 3 ). I n the latter case the inten s ity w ould mainly be "borrowed" by vi bronic interactions with h i gher , allowed electron ic states. The constancy of the dichroic ratio from 29 5 m;J. to 2 65 m~ s uggests tha t the b a nd is allowed. 88 V..'e now consider the "resonance-force 11 ( 26) or "exciton" ( 4 ) i nteraction between molecules . The dipole-dipole i nteraction energy of two transition dipoles i s - .... R 3(; 1 - it><~ 2 · R.> 3 R5 The important near neighbors are molecules 1 and 3 in Figure 18. The centerl to center distance i s 4 . 38 A . energy is .:t 200 em -1 The calculated interaction For the large number of stac ked molecules ( several hundred) the interaction i s doubled to!, 400 em -l • The vibra- 1 tional half ~band w idth for the solution spectrum is 3720 c m- • Accord- ing to the S impson criterion (26 ), the system may be considered "weak -coupled." Therefore, assuming 800 em -1 spacing for each vibrational level, the i nteracti on of the vibrational levels should be about t of the calcula t ed strong coupled system. intera ction or 100 em - 1 total splitting for each vibrational level. The crystal spectrum is red - shifted about 800 em t o solution. -1 Thi s is about a 50 c n'l (See F ig. 24, p. -1 compared 110 • ) The calculated exciton interaction cannot account for the overall red s hift . The difference in solvati on by water as compared to other 1-rnethylthym ine m olecule s probably accounts for the relative red s hift. 9 - Methyladenine and the H oog s teen Dimer. S ince the · crystal s tructure of 9 - methyladenine i s not yet k nown , it is not po ssible to dr a w conclusions 89 about the directions of tran s ition moments with re spect to molecular axe s . A pla usibl e assignment can be made , however, by consideration of t h is crystal and the Hoogs teen D i mer; this cons ideration lea d s to a sugges ted molecula r orientation f or the 9 - met.'11yladenine cry stal. (S ee P roposition I . ) The polarized absorption s pects.·a of 9 - me thyladenine (Fi g . 13 repeated he re for the reader's convenience as F igure 2 0) s hows a strong band w ith a peak a t 275 mJ.J. which i s strongly polar ized along the Down to 280 m i-L the dichroic ra ti o of (a!l b~alb) i s constant b - axis . with a weighted average ratio equa l to 5. 1 + 0. 5 . T he absorption from 280 mp. to 2 55 mi-L perpendicular to the b-a xis c an b e p l a<.1sibly deco m po ~ ed into a componen t of the !lb band with a d ichroic r a tio of 1/5 and a second weak band w ith a n!aximum n e ar 2 55 m !J.. The weak band so con structed has an esti rnated o s cillator str e ngth of • 008. There i s a very marked red shi ft of t h e cry stal s pectrum w ith a maximum at 275 mi-L compared to the solution spectrum with a m axim um a t 263 mt.J. . T h e hy d rog e n bonded com plex of 1- methylthy m ine and 9 - m e thyladenine lie s in t he (0 10} plane . There a re two dimer s per unit cell whic h are relate d by a t wo -fold s cr ew a xis. Therefore, a ll thymine s a nd adenines have their respective transition d ipole m oments a ligned i n t he s ame direction. unit cell. 3. 27 6 .l. Figure 21 i s a drawing of th e two dimer s per The molecular layer s are s eparated b y a ve rtica l di stance of 300 3.40 290 3 .60 280 -1 250 4 .00 v ( em ·10-4) 260 3 .80 A(mJ-l) 270 4.20 240 Absorption spectra in (001) of 9-methyladenine . 3.20 a(l·moie-'· cm- 1·10-4 ) Fi gure 20. 2.00·- 2 .20 320 310 T 4.40 230 0 -,!) vC~ / c / Figure 21 . I \-c CH 3 \\ o I cH3 N--e I c\ c 3 c / c~ N'\ I j /cc~ / c\\c j N --4 c I \( -_c~ _-\ - N c \ / ..,./ c. ----\-- -·· ,\ ~N----\:-----~\ . . __ . ,. c~N/c"' c N--- The (010} of the hydrogen bonded complex of 9-methyladenine and 1-methylthymine, showing the two dimers per unit cell. Molecules drawn in light type are below the plane of the paper. N--- cH 3 I o--\-----N"-.c/N"-. / · \ __ _ \c I o \-~--N / \ ______~H3 c lOIOl c. ~N/c ~ \. N/ I ;N c~/ a c--+ ,_. -.D 92 The general feature s of the polarized abso r ption in the (010) are as followso The tabulated values for the absorpti vity ellipsoid s are repeated here for convenience i n Table VIII. The m i nor axis of the pri n cipal directions has a maximum absorption at about 277 m~ . while the m a jor axis has a maximum at 273 m~ . from 1. 3 at 295 m~ to 2 . 1 a t 255 m!Jo. The dichroic ratio increase s Over the first absorption band the angular orientation is relatively con5tant with the exception of wavelengths at 300 m !Jo and 3 05 m!J.. Between 245 m!.L and 240 milo the directions of the major and minor axes reverse about 90• and the dichroisrn at 230 m~ become s l a rge (--...3). At 240 m~ the d ichroic ratio is about 1. 5, but for this wavelength the two different secti ons are i n poor agreement. The relatively sm~ll dichroism in the (010) plane from 305m!:!' to 290 m;..o is surprisi ng. ~d expec~ only From the solution spectra (Fi g o 10), o ne thymine absorption from 310 m~J. to 290 m!J. . If this were the ca se , _!he d ichroism would be very large with essentially a ll the absorption i n the d irection of the transition m oment (or !-methylthymine . The _yery s mall dichroi sm on the red side of the ab s orption cur ve suggest s several a lternate hypc:;>theses . S uppose th at the crystal i s di s ordered. The N 3 -c 6 axis in 1 - methylthymine i s almost a two -fold s ymmetry axis . · I n the hydrogen a xi s is essenti ally parallel bonded complex crystal s tructure the N -C 6 3 to the c-axi s ( see Fig. 21 ) • . If the 1-methylthymine molecules went into 93 TABLE VUI. Mol ar Ab sorptivities of Principa l Direction s and Position Angle s for t h e Hoo gs te en D i me r t a A. (m~ ) max • 10 {!· mole -1 -3 •e m =0. 22 .:!: • 07 a -1 ) m in ----------------------1-.1. • 10- 3 (l• mole (' -1 ·e m -1 ) ( degrees) Dichroic Ratio s 230 11. 6 + 4. 5 3. 6 +1.5 91 . 9 +1.1 3.2 235 9. 3 + 5. 2 3. 9 + 2 . 5 92 . 2 + 5 . 2. 2. 4 24 0 7. 6 + 3. 0 4 . 8 + 2. 0 8 3. 4 + 2;9 1. 6 245 7. 4 + 2 . 6 5 . 9 + 2. . 2 28. 8 + 4 . 0 1. 2 5 250 9 . 4 + 3.2 5. 5 + 1. 8 14 . 2 + o. 6 1. 7 255 12.0+ 4 .3 5. 7 + 2. 2 10. 4 + 1. 1 z. 1 260 13. 4 + 4.6 6. 1 + z. 2 1 2 . 2 +1.1 2.2 265 14 . 6 + 4 . 9 7. 2 + 2. 5 !1.0 + 0 . 6 2. 0 270 15. 9+5 . 8 8. 8 + 3. 3 9 . 1 + 1. 7 1. 8 275 15. 4 + 5. 1 9 . 9 + 3. 2 7.3+0.6 1. ss 28 0 14 . 2 + 4. 8 9 . 6 + 3. 2 6 . 0 + 1. 1 1. 4s 285 11. 6+ ·!.0 8 . 4 + 2. 9 6 . 2 + 1. 7 1.37 290 10. 0 + 3. 5 7. 5 + 2. 8 4 . 4: + 2.. 9 1. 33 295 8. 1 + 2. 8 5. 9 + 2. 0 7 . 8 +1. 1 1. 3 7 3 00 4 . 0 + 1. 6 3. 2 + 1. 4 - 29. 4 + 9 . 4 1. zs 305 2 . l + o. s 1. 2 + 0. 5 -1 2 . 6 + 2 .3 1.7 240 11. 9 +1. 6 10. 8 + 1. 4 96. 9 + 5. 0 295 7 . 9 + o. 8 7. 6 + o. 8 16 . 6 + 6 . 0 300 3. 0 + o. 6 2 . 2 + o. 4 - 54 . 7 + 5. 2 94 t h e cry s tal w ith equally probable or ienta ti ons about the N -C axi s 3 6 a nd if the transitio n mom ent were a t an angle of -~ 4 5 ° with respec t to the c-axis for the orientation shown in F i gure 2 1, then the other orientation would have a moment at"' 135•. H ence the moments of the respective 1 - methylthymine molecules would be nearly right angles and the absorption on the red side of the band w oul d be almost isotrop ic. F rom the dichroic r a tio a nalysi s of s ingle 1-methylthymine cry s tal s , o n e of the two possible tran s ition .moment directions i s at an angle of 45° !_ 2 ° with respect to the .c-ax is. pointed out that the molecule has However , D r. Hoogsteen ha s s u ffi cie nt asymmetry to re move any ambiguity as to its atomic positions ; the c c~nsiderably shorter t han the c 6 - N bond . 1 5 -c 6 double bond is The refined s truc ture of the crystal, moreover , indicates that any disorder !:nust be less than 2 0 % of the structur e . If 20% i s the up_i)er li m it for the type of d i sorder mentioned a bove, then the smalle st dichroic ratio 4 : I. should be a bout Therefore, the x -ray cr ystallographic data rul es out t h e disorder h ypothesis • .A s ec ond hypothesi s is t o as::>ume t.~at 9 - methyladenine ha e shifted to the red compared to solution ( or even compared to the s in gle crystal spectr a ) and that the tran s ition m o ment for 9-rnethyladenine is at near ly right angl e s to the tran sition mon~ent direction for !-methyl thymine . The purine and. pyri m idine moieties are s uffi ci ently s epa rated 95 ( 6 A ) that one ·would expect only weak c oupling of t he respective transition m o ments . T -::• test the feas i bility of t.'!Us second hypo the s i s , the pol ari zed a bsorption in the ( 0 10) mus t be i nte rpreted. I n order to a n alyz e the polarized a b s o1· p ti.on data , the rela tion al'...ip be1.1.veen the p rincipal direction s and the directions of molec u lar absorption must be under s to od. The two different molecule s .in the Hoog steen d imer are v i ewed as t wo oscilla tor s which are perhaps w e akly ·coup l ed. Regardless of t h e co upling s trength , the crystal can be appro:;-ci.r11ated as t wo i ndepende n t oGcillators ( the e i gen oscillator s ) who a e d ir e c tions of vibrations (a t any one wa velength) are at a fixed a ngle x w i t. .'l-:1 re spect to each other. The oscillator s have r espective cros ·s - ~> ections a absorpti on . 1 and a 2 for photon Let "' be t.~e angle fr om p rinci pal directi on P 2 to the oscillator with cross - section a • . 2. The n p -·' 2 2 = a cos c: + a c os (ry - x ) 1 2 2 ' ·.- ' 1 =a s.tn 2 n· . + a 0 2 s 1n 2 ( !'Y - X ) 0 1 ( 1) 96 S ince a principal direction is an extremum for the projections of a 1 -ocr =0 or a cot 2-"V = +a 2 1 cos 2x ( 2) al a i n 2x R +cos = zx where R ::: a. /a 2 1 sin 2x If a is constant throughout an absorption band cha r a cteri s tic t o the two osc illators, t hat iu, O':er a region in which x t.~en either R is constant or )( is 90 •. i s constant , A constant r a tio for the oscillator cross - s ections over an a bsor p ti on b and wou ld determine a con::>tant ratio P 2 /P 1 • Thi s was not observed for th e Hoogsteen dimer. T h e angular position of the principal d irections , h mr.;ev er . was nearly constant over the firs t absorption banci. Figure ZZ i s a plot of th e angular position of t he pr.iacipal direction s , length . a~; r; a func tion of wave - The calculated standard deviation s of ' are also shown. The small variation of 8 indicates that the oscillators are almos t at r i ghtangles to one another. Any change i n c~ i s the sarn·e change for I!; • 2 may be solved s imul taneous ly fer two different wavelengths. final result i s : Equation The Figure 22. Variation of angul ar ori enta tion o f the absorptivity ellipsoids in the (010) of Hoogsteen dimer with wavelength. eo -J "' 98 [ (R 1 +R ) 2 +(R 2 - R 1) 2 cot 2 2~ !::1 ] cos-) 2x+ 2( R 2 + R 1)( 1 +R 2R 1) cos2x + 2 2 2 ( 1 + R R ) -(R - R ) cot 2ll G 1 2 2 1 whe r e R 1 and R are respective r a ti os of the o scillator cross - sections 2 at wavel engths A. =0 1 and f.. 2 and 2~ 8 = 2(a 1 - 0' ). 2 x is To the extent that near 90 •, the rati os of the pri n cipal axes ser ve as appr oximati ons to R 2. and R • 1 tion in cos The angle X can then be determine d. Zx The quadratic equa - will yi e l d a solution of four possible angl e s , two sup - pl e rne n ta ry pai rs . The equation was solv ed for the three wavelengths of 290 m~ , 275 m;.t. and 2 6 0 m~ . One s uppl em entary pair of angles vari ed c onsi derably for the three d iffe r ent solution s . X The other pa i r =ss• or 95. was conotant YJitrJ.n one degr ee . By elimi nating C( f rom equations 1 and 2 , the cross- r;;ection ratios over the absorp tion band can be solved in terms of the p r inci pal a xes and the angle x . The equa - tion for the solution i s: where B = For t..~e Hoo gs teen d i mer , th e first approximation of the r a tios was adequate for determi ni og x within the err ors of the p rincipal a xes. 99 'Nith R and x cle ter rnined in a self-con s i s t ent manner , a determi n ed from e q uation 2 . sin c e )~ • m ay n ow be T h ere a re two s et s of val ues for Cl frorrl the treatn>ent above. c anno t b e resolved frorn a pair of supplementary angle s . T h e a um of r:t a nd P for the wavelength s of interest locate s on e of the oscillators w i th r espect to a crystal axis. One of the s upplementary angle s , x., ~hould give a constant value fo r t l1 e angular position of t he oscilla tor. estimated er ror s are li s ted below . a th ree degree uncer tainty in a . < c 1\ a 2 The c a lc ulated val ues w i th the < c 1\ a The columns l abelled il is and are val ue s for the angle from the c - axis to the vibra tion direc tion o f the os cillators with respective ero se - s ection s a i\. (rcJf. L ) x A one degree unc ertain ty i n e Ci X =qso <c 1\ a 1 < cl\ a 2 a Y.,.es'" <cl\ a 1 1 a nd a • 2 <c A a 300 55+5 ° 168°+4 28+ 9 113+9 Z21 + 1t 166+ 9 81+9 295 7 . 8 + l. 1 18 + 4 26+ 6 11 1+6 162+ 4 170+6 85+ 6 290 4 . 4 + 2. 9 P+4 23+ 8 - 108+8 16 1+4 16 5+8 80+ 8 285 6.2+1.7 18+4 24 +7 109+7 162+4 168+7 83+7 Z80 6 . 0+ 1. 1 17+ 4 23+ 6 108+6 16 3+ 4 169 +6 84+6 275 7 .3+0 . 6 16+4 23+6 108+ 6 164+ 4 17 1+6 86+6 270 9 .1+1. 7 13+4 22+"1 107+7 167+4 17 6+7 91 +7 265 11. 0+0. 6 12+4 23+ 6 108 +6 168+,1 179+6 94+ 6 260 12 .2+1.1 11+4 23+6 108+ 6 169+4 181+ 6 96+ 6 2 55 10. 4 + 1. 1 12+4 22+ 6 107+6 168+4 178+6 9 3+6 2 100 The a ngle '-< = 9 5 • + 1• gives fixed angle s for the directions of tl:e two oscillators . T h e corre s ponding direction s are shown w ith broken lines in Figure 21; one line is over 1-methylthymine and the other is over 9 - methyladenine . From the dichroism studie s of 1-methylthymine crystals, the transition dipole moment a ssignment places the dipole vector at either 78 ° + z• or ·1 5 ° + z• with respect to the c-axis in the Boog s teen dimer . Both of these value s are i n gross disagreement with the oscillator directions deterrnined from the a s si gnm ent for '{ = 95•. F o r the assignmen t '/ = ss•, one of the hyp,')thetical o s cillators i s i n a g re em e n t with one of the two possi ble dipole mo m ent direction s of 1-methylthym i nc . FrotCJ 300 ;.-n~ to about 275 m~ the oscillator direction i s c on s tant t o within th e error ( 83 ° .:!:. '? 0 ) . B e low 295m~ the o scillator of lar ~er magnib.de correspo:1d s to one of the tran s ition :.r:o m e n t d ir ecti on s for 1-methylthy m i ne. of '.:he tw o o s cillator::; arc re v er s ed. At 3 00 m~ th e magni tude s For th is wa velength. the "phase" a ngle 8 was deter m ined from a th icker section ( t = 0. 4 9 1.1 ) sinc e the absorbanc es are more reliable than for the thin section . The reversal in the oscillator magnitudes at 300 rr!IJ. mean s that the toe abs orption of 9 - met..~yladenine is to the red of 1-n•ethylthymine. Below 2 7 5 m\.L the calculated di rec tion of the proposed oacillator c'hang es from ,....g6 • to -96°. But for 9 - m eth yladenine the dichroic ratio was no longer constant below 280 m~ and a s econd. weak band was evident. This second , weak b and i s perhaps polarized i n a direction 101 more o r le s s at right angle s to the maj or absorption band . The con- strllc ted , weak band had a molar absorptivity of about 1000 to 200 0 from 270 mi-L down to 255 m!J. . This a bsor pti vity val lle is about 15% of the molar absorptivity for the major, principal axis , whic h lies neare st the transition dipole moment direction for 1 - methylthymine. If the weak ban d wer e polarized at an angle of about ~20 • or 130• with respect to the c-axis , then the cha n ge in the principal d i rection from 2 80 mJ,J. to Z55 mi-L can be a ccounted for. Unforti.lnatel y , the full anal ys i s of th e principal directions i n terms of three oscillators is an indeterminate probl em . The i ndependent eviden ce of a weak absorption band for 9 - methyl a denine , however , is qualitatively consistent .with the directional cha ng e of the p rincipal axes. On the basis of the above argument a nd on t he b a s i s o f dichroism studi es of 1- methy lthymine , the transi ti. on d i pole m o m ent d irection for 1-methylthymine is assigned to the angle 16 1• !_ z•, where the angle i s defined by the T i noco c o nvention { 5 1 ) . The tranGition dipol e moment f or the str ong a bsorption band of 9 - methyladenine i s assigned to th e . angle 168• .:t_ 3•. T he c o rre spondi ng assignments are shown in F igure 21 with solid arrows over the respec tive molecules. On the basis of a two oscillator model , y 2.n d m i n ed in the self -consistent rnanner outlined above. a 1 R were deter- Vli e now calculate and a , the molar absorptivi ties of the two eigen oscillator 8 respon s 2 i ble fo r the absorption of the c r ystal. T h is calcula ti on is easy because 102 a 1 +a 2 = P 1 + P 2 and a 2 /a 1 = R. (Actually, a 1 and a 2 are almost e xactly equal to P F igure 2 3. 1 and P 2 , respectively.) T h e results are shown i n As discussed a bove , we believe that o s cillator a 2 is mai nly due to 1-methylthymine down to about 240 m).J. , although the weak perpendicular band of 9-methyladenine makes some c ontribution from 27 0 m).J. to 2 50 m!-L • . The maximum for 1-methylthy mine in the pure crystn.l , in the Hoogsteen diner, and i n the solution all occur at about 273 m).J. • We believe that oscillator a 2 is mainly due to 9-rnethyla.denine down to about 2.50 m!Jo , where the s trong second band of 1-methylthymi ne begins to contribute. The maximum for 9 -methyladeni ne i s about 277 m!J. in the single crystal and in the Hoogste en d i mer. In sol u tion 9 - methyladenine has a maxi mum at 261 m!J.. From the ass ignments of the tran s ition dipole m oments , the resonance force, electrostatic interaction between nearest nei ghbors was calculated. • 3. 8~ A. For 1-methylthymine the ce nter to center distance is The transition dipole momen t i s 3. 3 from solution . 2 Debyes as determi ned The calculated energy of interaction i s 31 6 e m -l, or a total of 632 em -1 for t h e number of molecules stacked above o ne another. The transition dipole moment, calculated from soh:tion , for 9 - methyladenine is 3. 9 4 Debye s . The center of gravity of the e lectrons for 9-methyladenine was c alcul a ted f rom Pullman ' s electron ic charges of adenine ( 23 ) and from an estirna te of 2 for the formal charge for the methyl gr o up in the 9 position. The c enter o£ g ravity for the n electron s Figure 23. 250 240 230 v(cm-' · r6 4 ) 4.00 4 .20 4.40 ~ 260 3 .80 .A(mf) 270' See t ext for detailed discussion. A 1-methylthymine spectrum down to""' 265 mj..L B 9-methyladenine spectrum down to"" 260 m j. L Below these wave l e ngths spectra are unresolv ed. Partially resolved molecular spectra from polarized abs orption in (010) of the Hoogstee n dimer. o(l·mole-'·cm-'·I0-4 ) 280 ...... 0 w 104 lie s essentially at the midpoint oi the c taken as the center of t."l-te molecule. nearest neighbors is 4 . 19 233 em -1 1 A. , or a total of 466 em 4 -c 5 bond. This point was The center to center distance of The calculated energy of interaction i s -1 for molecules above and below. These calculations show that the purine and pyrimidine moieties are w eak coupled to them selves by the S impson criterion ( 26 ), because the 1 sol u tion band widths are 3000 to 4000 em - • Thus the 2000 em - 1 red shift for the maximum of 9-methyladenine compared to solution cannot be explained by this s imple exciton calculation. A more detailed discussion of the various m olecular spectra in the several crystal systems and in solution is presented immediately below. I ntensities as well as spectral shapes are compared. I n tensities and Comparison of Molecular 3pectra The various crystal spectra , when compar e d to solution and to each other, have interesting features . Unfortunately , the intensi ties for the cry stal spectra have uncertainties varying from 10% to 40o/o. Thus any intensity differences between solution and the crystal which are outside of the error must be relatively large t o be observed. Tinoco has presented a di spersion theory to account for the loss of or gain in i ntensity for a pa rticular absorption band when m~lecules are conden sed from the free state i nto a polymer ( 27 ). 105 Hi s treatment is ba s ed on a first order perturbation theory and on the assumption that no excha nge for optical electrons takes p lace betwe.en t.l:l.e individual molecules. for intensity changes . Hence, only coulombic interactions account A comparison of the intens ity of the polymer to the intensity of the monomer i n o;olution is justified w ith i n the first order approximation if the solvent molecules are in a spheric a l array about the mono mer . T h us to first order • the intensity of the free molecule is the same as for the molecule in solu.tion . W hen a molecule is placed i n a non -spherical environ ment of othe1· species that have absorption bands near the band of the molecule of h1terest, then the dispersive interaction of the optical electron with bands of the other species will have a non-zero effe ct on the intensity for a bsorption of that optic al electron. The optical electron w ill also be perturbed by permanent dipoles of the grollnd and excited states of ne i ghboring species . But Tinoco has shown that for purine and pyrimidin e deriv~ atives the latter i nteraction is s mall compared to the f o rmer { lf FA is the area under band A for the polymer and f a 5 ). is the area under band a for the monomer. then the hypochr omism or h yperchromism is given by H = 1- F 2.015xl0- 3 A >...1a >... J'b /f =--=----a :;-: p. 2. i 1a /'A. • v i a;jb 1a 1a where v. · tau'b = ~L • ...1.1 • ••....1-L 'J-.. - 3(ij;··1:a.·lt tJ .. l(i1 J.b · ·R. lJ .. ·1a )Y 2 R .. lJ )J .... • IJ, 'b J 106 F o r correc t dimensions, \ i s i n m~ , R i s i n ang s troms , a n d th e transi tion dipole mome n t , i s in Debye s . T h e index b ~ , refers to all other absorptio n bands which are not the same a s a . Only the term for the dynamic e lectric field is in the above expression . F or H positive , there i s a decrease i n intensity for the polymer compared to solution , and for H negative there is a n increa se in intensity. I n h i s inte nsity analysis of va rious polynucleotide s Tinoco c alculate d the transition dipole moment d irectio n s for the first two ultraviolet bands of th e several nucleotides from mol ecular o r b i ta l theory . The magnitude s of the momen t s were c a lculated :rom s olution oscillator strengths. The second band s of the nucleotides were c o n - si dered "i:o make the major contr ib uti on s t o the hypochromi sm o f the fi r st absorption band i n DNA and i n other polym1cl eoti des . Vac uum ultraviolet bands of the nucleotides and of the phosphate - sugar g roups we r e con s ider ed negligible in thi s detailed calculation. · The crystal s studied i n this wor k are r ough appr oximations to n ucleotide polyme r s . pair s . The molecules a re stacked , hydrogen - bonded The separation between p airs in the same plane i s l a rger t han the vertical separation. The c a lculated vertical interaction of nearest neighbors is larg er than planar intera ctions by a factor of about two . For an approxima te an swer to H , it i s s11fficient to calculate the i nte r - action of the two molecules nearest the molecule i n excited state a . 107 These nearest neighbors are just above and below the mole c ule. Therefor e , ,... .... .... IL e P • e h - 2 IJ.b A2 _ A2 a b _. _. ..... ..... 3(e a • R )( eb • R ) - -R-2- - ] ... is the uni t vec tor for t h e res p ecti v e trans ition dipol e moment s. whe re e U nfortun a te l y , we h a ve no lmowledge of t h e absorption bands i n the vacuum ultrav i olet; only very q u a li tati ve i nCorma tion on the transitioa m or.1ent direction s for the second absorpti on bands of adenine and thy::ni ne was obtai ned i"l th i s research. The absor p tion of these bands, h o w ever , can be approxi m ated by pola-dzabili tie s ( 28 ). j pone n t of t!1e polar i zability of m olec ules 1 at frequenc y t' The com - along t h e principal; direction is 2 Ct jl = 2 / f:. L: b ".b J 1..1. J.bJ ,C.11 2 2 " jb - " The fra c tiona~ change i n i n te nsi ty may now be written H = 2 1 \ _; j:;li 0! j.R -3 {: COG " ij ( .S ee r eference ( 5 ) . ) R3 w h er e 0! j.l is t.~e polari zability o f the j along: d i rection o ... a a nd--R if 1..1. i ntensi t y is rnol ecule s at f requenc y .... 1 , which i s -parallel to 11· a • " a e. . i s t he angl e between lJ For nearest nei ghbor i nterac t i on the fra c tional change i n 108 ( 1) The polarizability • et I., can be approximately determined from the refractive index of a rna terial. By using the computed refractive indice s i n the absorption band region and the ClauGis-Mosotti expression, t..he fra ctional change i n inten s ity can be estimated. T h e refra ctive index at the absor ption maximum is due to the absorption of all other bands and the contribution from the band of interest is eliminated. For both 1-methylthymine and 9-methyladenine the computed refractive i ndices along the principal directions at the respective maxima have small differences. The se differences are reasonable s ince one would expect the polarizability to be approximately isotropic due to all other electrons in th e system. T he polarizabiliti es of 1-methylthy mine and 9 - methyladenine were calculated from the single crystal, refractive i ndex computation s i n Appendix A . I. 6 x 10 -23 The polarizabilities at the first absorption maximum are em 3 and 1. 9 x 10 derivatives , re s pectively. - 23 em 3 for the t hymine arid adenine These polarizabilities are due to all the optical electrons of each molecule with the e x ception of the first band. It should be emphasized that in the c alculations made here , the con tribution of the second band i s not c a lculated separately . The total con- tribution to the hypochromism ( or hyperchrornism) from all the bands below the first ultra violet ban d i s c a lculated by equation 1 • 109 Figure 2'~ i z a p l ot of the solution spectrum and the c ryatal spectrum for 1- rl ethylthymine whe r e both spectra a r e assun1ed to come from a fixed one dimensional oscillator. Tha t is , for the solution spe c- truro we plot three times th e rx: olar a bs orptivity from the isotropic absorption of 1-m ethylthy mine in wa t er a nd for the crystal ·,ve plot the sum of the in-plane absorptivities and as s ume the ab s o r p tion perpendicular to the molecular p lane i s neglig ible . We c a ll the l atter con- struc tion the "single crystal sum spectrum . " The intensi ty of the crystal spectrum has about a 25% error; near the relativel y flat maxi mum the error i s probably l a r ger d ue to pho todamage from the tran s m is s ion r.o easurements. The experimental hypochromism i s 0 . 2 5 !.. 0 7 . The hypochromism c a lculated from e q uation 1 above is 0 . 40. The spectrum for 1-n•ethylthymine , rath e r poorly resolved fr o m the polarization studies o f the Hoogsteen dimer , is shown i n F i gur e 24 . ( S ee the section above on the Hoogsteen dimer for d etail s oi the resolution. ) T he sh oulder at 255 m 1Jo i s p r obably due to a major contribution from the w e ak bc>.nd i n 9 - methyladenine . uncertainty is 40%. The i ntensity The i ntegrated absorption f or the solution spectrum i s about twi ce that £or 1-methylthymine i n the Hoo gsteen dim e r . experimental h ypochro m i s m i s thu s 0. 5 !. 0 . 2 . The The calculated hypo - chro m i sm from the d i s per s i on theory outlined above i s 0 . 36. A spectrum which we c a ll the s i ng le crystal sum spec trum of 9- m ethyladenine is shown in F igure 25 . It i s the s um of the molar 11 0 310 280 300 290 270 260 250 240 230 A(mj..t) A B c 2.40 1.6 0 Sol u ti on S i ngl e c r ystal H oogs t een d i mer _,Jr-,. )( )C / XC '~ 3 . 60 3 .80 I l( I 0 .80 0.40 3 . 20 F i g ure 24 . 3.40 4 .00 4 .20 Absorpti on spec t r a of 1 -methyl thy m i ne i n differ e nt envi r onmen t s. 4.40 ! l Oa 310 300 290 2 80 270 260 250 240 230 A(mjJ) A c a (I· mole-•· cm-1·10 - 4 ) 3.20 F igure 25. 3. 40 A B 3.60 3.80 4.00 v( c m- '·lo- 4 ) Solution Crystal Hoogs t een d i mer 4 .20 4.40 Absorpti o n s pectra of 9 -methyladenine in d i fferent e n vironments . 111 abeorptivitie s for the two principal directions in the plane of the m olecular layers (001). The solution spectrum i s also shown and was constructed similarly to the sol u tion spectrum for 1-methylthyrnine. ( See above discussion and Fig . 24.) The i sotropic spec trum of 9· methyladenine, however, probably has a component perpendic ular to the molecular plane. The component was assumed to be comparable to the ab s orptivity along t.~e b-axis of the Hoogsteen dimer and has been subtracted from the s olution spectrum shewn in Figure 25. The sin..gle crystal su.m spec t rum of 9-methyladenine i s shifted to the red by 2000 em -1 c ompared to sol ution. spectra are grossly different. Moreover , the shapes of the two The weak and strong components were not observed under the main band of the solution s pectrum . Crystal- lization seems to have shifted the strong compon ent to the red and perhaps the weak component to the blue. The intensity of the single crystal absorption ha s an uncertainty of about 15o/o . The integrated absorption under the first absorption band has a hypochromis m o f 0. 2 .:!:. 0. l com pared to s olu tion . A cal- culation of the hypochromism cannot be made beca use the crystal structure is not known. The resolved spectrum of 9 - methyladenine f ro m the H oogsteen dimer i s also shown in Figure 25. {'3 ee the section a bove on the Hoog - steen dimer for details .) The integrated absorption is d ra::;tically smaller than that for the single crystal (a facto r of a bout 0. 1 of the area 112 under the s ingle crystal band). to s olution i s 0. 7 5 +.10. The observed hypochromi s m compared The calculated hypochrom ism for adenine in the Hoogsteen dimer i s 0. 29 , from equation 1 above. The spectr um , moreover, i s red shifted on the toe absorp ti on side of the curve relative to the single crystal of 9 - methyladenine . Th e adenine derivative evidently s uffers a major perturbation when taken fl·om a s i ngle cry stal of i ts elf and placed in the Hoog ste en dimer . T he molecular pac k ing for 9-methyl~denine in the Hoogsteen di m er is ver y close. The nearest atom s , C separated by onl y 3. 28 6 A. 4 and C , of the molecule below, are 2 The electro s tatic interaction o f the formal char g es on these cores is large at this distance and can gro s sly chang e the wavefunction of the mol ecule . Permanent dipole intera ction s c an also change the elec tron density of the molecule . Regardle s s of the nature of the interaction , the perturbati on is s u fficiently s tron g t o m ake iden tification o £ the strong band u nce rta i n . The H oog s teen di m er a bsorption a ssigned to 9-methyla denine , however, i s very much larger ( a factor of about 20) than the weak component obs erve d in the single crystal. The maxi mum o f 9 - m ethy ladeni ne in the H oogs teen dimer a g rees w ith the maximum for t.h e stron g compone n t of the s ing le c ry s tal. It seems unlikely that th e perturbation on 9 - methyladeni ne w ould shift the weak c 01npon.ent about 3000 em i ntensity by a factor of 20. -1 t o the red a nd al s o increase th e lf this were the c ase, t.h en the strong com pon ent, observed in the singl e crystal , w ould ha ve to be either 113 shifted to the blue about 10,000 em -1 or lose its intensity by a factor of about 50. With reservation then , the tra n sition dipole n1oment direction, calculated from the polarization analysis of the Hoogsteen dimer, is regarded as the same for the strong band observed in the single crystal. Furthermore , the strong component of the single crystal is considered to be the major contribution to the first absorption band observed iri solution. The polarization for the major absorption component in adenine, therefore , is alon g the short axis of the molecule (1 68° in the Tinoco convention). This result is inc on sis tent with Mason's assignment ( 18) based on substituent effects on purine. 6 - A minopurine (adenine ) ill: solution r.as a main , first absorption band peaked at 260 m~-~o with a small shoulder at 2 67 mJJ.. essentially identical to adenine . 283 m!J. The spectrum of purine is 8-Aminopurine has a maximum at and a second maximum at 241 m~ with the former band ~ times more intense. 2 - Atninopurine has a first maximurn at 305 m !J. , a second at 236 m!J. , and both bands have comparable intensity. Ma::;on argues that the amino group in the 8 position adds further con jugation to t..he purine ring and shifts the rna i n component of the purine absorption band to the red. Hence , the major component is long-axis polarized. The amino group in the 2 position, which is 30° to the long axi s , shifts t.""le spectrum further to the red and decreases the i ntensity. ca ses the minor component i s peaked around 240 m JJ. . For both The main 114 assumption here is that the red-shifted band, with intensities comparable to the adenine band, is the same as the major absorption band for adenine. Substitution of the amino groups, which have two ., electrons, onto the purine ring cau ses large perturbations as compared to crystallization effects. It is hard to know with certainty which purine component is being enhanced by the substitution. The assignment of the polarization can be resolved when t he crystal structure of 9-methyladenine is determined. It is intere sting to note t.hat Rhodes could account for the hypochromicity of polyadenine i£ he assumed the fir st absorption band for adenine to be short-ax is polarized ( 24 ). Tinoco's calculation for the hypchromism of poly AT is closer to the experimental value if short-axis polarization is a s s~m ed ( 5 ). The last t wo points, however, are not par ticularly weighty, because the dispersion theory for polynucleotides is highly approximate. From molecular orbital theory, Tinoco has calculated the transition dipole moment directions for the near ultraviolet absorption bands of the several nucleotides ( 5 ). For adenine the first abs o r p tion band consists of two components, one polarized at sz• a nd the other at 147 •. The assignment from our polarization experiments is 168• for the ma jor component. the sz• direction. i s 3 •. This is 21• from the 147 • direction and 64• from Tinoco's calculated transition direction for thymine The polarization experiments indicate that the direction is 16 1°, which is a d iscrepancy of 22•. 115 The absorption perpendicular to the {010) for the Hoogsteen dimer is probably due ton - n * transitions in the purine moiety . the polarization and rather low in.tensitie5 (100 to 1000 I.. mole of the spectra suggest this assignment. 1 Both em -l) It i:J intere s ting that the ab - sorption per pendicular to the {010) i s about 1000 cr.o -l to the blue of the in-plane adenine absorption resolved from {010) polarization studies of the Hoogst een d i mer. For a variety of hetcrornolecules i t has been observed that the longest wavelength transition ( s i nglet-singlet) is an n - ..-; * transition ( 13 ). '~Vh en the weak, out of plane absorption f ro m the Hoogsteen dimer is compared to 9 - methyladenine in s olution , the former is about 1000 e m -1 to the red; when it is compared to the single crystal sum spectrum f or 9 - methyladenine , it is near the edge of the i n - plane absorp tion. Figure 26 is a plot of the £our spectra of 9 - m e thyl.c1.denine in different environment s . Pyrimidine in cyclohexane has an n - rr ( 19 ). * transition at 300 The transition is well resolved f ro m the fir st r - ..,. m~J. * transition with a maximum at 245 n11Jo • The addition of an i mida zole ring to the pyrimidine red shifts the H "' * t ransition to 260 lTIIJ. , but the n - n * - seems to r emain peaked at 295-300 mjJo • The only purine which can be dissolved in cyclohexane i s 9-me thylpurine ; the n - n * transition appears as a shoulder , but i s distinctly evident at 300m~ ( 18 ). No n - n 4t transitions of adenine or its deri vative s have been observed in s olution because t he con-1p ounds are only sol uble in water . The n - n * 11 6 310 300 290 280 270 260 250 230 A{m.fl) 4 .00 3.00 log a A B C D 200 3.20 Figure 26. 3.40 3 .60 3.80 V(cm- 1·ro-.q) Hoogsteen dimer (0 10) Single crystal (001} S olution Hoogsteen dim er ( II b-axis . 4 . 00 4 .20 4.40 9 -M ethylade nine absorption spectra in several systems . 117 transition energy is relatively insensitive to substituent effects, but it~ strongly blue shifted in the presence of hydrogen bonding solvents ( 16 ). The transition is relatively localized o n the nitrogen and may be thought of as an .:;. to £. transition , where absorption by the optical e l ectron involves a transition f rom an sp 2p orbi tal on the nitrogen. 2 orbital of the nitrogen to a The success of the " independent system 11 view has been demonstrated by Robinson in his diazine studies ( 7 ). I n the absence of a hydrogen bonding solvent, then , one would expect the lowest n- -:-.: * transition energy o£ adenine to be similar to purine , ju st as pyrimidine and 9 - met hylpuri ne have their lowest n- n near the same energy . The ( 0 , 0) band for the allowed n - n * transition of cry sta.lline pyrazine is - 200 em - l ( 7 ). * transitions to the red of the vapour spectrum Crystallization of the diazine does not s trongly shift the n - rr transition , but it does s pread the band out. not expect a large energy shift of then - n * On these grounds one would * transition for adenine in the crystalline state. Therefore , perpendicular absorption is viewed as a normal n - n * t-ransition for adeni ne and has s hifted about 1000 e m -1 to t..,.e red in going from water into t.'-le cry s talline environment of t.~e Hoogsteen climer ( similar to a hydrocarbon solvent). The grossly red - shifted n - n • transition for adenine i n the Hoogsteen d imer i s the feature whi ch is difficult to under s tand. 118 The continually ri s ing absorption perpendicular to the molecula r planes is thought to be due to overlap of other n- rr The hydrogen bonded N 7 provides a site for the tran sition which is e x pected to be to the blue of the other n- 1'1 from n- n * transitions. * tran sitions . Contribution s * transition of the carbonyls in 1-methylthymine should be relatively small due to the pure p o n the oxygens. character of the non-bonding orbitals As mentioned earlier, the adenines are packed closely with a neare st atom distance of 3. 28 6 I. for two c arbons . ( '3 ee F i g . 2 1.) The calcu lated overlap, usin g Slater atom ic orbitals, is • 03. It may be that the absorption near 230 m!J. i s a char g e transfer type between the rings, with some degree of delocalization o£ the excited s tate provided by the rest of the rr ... electron system. An absorption spectrum perpendicular to the (001) oi a 9-methyladenine, single crystal would shed some light on this conjecture. The spacing of molecular layer s is 3. 6 A • It was pointed o ut i n the crystal preparation section , h owever, that the {010} was too poorly developed to mount the crystal for slicing in this direction. 119 APPENDIX A Optical Dispersion Theor~. The Drude theory for optical dispersion is based on the assumption that an optical electron is bound by Hooke ' s law forces and subject to a damping force proportional to the displacer.nent velocity ( 6 ). Under the influence of an external electric field the equation of motion for the electron is =eX- where X r a 2 9 re 2 is the component of the external electric field. 4n e and "1 rr e 2 is the restoring force, is the damping force. and G are positive constants. Under stationary state conditions the displacem ent variable may be expressed aa a periodic function of time. The solution to the equation of motion is then e~ where T r e a= 4- T = 4n1 a X = T I 2n i s the angular period of the externa l electric field, and b = me 2 4 rr e 12 0 'ib:! current i n the x - direction i s .. j·~ ·~ 1 411 - b ~. ( .x 1 ()t + >;: ::: !-'' -l.. at -8t ., (l + J dx J''' :::: -1"if ·~ I"~ j 1 9 . . • \1 J - i/ 'f a. J - ) b ./ ..r 2 J F ror.•-, Max well 1 s eq'..lC'l tion s we identify P; N 1 + i/'T a1 .J 6 1 :> ' )2 • n 2 ( 1 ..... :t' :r.. :c: i..:i J-r ~ J it> t:;.<C cornplcx diclec t:ric c on.::; tnnt, 11 i ::> the reiractivc it;d ,~x a nd lt i s th e nbco r p tivity per ~ in th e m ediu.m . For the general linear diff:.:lren tial r~qua. tion , ' N' \ L C ( ~ )j j dt X =e . -1 l -· iw t c . ( i!O )' ; J _! j c:o i u a tiolution. :: J .\i(ttl ) - i n ,•"\'.. (w ) r • .< Then ., J.) I.O ) ::: " ... 1T 0.) r e;· H (y ) yciy "',;· ' 2 ... <U aad L c. lw N (u; ) : : : 1T 17 ) • B :.1t e .:N U,. .(tO) ::: l:. .......;;J_ _ ___ ____ !"l J'' 1 + t' / ,~, e , - T1:.: I •r 2 .i is the solu tion to Drude 1 s equation . J ro (' I (I J ( y) ciy w 2 - y 2 121 .l CI = n • n (1-ik ) 2 7 - ( nl<:.) ~ 2 =l+ Q('.t> )ml+J(·,: ) • iH ( w) = 1 + J ( :>' ) 2n ( nk) ::: B ( tl' ) 00 r- J ('r ) :s: 2 l .: 1T 00 0 r· H(y)ydy ,J 2 2 y - (ll 0 H (y )ydy ---~ 2 2. iB appr oximated with the meaaur ed abs.orp- tio n band, a dispersi on term for the s econd absorption band near 2 0 00 J. and a constant term. 2n( y )nk{ y)dy z y - lll w wher e 1 to 1.1) a bsorption band. 2 covers the angular frequency o ver the n'leasured In terms of '" a b sorptivity ter m in em -1 with n (l.. ) =n 0 + wher e i s a constant, 0 n ~ f and 0 a 2. the v acuum wavelength , and a {A), an , the expres::;i.on rearranges to is t."'-le maximum for the sec ond ab s:.l r p tion band , is the o scillator s trength , N i s the density o £ optical electrons . The proc edure for calculation i s a ::; iollow 6l : 1. r).2 n ()1.)1 n.(2 \ ) d2J.. 0 Compu te A ( 589 mil ) r: ( 0 . 226 102) ( 589) -;> A. w her e \ l t o >.. ( 589 ) 1 - )._ is ov er the m e <-. ;;;ured a b f~ orpti. on band and n {>. ) 0 1 2 ha $ been fi r :>t a ppr oximated h ·cm the os cillator strengths o£ t.~e fir s t two ..:d tr a v-iolet absorpti o n b and :> in sol u t ion . 2. · ., Then \/ N'- ( 58":J) rnea::>\.lr ed - A = n ( \ ) =n I1 o ~2 £ e n l\ oil + _ _ _r_, - - - n1c ~ '' (l • \2 . / ( ~''' B9 ) z) s ! . With n (>..) , refr<lc th•e i ndic e s for a ll w av elengths o f i nterest 0 11 a re calc ul;,_ ted ; ( -1 n ( \ •) 0 v "1 .. 2 ... whe re c:. ( 1.) 3. ,r.'-, n ('"· '\'lla (' ')a,_"- . .,1., log ( _, ' 1 ) + ! o 2. ., ~ ( \) a (\ ) a(~') etA. ' + _n o__ 11 11 2, + 1 2\ - \ 2 e ;:.,~. - }, A "· + l ' 1\ . ' •" - " = .-:~ ( i•. - 1) = c..( \ + 1) for .. iJ~i mv,. G.nd a (\) c 0 fo r ;.., > h. 2 • Reflection coeffiden.t,;; for w a vel ength;:; of i n t e re Bt a r e cornp'-'.tecl: R (\ ) = ( n( i..) - J.t +_[ ~~-~ ~q _1 2 (!·,(A.) + 1)2+ ,- .\ ~t(\)_ ; 2. L ··i TT _, 123 The calculation 5 were done on an l B I\,1 ·; 0 9 0 c omputer with a F c rtran cod e . Ten iterati;.)ns were more t han ~dequate to gi ve a c o nai stcnt ::. et of refr a ctive indic e o t o t hree decimal place s . The i n put data and c alculated refracti v e in.dice s for t ho several crystals a.re tabulated b e l ow . T he raw ab:;;orbance data is omitted . b - A xis Disper;;;ion i n { 102) of 1 - Methylthyrnine f2 07 mp. ~:: O. 17 ny ( 589) Cycle = 1. 660 N ur.nbel~ \ ( miJ.) N R 240 l . 7 15 1 . i' 2 1 • 070 1. 720 1. 710 1. 7 01 1. 700 1. 7 03 1.71 5 . 0 70 24 5 25 0 255 .2.60 265 2 70 275 280 285 290 295 300 305 310 320 3!~ 0 l . 729 1 . ? 3J 1. 748 1 . 'i'·l9 l. 7 4 1 l. 730 1. 716 l. 70 5 1. un. 3 60 30 0 1. 684 400 l . 07 •1 l. 678 • 0'1 0 . 0 6<) • 068 • 0 6"7 . 0 68 • 070 • 07Z • 0 13 • 0? ·i . 0 74 • 0?3 • 0 '/1 • 0 69 7 p·Axis Dis per eion i n ( 102) o f l•Methy1thymine 1207 1 : . 01 5 6 f270 =• 11 6 "1(~ ) :r: 1. 700 + • 0036 2 n ( 589) :z. 1 _( 207) /"J... 2 Cycle Nu:r:nb,~:r R " ( rrw.) N 235 1.360 1. 31 9 1. 29 9 1.3 01 lo 244 1. 250 1. 3 06 1. 503 1.728 1. 9 12 2. 042 • 025 . 020 • 0 19 290 295 300 305 310 315 320 2. 169 2. 257 • 144: . 153 2 .330 2. 281 z. 176 2 . 085 . 162 2. 007 • 11 2. 340 1. 913 1. 864 1. 83 {, 1. 8 l"i' 2<!0 z ,;~: s 250 255 260 265 27 0 275 zso 2 85 360 3 80 400 • 020 • 016 • 023 0 0~4 . 063 . 09 1 • 113 . 128 • 153 • 137 • 1Z4 ? = 1. '762 125 b - A xis Disper s i on i n ( 00 1) of 9 ·Methy la d enine f 2. 0 7 = o. 16 £270 = • 1 5 5 • 0366 n ( 589 ) z Cycle Number 7 ;., (ml") N R 23 0 235 240 245 2 50 255 26 0 265 270 275 280 285 290 295 1. 640 1. 562 1. 500 ).. 454 1. 428 1. 433 1. 502 ! . 597 l. 775 2.. 059 2. 306 305 310 3 20 340 2 . 563 2 . 6 31 2. 48 4 2. 3 27 2. 220 2.. 170 z. 096 2. 040 360 1. 977 380 LJ:OO 1. 954 1. 9 3 6 300 • 059 • 049 041 . 037 036 • 04 0 • 054 • 0 7 1) 0 0 098 . 139 • 169 0 • 200 203 . 18.?. 0 159 • 144 0 . 136 = l . 880 1Z6 a • Axis Dispersion in ( 001 ) of 9 - Methyladcnlne !207 =Oo 16 f270 =o. 031 n (). ) = lo 6 2.8 + 1 \ ( rr~ 230 235 240 245 2.50 2.55 260 265 270 275 280 285 290 295 300 305 310 320 340 360 400 • 0366 2 1 - ( 207 ) ,.,., l n ( 589) c: lo 783 y Cycle N Number 7 R 1. "/41 1. 796 1. 822 1. 8 18 !.. 794 1. 780 • 082 086 o085 • 081 . 079 1. 799 1. 8 2 7 1. 854 1o909 1. 945 1.984 1.989 l . 1H9 1. 919 1. 689 1. 875 1.856 1. 833 1. 820 1. 805 • 075 0 . 082 087 • 091 0 • 099 . 104: • 109 110 0 • 104: • 099 127 "M ean" DLper :;i on in ( 01 0 ) of H oog s t een f'imer izoo = o. 5 fZ7 0 = 0 . 2. • 0 5 39 1 - ( l OO) z , 2 .v1-;:--u y z = 1. 7 6 4 I·\ .,. ( mi~ ) N p 230 235 L 71~ l. 7 3 0 1. 7 35 !. 727 A. 7 7. 3 l. 72 3 1. '/23 1. ·u.7 · 1. -ISZ 1. ~-so-J i . <;61 l. ~ 0 8 i. 94 l l . '-18-1 1. 987 l. '}(,1 1 . ·H3 1 . 908 1. 886 1. 839 l. 8 13 . 0 69 ~>1: 0 ~ ~15 ~~ !:.1 0 ~:, 5 l t:.o ~(· 5 ~i' O ~75 t!&O ~l33 2)0 ,::~?5 300 3 \.l:.i 3 10 31S 3 20 3 ·-W 360 3 80 4:00 1. 80 4 1. 7 95 ·" 0 72 • 073 • 07 2 • o·i 1 • C7 l 0 0 071 0 07 2 • 0 '{ 6 • 085 09 3 0 • 099 • 103 • 109 • 109 . l 0 :) • 101 098 0 • (.9 -1 128 APP ENDI X B Least s qua re s analysis of polarized absorption . O ne m a y think of cry s tal ab s orpti on as involving a proj e ction of the electr i c vector frc m the i ncident light onto a set of or thogonal axes ( princi p a l axes ) . the a mplitudes of these ele ctric vector c::>mponents a re then attenuated i n the usual Beer's law form along the princi pal di recti o ns as the ray pa s.:::es t h rough the cry3tal ( 21 ). If r.f' i s the angle between a crystal face and. the de ctric vector o f the incident light, and FACE e i s t h e angle from the same cr ystal fa ce to a pri ncipal axi s , then the transm ission 2 1/ 1 0 w here .A.l. and A direction s P 2 1 = cos (<:' - e ) 10 - A2 + sin 2 ( ~: - e )10 -A 1 are the ab.s o rbance a along th e c o rre s ponding princi pal and P 1 • idth rearrangements the expres s io n can be linea r i zed to give T(r:- ) = 1!1 w h.ere T 2 0 = = ~ (T 2 - T 1 ) c os ~ 9 c o s 2~ + ~ ( T 2 -T 1 ) s i n 26 sin2c;' + ~ ( T2 +T1 ) - A., '" an d 10 -A T 1 = 10 Thus the meas ,.1red transmi s sion l ag a fan c tion o f the !JOlari zed angle cp i s 129 TL ) = JJ e + v Tl + & where t: = co :3 2 c: and n = s i n z~~ '-\ = ·~l tan -1 y I S 0 co s 2~ + '3 co s 28 a nd Tl = 8 c os 28 co s 2~ - ;:\ For a lea s t squares analysis the linear for m for T((~' ) i s con ven ient. s and Tt are e r rorless and the erro r i n T i s propo r tiona l to T. The par ameters 8 . y, and 6 a r e determined fr om the least s q u a res c onditi on, B£ ar a£ vf3 = Dv = 1M = o where f( 3 ,y, o ) =fw. ( T. - B ~ i -v il. - o ) and w 1 i = 1/ T. 1 2 1 L: ~ . 2/ T. 2 1 Hence , Det = 2 1 1 L: ~ i 1l /T/ L' F.: .I T. 1 2 i:~ i 11 /Ti 2 2 l.:: 11 . /T. 1 1 ;: Tt ./ T. 1 1 2 2 ~ s/Ti 2 'fi) , I T_ l 1 1 2 L: 1/ T. 1 1 and s = ~ ~ 1.11.1 1T.1 2 r.: s./T. ~ 11. 2 /T.z ·- Tt . / T. 1 1 L: 11./T. 1 y = 2 :n . IT. 2 L: T. 'I! ./T. Z t; 1 1 F s 1/ T/ 1 1 1 1 L: T./ T. 1 2 1 2 2 Y:,f{. ./T. 1 1 2 2 1 r 1/T.1 Z T. t: .IT. 1 1 1 1 L: ~ i 2 /T/' 1 1 2 2 1 r: n . /T . 2 1 1 'l: 1/T. 1 2 130 2:!; ./ T . 1 6 2 l: E; i ll i/ Ti 1 2 = L: 11. / T. 1 2 L. T. ~ ./T. 1 2 1 2 ~ T 1.il./ T. 1 1 1 7 ~ L: T\./T.1 1 2 .:. T / T i 1 2 From the general theory o f stati s t ica l ana ly s i s the i nverse ma tr i x e lements from the m a trix whoae determi na nt i s Det c an b e used to c alculate the errors of the parameters a • "V • 0 0 '(lith the s tandard deviation s of the parameters , the standard devi a tions of e , A 1 , and A 2 •Ner e c omputed. e = ,14 -1 , H I i,j !-=-I i s Det . 1, 1 h = ?r tan ? _ ~( ~ ) ... crA .: . c6 max · 2 + 2 cr A +.c- 7-Q ah uh ,. u-y dp are the i n ver se ma t r i x elem en t s of the matri x whos e de t ermi n a nt A nd g -1 I--I 2 C1 The algebraic expre ssions are: .. } -y I f3 ~ - 1 + (~) ,.!:!., vy 2. ? -1 1--1 Ji_, 1, 1 2, 2 +( $! ) ~ 1--1-1 + 2- ( £a )( .£a) .· H " - 1 85 IH P '6 o ~ 3, 3 ° 3 ) ~ - 1 ( ~ )( 3 ) ~ - 1 l ( )2 2 ( ~)( aS ao A 1, 3 + 2 o-v De ~ 2, 31 2 . 303 crA = -log 10 ( 6 - VS 2 + -y 2 2 ) 2 = above for cr A except u s e m in --max w h ere f = - l og 10 (t + f Vs2 + 2 ) -y y 1. 2 131 2 {er ror) . 2 crA = L {n - 3) 1 from t h e c u rve fitt e d to A ll computations we re carried out w i th an I B M 7 0 90 . The program was w ritten i n Fortran . '.f.l ith the appropriate reflection corr e ction , ass um ed to be i so tropic, A ( r;: ) ·wa s converted to molar abs o rptivi ty units . The computed curve s are s hown below on polar coordinate s with the experirn ental poi nts. The ac plane wi th the refractive indice s N on a pola r coordinate graph for conveni ence. z and N y is shown 132 a(l·mole -I . em -I. 104 ) 13 3 1.5 0 13 4 O(l·mole- 1 · cm- 1·tcf 4 } 1.50 135 1.50 1.00 136 a( l·mole-r. cm-r.,o- 4 ) 1.50 137 138 a( /·mole-'. em -t. 10- 4 ) 13 9 a(l·mole- 1·cm- 1·I0- 4 ) 1.50 14 0 a( l·mole- 1• cm- 1·10-4 ) 1.50 0 0 A=260mf 141 1.00 142 a(l·mole- 1· cm- 1·16 4 ) 1.50 1.00 A= 250 m)-l 143 a(l·mole 1· cm- 1·10-4) 1.50 I I 144 a(l·mole-•. em-' ·to- 4 ) 1.50 14 5 a(l ·mole-l. cm-1 · to-4) 1.50 / 146 1.50 J 147 The (010) of the Hoogsteen dimer. The c-axis is parallel to the 0° radial line. N and N are the refractive index directions at st39 m~ • z 148 Ai:.>?E N D IX C Theor y o f A b so rpti o n f or P l a n e F' o la ri z ed Li g ht i n a Soli d An gle b y an . A :l i sotr opi c A b sorbi n~ P l a ne . A b so rbing pla n e i s xz . P l a ne of p o lariza tion i s yil!. I t i s ass>.1med t h at t h e e cc en tricity of t h e p o l a r i z e d ligh t i s :mi t y a n d tha t th e solid a ngl e is uniformly filled w i th ligh t. C ompo nen t~ - of w ave vect()l" I<.:: y ( s i n'p s in9, c osq.· s i n S , cosa) . - C o m p onen t s of electric fi e ld E : (0 , ry • 6 ). -= By o rthog onality , E • K s c o s e = o. or ::t cos 8 sin 8 + 2 + B 2 = 1. B y nor maliza ti o n : 2 0 r,· 1 2 1 + co s q; t an 2 and ~ The tran rnnis s i on o b se r ved i s 13 2. = c os 2 ~: tan 2 ~ e 1 +co ., cp tan 2 a - e yt/co s80' I/I 0 = 2 • Gzt/cosea e f\. e r 2 dru w e y is the absorptivity in they direction . e z is the absorptivity i n the z direction. t is the thic k ne ss of the absorbi ng material. III 0 = 1 IT\ .lo - .Ay( - . e - 2 1 2 2 \ cos e l+cos cptan 0' l i1 lQ r z, -i O 1 - Az( - · e . cos8 co s c:• tan 2 2 A l+cos q: tan Z. es1n . 8dSdcy ~;inA dA dt~ ·q i s the angle between the c entr al pole (z - axis ) to the envelope of the solid angle. . a 1 va 1Je ~q extren1e 1. s ...., - 10 - l . F o r rnea s ure n1ents o f practtc 2. to a good approximation tan 8 = EJ 2 , N e need therefore to eval-..ate sin 9 = A and CO S C\ = 1. ·Th u s 150 2 2 - Ay - Az 13 cos q, e e 9d9 dq: III 0 = - Ay = 1l Zrr f' ' r· :b .Jo e -A 2 2 e cos q; z e I 9d9dq:· Integratin g over e • 1/1 0 • h. e = ~I ! 2 C OS 2. (~' ' - Ay 1 - e z 2 2n 11 A CO :> z 2 B ut 2 2 n +l (A 11 co s c: ) ro = \ 1 - e ( -l)n ·- z {n+ l)! n=O . - Ay Zn .. I /I 0 = e2.-r y w here - y =A 00 ) 2 Jo n =O ( -l)n l ...' ~yc os cp ~ n+l {n+ 1)! c os 2 d r~· ~'" ~ ' !12 z or - Ay III 0 = e 2"1"T 00 J.· (- l ) n n =O 2 (-y cos T) ( n + l)~ n 151 N e note ·that , n-1 cos Zn cp = 2n - l [ ) 1 ·- 2 Zn C c os Z( n - r ) (f' + ~. ZnC r n -, I J r=O I ntegrating term by term , .,rcos Zn n -1 ,- 1 q: d q.· = Zn -1 2 ZnC sin 2(n - r ) ~n + ~ 2n r -· 2( n - r ) r=O ) !_ Thi s gi ves a s i mple , finite polynomial i n s i n 2( n - r}ct•. c n q: + constantj M oreover w e n ote that c n -1 ?_, r =O converges . 2n r z( n - r ) ( ) .1,. s in 2 n -r '·P + <: Zn C n rr Thus w e may i nterchange the sumrna tion and integration opera tions above . :. III - Ay -z,. e 0 = 00 ) ·-- (-l)nyn ( n+ 1) ! . -;:;:-r 1 z n =O c n-1 2n r 2 (n-r) > r =O The sine terms vanish . so 1/I 0 =e - Ay 00 ) n =O n (-1} y (n+ 1)! n c Zn n 2 n 21i s i n 2( n - r )cp + ~ c Zn n q' I0 152 But = ~<-;/;;..n~}:...;.!_ _ 2nC n ( 2n- n )! n ! 153 REFERENCES 1. A . Bree and T. Thirunamachanbran , Mol. P hys., 5 , 397 - 405 ( 1962) . 2. C hargaf£ and Davidson, "The N u cleic A cid s . " A cademic P res s , New York , 1955, Vol. I { spectra in fly leaf). _, 3. D . P . Craig and 3 . H. Walmsley , Mol. Phys ., ..!.• 113 - 12 ~ (1961). ·'1 . A • .3 . Davydov , "Theory of Molecular Exciton s . " ( Translated from fir s t Rll s sian edition by M . K asha and Max Oppen hei mer , Jr.) M cGraw - Hill Book Compa ny, I nc. , 1962. See Chapter III in par t ic alar. 5. H . DeVoe and I. Tinoco , Jr., J . Mol. B i ol. , 4 , 5 00 - 517 , 5 1 8 527 ( 19 6 2). 5' . S ee p. 504 i n abo ve reference. 6. P . Drude , "The Theory of Optics . " Dover Publications , Inc., New Yo r k , 195 9 , pp . 382-387 . 7. M . A . El Sayed and G . W . Robin s on , Mol. :!:Jhys. , i • 27 3-286 {1 96 1). 8. V. Gilpin and VJ' . McC ron e , ~· Chem ., 2 2 , 3 68 (1 950) . 9. C. H i ntze , H andbuch der M inera log ie. Z w eite Abtheilung V e rla g v on Veit llnd Comp., Lei p z i g , 19 15 , pp. 1 277 -1 218 . 10 . K . Hoogsteen , Acta Cryst., in pre ss. 11. I~ . Hoogs teen , A cta Cry s t. , 12 , 82 2 - 82.3 {1 95 9). 12 . K . Hoogs.teen , private c ommunica tion. 13. M . Kasha, "The Nature and Significanc e of n-·• * Transitions. " P re s ented at the Sy mposium on Ligh t and Life, J ohns Hopk i ns University. Also see , J. Sidman , C he rn. Rev., 58, 6 89-713 (1 958). 14·. L. E. Lyon s , J. C hem . Phys., 20, 181 4 (1 952). 15. D . S . M cClure , Canad. J. Chern.,~· 59 - 7 1 (1958) . 16 . See , e.g., H . M cC onnell, J. Ch e rn. P h x;s., ~· 70 0-704 (1 952). 17. J. R. MacDonald and M . K . Brachma n, R ev . Mod . Phys ., 28 , 393- 4 22 ( 1956 ). 18. S . F. M a son , J. C hern . Soc., 2071-2081 (1 95 4). 19 . S . F. Mason, J. Chern . S oc., 124 0-1 2·4 6 (1 959). 20. G. S . P arr y, A cta C rx:st., 2.• 313-320 {1 95 4). 21. Cf. D. L. Peter s on and W . T. S im pson , J. A m . Chern. Soc., . 21· 23 7 5 -23 82 ( 1957 ). 22. K . :3 . P itz er-, '\.2uantum C"he m i s t ry , " P rentice-Ha ll, In c., .E nglewood Cliff a , N. J., 1953, p . 23. \, 24. 25 . 2~6 . A . Pullman and B. P ullma n , Bull. 3 oc. Chi m ., 766 - ~ 72 ( 195 8). 'N . Rhodes , J . P_m . Chern. S oc., 22• 3 6 0 9 -3 6 17 (1 96 1). W. E . S eeds , P r ogr . Biophy s . & Biophy s . Chern ., 3, 27 - 4 6 I (1953). 26 . W . T . S i mpson and D . L : Peter son , J. Chem . P hz: s . , 2 6 , 588-593 ( 1957). 155 27. I. Tinoco, J r., J. Chern. Phy s . , 2l• 1332 -133 8 {1960). and £or erratun1 s e e J. C hem . ? h y s ., 2.!• 1067 ( 1961 ). 28 . Tinoco , H alpern and S impson ( 1961). P olype p tide S z:mposium, Madison , Wis ., i n the p r ess . 29 . F . J. Wall~·, J . Am . Chern . Soc ., 11:• 4 7 69 - 47 73 (19 5 0). 30. D . L . N ulff and G . Fraenkel, B i ochim. B i ophys . Acta , 51 33 2 - 339 ( 196 1). 31. D. L . N ~lff , private communica tion . 156 PROPOSITION I The cry s tal s tructure for 9- methyladenine has not been deter· mined. The unit cell dimensions and space grDnp of the anhydrous, monoclinic crystal have been reported (1). (The u nit cell dim-e nsions are listed at t~1 e end of this proposition.) The crystal ha s a pronounced cleavage along the (001); this plane ia believed to be the plane of the molecular layers ( 2). The angular orientation for 9-methyladenine in the crystal is proposed below. My reaso r1s for presenting t h is proposal are two-fold. I hope to entice someone to d o the cry stal structure of 9-methyladenine. T h e crystal structure determination would provide a test for the atomic positions given 9-methyladenine in the hydrogen bonded complex of 1methylthymine and 9 - methyladenine. The s truc ture determination may, furthermore , provide some clue as to the relative stability of the hydrogen bonded complex _of 1-methylthymine and 9-methyladenine compared to th e single crystals of e a ch, re spective compound. The structure w ill al so , hopefully, s ettle the que s tion as to the transition moment direction for the s trong component of the first ultraviolet a bsorption band in adenine. ~..1y s econd rea s on i s to s how that our tran s ition moment direc tion assigned to 9-methyladenine can be Llsed to con s truct a reasonable ori entation of the 9 - n•ethy lade ninc m o lec ales in the unit cell. 157 The dichroic ratio for absorption i n the (001) has been. deter- m i ned for the fir st ultrav i o l et a b s orption band. (S ee the section on polarized absor ption spectra of 9-methyladenine of this thesis.) Since the s pace group is P z 11 c and there are fo ur molec ule s pe r unit cell, the transition moment for one pair lies a t an angle and for t he other pair at an angle o£ - ''· . '~· from the b-axi s , From the dichroic ratio value of 5. 1, the mom~nt lies at an absolute angle of 24•_:tz• w ith respec t to the b-axis. From the analysis of polarized absorption spectra for a hydr o g en bonded complex of 1-rnethylthymine and 9-methyladenine, the transition moment for 9 -methyladenine was assigned to a direction of 16 8•+ ·1 ·. B y the Tinoco convention (3), th e transition moment angle is measured from the c 5 -c 4 bond i n the purine compound and increases by rotation into th e six membered ring. Wi th the knowledge of th e transition moment direction for the molecule and of the dichroic ratio in (001) of 9 - m ethylade nine, two angular orientations for 9 -methyladenine can be considered . One of these orientations should correspond to the true s tructure of the crystal. From the pol a ri zation data obtained for 9-methyladenine studie s the C -C bond should lie at an absolute angle of 12•+6 • 4 5 r espect to the b-ax is. I have assumed that the two pair s of the four m olecule s per unit cell are hydrogen bonded from the N g ro up. or 3 6 •+6 • w ith 7 to the 6-amino This hydrogen bonding scheme is the one reported by Broornhead in her determination of t.'-le adenine hydrochloride crystal structur e ( 1). 158 By using Broomhead' s center of symmetry for a hydrogen bonded pair, K . Hoogateen 's atomic coordinate s for 9 - rrH~thy ladeni ne from the crystal of the adenine-thymine dimer ( 5), and assuming all molecule :. c oplanar to the (001), I have calculated the atomic position s for the 9 - methyl ade nine molecule for the two possible orientations. Both ca se s are presented below; one s tructu re is preferable and s ug~ests in a gross way the orientation of the 9 - methyladenine molecules in the reported uni t cell ( 1). Figure 1 is a representation of one pair with the C 11 -C z an angle of 36°. The plane o£ the paper is (0 01 ). 5 axi s at ( The arrow over one molecule is believed to be tbe d ir ection of the tran s ition moment.) The other two molecules, not shown , of the unit cell are in a plane hal£ way up the -.c -axis; this plane has a vertical separation of 3. 6 0 A from the (00 1). Although the unit cell is filled up by the molecules w i th adequate spacing, the hydrogen bonding for the 6 - a mino group i s unacceptable. One proton of the amino group bonds to N 1 {by assumption) but the other If one trie s a hydrogen bonding proton has no nearby site for bonding. scheme to theN 7 position ( that is, reject the N 7 hydrogen bonding scheme), then the pair overfills the unit cell ; the a - axi s i s too short to accommodate this latter configuration. The sec ond possibility for the angular orien tation provides an attractive hydrogen bonding scheme. per unit cell are shown. I n Figure 2 the four molecule s Molecules 1, 2 , and 2. ' are in the (001); 159 (001) c / ..-? Figure 1. = 36°. 4 5 is unacceptable. < b /\C -C The hydrogen bonding scheme 160 ( 0 01) Figure 2. Proposed orientation of 9-methyladenine molecules in the unit cell. (S ee text for discussion) 161 rnolecules 3, 3', and 4, projected onto the plane of the paper, are above the (001), half way up the c-axis. The arrow o r1 molecule 1 represents the transition moment. The major feature of the proposed str uc ture is the hydrogen bonding scheme. The 6-amino group is no-w in a favorable position to hydrogen bond to the N 1 of a 9 -rnethyladenine i n the adjacent cell. The two centers of symmetry on the a-axis prov ide the system with alternate types of hydrogen bonding betwe en the molecules along the a-axis. If this is a correct scheme, then the crystal is an interesting structure to study in thci.t there ar e two ldnds of hydrogen bonding between the adenine molecules. The present spacings of the molecules, as they are now shown in the unit cell, are not acceptable. N 9 The methy l g rotl p, attached to the in the purine ring, is too close to the methyl group in the next cell; • the separation is~ l A . only 2. 5 A . Furthermore the N 10 to N 1 hydr ogen bon d is There is a bout a 6° error for the transition moment direction from my experimental n1easurements of t..'I-J.e dichroic ratio and from the polarization analysi:3 of the 1-methylthymine , 9 -methyladenine hydrogen bonded complex. Rotation of the C 4 -C 5 bond close r to the b-axis increases the separation of the nei ghboring methyl groups and a lso increa ses N 1 toN 10 hydrogen bond distance. The center o£ symmetry taken f rom Broomhead 1 s a t omic coordinate s may not be completely correct for thi s s tr'-lcture. By decrea s ing theN 10 -N 7 162 hydrogen bonding distance, the methyl groups are separated further and the N 10 -N 1 distance is also increased. The methyl groups. moreover, may be out of the plane of the molecules as well. My polarization data cannot be used very well for constructin g a more accllrate structur e than what is shown in Figure 2 . I t is useful, however , in establishing an approxima te orientation of the 9 - methyl adenine molecules in the unit cell. Unit cell dimensions for 9-methyladenine taken from K. Hoog steen ( 1). a=7.67+.03A b = 12. 24 + • 0 4 = 8 . 4 7 + • 03 e : 123 2 6 + 10 c e Space group: Density: I I P 2 /c 1 l. 4 71 g • em -3 {meas) REFER E NCES 1. K . H oogste en , A ct4. Cryot •• 12, 8 2 2 - 823 (1 9 59). 2. K . Hoogsteen , p r ivate communication. 3. H . DeVoe and J. Tino co, Jr.,, J. Mol . B iol., 4 , 518 - 5 27 (19 6 2.). (See p. 50·~ in preceding article) 4. J. Broomhead, A c ta C 1•ys t. , .!.• 324 -3 29 (1948). 5. K . H oogsteen , Acta Cry s t •• in press. 163 PROPOSITION II It i s proposed that orientations of macromolecules be looked for in the analytical ultracentrifuge by measuring the dichroism or birefringence. Hearst and Vinograd have studied the very interesting "speed" effect on the sedi mentati on behavior of macromolecular subs tances in an ultracentrifuge ( 1). The i nvestigators report that for T - 4 DNA at concentrations above 10 J.Lg/ n"ll , there i s a pronounced dependence of the sedimentation coefficient on the angular velocity of the rotor. (These experiments for sedimentation equilibrium had :;p approximately equal to 0. 5; the investigators studied the sedimentation velocity in 0. 15 ~ NaCl solutions .) For example , at a rotor speed of 2.0 , 4 10 r. p . m. , the sedimentation coeffici en t for T-4 DNA solutio n at 15 J.Lg/ml was 50 S vedberg units and at a roto r speed of 4 , 908 r. p.m. , the sedimentation coefficient wa s 38 S . The author s report a similar , but less pronounced speed dependence for T M V vir us ; for this case the concentrations were several hundred v.g/ ml. The dependence on rotor s peed suggests that the molecules are being oriented by the effect of the centrifugal field. The effect of con- centration also indicates that the macrom olecular specie s need to be at a certain concentration before the speed dependence can be observed. Thus intermolecular i nteractions as well as the effect of the centrifugal fi e ld seem to be important factors for the speed dependence. 16 4 Dr. James Peterson has investigated several theories to account for the sedimentation phenomenon (2). Of the several mechanisms con• sidered, none could successfully account for alignment of the rod-like particles in a centrifugal field. It is clear from Peterson's work that 1norc experiments are required before o ne can proceed further on theoretical consideration s . should be answered. I n particular the question o£ alignment If the macromolecular species do orie nt in the presence of a centrifugal field, how do they orient? A re the rod-like particles oriented i n the direction of the field, perpendicular to the field, or merely constrained to lie in a plane perpendicular to the axis of rotation of the rotor? For the first t wo possibilitie s , both dichroism and birefringence of the t:lample would develop with the field strength; f o r the last ~ase one should obse rve a decreas e in abs orption compared t o the i s otropic solution. It s hould be n oted here that th.:!se k ind s of experiments were c onsidered (3) and were ruled out, because it was believed that the quartz windows were under too much s tra i n at the high fields in an ultracentrifuge. intolerable. The atrain on the quartz w i ndows , however, is not Since the w indow s i n ultra c entrifuge cells are crystalli ne quartz cut perpendicular to the optic axis, rotary dispersion of the plane of polarization m a kes it impo ssible to extinguish polarized, nonmonochromatic light w ith an analyzer. If o ne uses monochromatic light, the rotary dispersion is not a problem; the emerging m onochroma tic 165 li:;ht can be extingui shed w i th an analyzer. The present quar t z windows are ideal for d ichroi sm or birefringence measurements. The rotation of the plane of polarization must be a cc u r ately measured so that the polari zer can be appropriately o riented. For quartz cut pe r pendicular to t..'!-)e optic ay.j s , the plane of polarization will not b e rotated, but very a ccurate a lignment of the polariz er with one of the principal d irections o f the quartz i s necessary . Othe r wise the quartz will make the i nci dent light elliptically polarized. Dichroism experiments are simpl er to construct than birefringence experiment s , because the tran smitted light does not have to be analyzed; only intensity must be measured. be r un in the centrifuge with a side wedge . A control sample can T ' 'vo s lits can be approp ri- ately placed i n t he focal plane o£ the optical sy s tem so that the control and sampl e can be measured under t."le sar.·1e c onditions. A photomul- tiplier device i s per haps a better detection sys tem than photogr aphic film , since the linearity of the former cover s a muc h larger intensity range than the linearity of the latter . REFERENCES 1. J. E. Hearst and J . Vinograd, Arch. Bioc hem . &: Biophys. , ~· 206 - 215 (1 961). 2. J. Peter son , "The Hydrodynamic A lignment of Rod - L i ke Mole cules in Centrifugal F ields , " P h. D . T hesi s , California In stitute of Technology, Department of Chemi stry , 196 3. 3. J. Vinograd, private communic ation. 166 PROPOS! TI ON lll It is propo s ed that photochemic a l studie s on 1-m ethylthymine be :.mdertak en. It was repo rted i n this thesi s that 1-m ethylthymine suffe red photodamage durin g tranomiss ion measurements . product is very lik ely a 1-methylthymine dimer (1). The photo- The neare s t neighbor in the crys tal i s situat ed above or below the molecule with the 5, 6 double bonds over each other . If a cyclobutane r ing forms between the two moietie s , one would expect a 5 , 5 '- 6 , 6 ' type bonding with the pyri midine ring s trans to each other. (S ee l'" ig. 18, p . 85 of thi s thesis.) S uch a structure correspond s to structure ll proposed by Wu lff and Fraenkel ( 2). J. compound ~ This particular di rne r can exist as a d or S ince a 1-rnethylthymi ne c an react with the near est n ei ghbor above or below e qually well , one should expect a racemic m i xture to form in the crystal. 1 - Methylthymine can be cry stallized as thin fla ke s on quartz plates . The developed face of the flak e s is the (10 2), the plane of the m olecule s . By irradiating the cry s tals from abov e and below with a n H g germicidal lamp (or some oth er c onvenient ultraviolet source), one shoul d get a r e asonable yield of the photoproduct. Thr ough frac tional crystallization , the photo p roduct can b e sepa rated from 1-methylthymine . A n easy way to indic ate that the photoprodu ct is a thymine d imer 167 is to measure the ultraviolet absorption of the pure photoproduct. The band at 273 miJ. should be absent. A m olecular weight deter m inati on by freezi ng point depr eBsion and an elemental analysis would establish whether the compound i s a di mer o f 1-methylthymi ne o r not. By me thylating the N 3 positions o£ the photoproduct, one c an now compare this compound to the N , :N '-dimethylt..hymine photoprodu cts I and II reported by W·..11ff. S nch a compari son would help to settle the que s tion of t he four pos5ible isomer s which are c onsi stent w ith Wulff's struct ural studi es of the several photoclimer s . If the s tr u cture proposed above i s correc t , then the photoproduct w ill be a r acemic m ixture. 9 . 5 (3). T he pKa for both thymi ne and uracil is The photoproduct will probably have a comparable a cidity. Therefore a str ong base of pure d or I. form will be n ece s sary to form <lia s tereoi some1·s from the ra c emic mixture. ::2uinlne methohydr oxi de or cin chonine methoh y dr ox i de may very well do the job ( 4 ). R. T. Major was able to res olve a r acemic m i xture of l actones wit.~ these reagents . vv-ith hydrochloric a cid, one can remove t...l').e base and rec over the respective d and J. photoproduc ts for further classification , ~ • m e as\lre the optical activity . Suc h an analysi s would establi sh the photoproduct a s is omer II or III i n ·,t{ulff ' s wo r k ; the known cry stal s tr ucture of l.;. m ethyl thymine makes it almost certai n that the optically ac tiv e compouncla would be isomer II. 168 REF E RENC E :3 1. Dr. D. L. Wulff, private communication. 2. D . L. Wulff and G. Fraenkel, Biochi m . Biophys. Acta, z.!.• 332-339 (1 961 ). 3. D . S hugar and J. J. Fox, Biochim. B iophys. A cta, 9, 199 -21 8 (195 2). 4. R. T. Major and J. Finkelstein, J. Am . Chern . S oc., .§l. 136 8-71 (19.4 1). 169 P ROP O SITION IV It is proposed that dichroi sm studies of a single pyrazi ne crystal be undertaken to help clarify the nature of gained i ntensity for the M. A. lowest, syn-1metry forbi dden , n - n • transition of the molecule. El Sayed and G. W . Robinson investi gated the lowest n - n • transitions in pyrazi ne ( 1). The system provided the workers with an i nteresting study of intramolecular excitation transfer. The n - ,.rlll transitions, whic h can occur at each end of the m olecule, are orbi tally degenerate . I nterelectronic i nterac tions remove this degeneracy; one transition is sym metry allowed, the other symmetr y forbidden. The 1 B g ... 2 transition i s symmetry forbidden ( the poi nt group for pyrazine i s D h). . 2 For the s ymmetry forbidden tran s ition there was s ome question as to how the transition gai ned most of its intensity. M o s t of the intensity for the symmetry forbidden transition lies in a b a nd abou t 82 0 em -l above t he (0, 0). ( For the crystal, a weak transition a bout 500 em -1 to the red of the (0, 0) allow ed tran s ition was thoug ht to be the (0, 0) for the symmetry f orbidden tran s ition. ) If this band at 820 em -1 above t..he ( 0 , 0) i s polari zed in- pl ane {of the molecule ) th en the i ntensi ty w ill be gained through mi~ ng w ith a n - n * transition. If the band is polar- ized out of pl ane , then most of the i ntensi ty will come from vibronic coupling between the symmetric and anti symmetric ( n , n*) c omponents ( 1, 2). 17 0 With the pyrazine molecule in a crystalline environment, however, there is always the question of crystal perturbations. One cannot state with certainty that the polarized electronic intensity behavior for the molecule in the cry stal i s the same for the free molecule. But the pol ariza tion properties for the molecule in a crystalline environment are interesting in themselves . The crystal s tructure of pyrazine has been determined (3). The orientations of the two molecule s per unit cell i n the orthorhombic crystal are pleasingly simple. The axis along the N , N atoms in the 1 3 ring is parallel to the a-axis. The two molecules have their respective planes at angles ,:!:22• 3' with respect to the c-axis. The cry sta.ls , which can be easily grown from a melt or by sublimation , can be cut to a thin section perpendicular to the a-axis. (I imagine 10 1.J. is a reasonable thic kness for this weak tran si tion.) The crystal will be cooled to 4 • so that the bands will sharpen up somewhat. (It should be emphasized that an n-r"* transition i s highly localized and is thus broadened con s i de rably by crystal lattice vibrations. th e broadness of the se absorption f>pe ctra see reference 1.) For The absorption measured for light polar ized along the b-a xi s i s where a X i s the absorption perpen dicular to the m olecular ring and a is the absorption i n the plane of the ring at ri ght angle s to the N -N 1 3 y 171 axis. a y a nd a X are the molecular absorptions along t he m olecula r coordinate s ystem used for Robi nson' s study (1). Si mila rly . F rotn these two a b s orption measurements we determi ne a X and a • y Now we section another single cry s tal p erpendicular to the b-axis. For light pol arized along the a-axis 1 the molecular absorption . a • is z determined directly. as before. m ent. For light pola rized along the c-axis , This measurement provides a check on t he earlier measure - Therefore . from these polarization studie s the distribution of i ntensity among the thr ee con>po nents of the m olecular coordinates is determined . One possi ble difficulty with thi s experi ment is a phase change in the crys tal in going f rom 300• K down t o 4 • K . that the experiment is worth trying. I do think. however • P olariza tion studies of this type will add to the under s tanding of the intensity gained by the symmetry REFERENCES 1. M . A. El Sayed and G . W . Robinson . Mol. P hy s . 1 !.• 273 -286 (1961). 2. M . A . El Sayed and G. v.; . Robinson . J. Chem. Phy s. I 1896 -1 897 (19 6 1). 3. P . J. Wheatley, A cta Cryst. • ~· 182-187 (1 957). 22.· 172 P R OPOSITION V A number of polymers have rod-like properties. It would be i nteresting to study the "rod statistics" of these materials by breaking molecular bonds at defined places. Professor Norman Davidson has suggested that oriented polymers may be sectioned with an ultramicrotome. Such a suggestion leads to a variety of experiments for the sta• tistical analysis o£ the rod-like properties of rigid, linear polymers. It is proposed that the analysis below be considered for these kinds of e xperiments. For analyzing the system it is convenient to adopt the following model. We con sider rods of length L and slice inter vals of equal spacing s. We are given a set of lines infinitely long and spaced at equal i nter vals s . The number of lines in the z direction more than span the rod length L. We shall drop rods onto these cutting lines and determine the weight average and number average lengths collected We always take L > s • below the line s . Casei: A paracrystalline polymer is assumed to be well oriented. All molecule~ are colinear, but the ends are staggered with equal prob·abilities. The molecules, moreover, are homogeneous i n length. This ca se corresponds to dropping rods onto the cutting lines with rod axes parallel to the z direction and in the plane of the k nife edges. 173 =ns + rs where n is an L ----~Z integer and r is a remainder. L D i stribution of Pieces I I I I I I I I I I I Num ber 0~ z s; s ( 1 -r) ~ST+Z. '4s-z n -1 s ( 1-r )~ zs; s s~ 1 L Length s - z 1 s sr + z 1 n s-z s 1 s ( r -1) + z I I I I I I I I I I ~s-z S(r-l)+Z s (l-r) J~ = 1 n s [( s - z ) +(n-l ) s+( sr+z)] dz + J s (l-r ) ( ( s - z )+ns +( s (r-1)+ z )] dz s( 1-r) s Jo or _J ( n+l )dz+ Ja(l-r) (n+Z)dz Tn = -Ls L +a s (l-r ) s f 2 2 . 2 _ J f ( s - z ) +(n -l)s +( sr+z) ] dz+ .. (l ) f ( s - z ) +ns +( s (r-l)+z ) ]dz 1 w 2 2 o s s( 1-r) ,s o s r ,J 2 -r ( ( s - z )+(n -l) s+ ( sr+z)lciz + .1I ( 1 ) ( ( s - z )+ ns+ ( s (r-l)+z)] dz -r = s ( l - ...!... ) 3L If the molecule s have a homogeneous density , then the len gths are proportional to the molccctl a r wei ght. The molecular weights of 6 very high molecular weight material (-10 ) are very hard to measure. By slicing the rods at different intervals s , one can determine weight average molecular weights by light scattering. a linear function of s with slope -l/ L. 3 give a value for the molecular weight. -1 w/ s = 1 - s/ 3 L is Thus Mw/ versus s s will (The linear plot will extrapolate to give p, the lin ear density , and have a slope of -pI M .) B y slicing 3 the rnaterial at smaller intervals, one can use colligative properties to dete1·mine a number average m olecular weight. From osmotic pre s sure n'leas urernents, for example, as a function of the slice interval, a plot of 1/ M ver s us 1/ n 5 should extrapolate linearly to 1/ M at th.e o1·clinate intercept. P erhaps an i deal systen1 for attempting this experiment would be paracrystalline TMV virus. T his virus can be prepared as a dried gel ( 1 mm x 0 . 5 mm x 0. 5 mm) which has two dimensional orientation ( 1, 2, 3, 4). The TMV virus is a rigid rod , macromolecular s tructure. Ar:; a dry gel , the viruses are oriented parallel to each other, but the ends are randomly distributed along the fibe r axis. The viruses are p acked hexagonal~y in the d1·y gel state . The expected root mean square value of leng ths i s 1 r. m. s = 5 L - s /3 + s \ / L I shall now outline how this result was obtained. As before we 175 assume the lengths o f all rods the same and L/ s =n + r. For 0~ Is; s r, we h ave two pieces le ss than s and ( n - 1) piece s sr s h: s we have tw o pieces le ss than s and n s l ong . For pieces s long . Thu s the d istribution is con s tant for pieces 0:!:: 1~ s a nd at s i t becomes like a "o •function ." Therefore the unnormalized distribution £unction, f( 1). is 1 s f( 1) = ( 2r + 2(1-r ) ) (2n + 3) (1-r)(n-1) + rn 2n + 3 OSlS: s 6 ( 1- s); 1 =s By normaliza tion, I f( 1) d 1 = 1I N =c 1 s + c 2 'o where C 1 = 2 ( r + ( 1-r) ) 2n + 3 s and c2 = (1-r)(n -1) + r n 2n + 3 The mean squar e length is thur:J 1 2 mean =N .I'S 1 2 [ c1 + c 2~ (1- s )] ell. 0 _E lectron microscopy m icrog raphs for s liced TMV would provide one with a number ave r age lengtb ; one c ould al:.:;o d eternline the root mean sqU;.lre length. T he slicing experimen t s ar e also p r omising for the a na ly sis of genetic markers on DNA , a rod-like polymer w h ich contain s genetic information. If one selects a DNA which can be genetically a s sayed 176 and aligns the DNA molecules ( by pulling fibers, for example) , then the theory for the analysi s of genetic marker frequency as a function of slice interval is relatively simp l e. It is assumed that the genetic marlcers are very thin discs on the rod-like DNA , that when sliced the molecules break ' 1 cleanly" at a pair of sugar - phosphate linkages , and that the genetic markers are incorporated by a replicating system with equal efficiencie s . I. Two simple models have been assumed. F or model I it is assumed that DNA has polarity in the genetic sense and that one end of the molecule is necessary for incorporation. A . D. Kaiser has studied the geneti c behavi or of A. - DNA from the bacteriophage A. , by breaking the"- - DNA molecule in half with a Hershey stirring system ( 5 , 6 ). One interpr e tation of his results is that one end of the m olec tll.e is necessary for incorporation; Kaiser sees only one half of the 11 genetic map" occurring for A. - DNA that has been broken in half. Presumably the other half lacked a n ecessary " hea d -piece 11 to become incorporated. We therefore envision a DNA with three genetic markers in the oriented fiber au follows: M3 M~ M, IE b c HEAD ~ 0. )t 177 The "head" m ay be a li gned in either d irection along the fib er axis. M 3 The d i stance f rom the "head" to M . is c. 1 i s a, toM 2 i s b, and to I t i s im p ortant that the "head" be a ttached to the marker; otherwi se we. assume no incorporation . In a straight forward way it can be shown that the probability functions , normalized with respect to t h e tota l DNA , for the occurre nce of n•arkers as a function of s , the slice i nte r val, are: PM 1 = ra/s as: as: b r-b/s b s: s s: c = 1-c/s s)! c (b ... a)/ s P~ , M 2= (c - b)/ s PM ,M ,M 1 2 3 a~b s~ c B y follow i ng the freq u ency of gene tic types (for t..lll.s model we can dete rmi ne the physical distances a, b , and c . S uch a clean cut experi ment w ould e stabli s h a m a p of gene s on t he DNA molecule by a phy sical c r ite rion . Recently , however, 3i mn:JOns and H ognes e h ave found that both p iece s of half - brok en X. - DNA will incor por ate t o show up w ith corre spond ing g enetic traits , but one pie c e has o n l y 3% of t.~e a ctivity of the other ( 6 , 7 ). H ence I p re sent below a second model; it is assumed that all pieces of DNA can b e a ssayed for gene tic mar k e r s. By som e method ( a H ershey chromatographic c olumn , for example ) the sliced piec e s 178 can be separated and relative efficiencies for genetic incorpora tion can be d e termined . The analysis below assumes that the rel ative efficiencies for genetic i ncorporation have been independently deter mined, and the freq uency for genetic markers as a function of slicing interva l s are corre s pondingly corrected to have unit efficiency for incorporation. The DNA molecule, for th e example here, r...as three markers , M , M , and M , which are separated by the respective distances a 1 1 0 2 and a • 2 For the slice interval less than a • the smaller of the two 1 spacings a 1 and a , the markers occur i n divi dually at a probability 2 of 1/3 when normalized to the total occurrence of genetic traits~ a + a 2 -l) l/ 3 ( 1 = al / • ? = • - M 2 = a2 /3 s -~ M o 3s M 1s 0 P PM 2 + M 1 = 2 /3(1 - a 21 J and , A t s :t a = 0, P M :? M l + M0 1 +a =a 2 PM 1 + M 0 = 1/3(1 - al/s) 2 2 /3 s , P = 2/3 a I , P 2 s M =a 0 Ml + l/3s = 2/3 a lf -:::. and P M M 2 "' a +a +M +M 1 0 2 =1- 1 A plot of the marker probabilities as a function o f 1/ s is:· G 2 179 1 Pes) Ya, Ys---~ T h e various slopes of the linear plot s and the di s c ontinuity points suggest an i deal sys t em for determining the physical separ ation of the severa l markers . Case n. Rods of length 1 are dropped onto cutti ng edges a t equal spa.cing a in a random fashion , ~, all solid angl es are equally probabl e . The polymer i s now in a glassy state , but again the molecules are assume d to be rigid rods , a ll of l ength L. L's onto th e z-axis. Consi der projections of 18 0 L co se = 1 I s = n+r I -1 For n /2 ~ e :. c os · s / L , y ~------1'------~ Distribution o f P i eces ( 1) ··~ /2 ~ e ~ c os -1 (b) s (l-r) :s: z IS: s ( 2) cos s/L ~ Length 1 s r/cos 9 sIL (a ) 0 :s: z ~ s( 1-r) .. 1 Number t ( s - z )/c os 8 [ z - s(1-r)] /cos e e~ 0 (a ) O :so z ~ s(l-r ) (b) s (1- r ) :!10 z ~ s {:-1 L ( s - z )/ co s e s/cos e ( s r+z)/ cos e ( s - z )/ cos e s/ co s 9 [ s (r-l)+z] /co s~ 181 2 1T :. ·1 = n J 2Tr cos -1 s/L r r !" si ne o 2Jo drl s (l-r) r - 8 2n r s r· 2__ • ~o___d -'q - ·-' rr_/_2 - -r-::-r-r---c_o_s_e_ _-r.Jo ~~-sr_ CJ._l _z_+ J ~( 1- r ) [{ s - z ) +z - s ( 1- r) Jdz 2.,.... c o s -l s /L (i r ) s r· dCf• J' I s i n fl d A '"'L dz + 2dz .. ..?. .;o n 2 .lo , s 1-r . d ·':f·Jc os -ls/L ; ; ; d 8 + 2 0 s i n9d9 r l' ( ) J, s {l-r) s 0 5 Jr {s - z )+{ n -l) s+{ s r+z) ]dz +J (l-r )(n s +r s}dz :· r s(l-r) - lstL sined8 c os L Jo ,s : (n+l)dz + .! s (l-r) ( n+z)dz .J - 2Ls =L+2s S i milarly , The r e Slll t a ind icate tha t a number ave r age molecular weight e x peri ment is better suited for s imple i nt e pretation . A plot of . 1/ M n venms 1/ s shoul d extr apolate linearly to 1/ M w ith a s l ope of ~ p where p is the linea r den s i ty . Th e tr an scendental exp r ession f or the we i ght a verage length demands an exacting experi ment and know l edge of L. F or small s lice in ter val s the dependence goes a s s log e L/ s a n d fo r rela tively large slice inter vals the weight average dependence goes as Ca se lll. Consider the realistic problem of a di s t r i buti on of rods a bout the z-axis with a p r obability d i stributi o n f unction p ( e ) . T he 182 azimuth about z is equally probabl e . One w ould expect 30me s o rt of d e;1sity distrib a ti on abo i.lt the z-axis {fibe r axi s ) f o r pulled fi ber s o f ri g i d rod macromolecale s. 3 u p po s e a fiber i s pulled under equilibri urn c o ndi ti ons. e x perience a torque which is p roportional to L s i n e . align the rod goe s as - L cos e. The rods The energy to .A Boltzmann -like distribution for the . p ropo rtt. ona 1 toe K CO B !?<, w h ere K . 1s . a constant ro d s , t h ere f ore , 1s characteri s tic of the tempera t ure and of t he forces exerted on the molecular rods during fiber pullin g. 4 n {e K e K I. cos0 l - 1) i s considered to be the normalized distribution function for the rods. The number average l ength becomes , 1 n Ls = L [ KeK - e K I< + 1~ K( e" - 1) = Ls L f( K) + s +s The weight average expre ssi on i s 00 l w K = e + ~(L/ ~ K}( +K 1 - L. +log nn ! n =l +e K s/L L2 {L/ sK ( K s / L - 1) - i) -2 K2 3s + 1 ( s /L)e-K - L/s K - L 2 / 3 s 2 K 21 e L/s) 183 A num b er average m o lec u le wei gh t experiment i s desirable. , li m its for f ( K) are between 1 a n d =~ • . .lim y,_ lim ..... The m f( K ) = l w!1ere the rod s =~ where t h e rods ha ve arc constrained to the z-axi s . K ... o f( K) equally p robable solid angles. These t"vvo limit s satis.:y the expressions for Case I and Case II respectively. If one can independently determine the linear density of the polymer , t hen a plot of 1/M n versus 1/s will determine K , the constant c haracter istic to the distribution p(e ). A more sharply peaked , normalized distribution function is l 1 c e - a _r:::-: -v n a + a =.l wh ere e -y. i B an i n co mplete gamma function. ln a --cos2e dy The number average expression is Ls = L/2 + s z -1 e -z d~ is a tabulated expo ne ntial integral. The predicted weigl:!t average i s a considerably m ore complicated expres s ion . 184 1 w/ s - + (L / s ) i e -av L/ 3 -Ls...rTfa11 b. {L / s )3/ 2. e -a...;r:TS 1 e - a- vrra + ra ~{- ~~ ) The number average expe ri me nt is the obvio u s choice . The point here i s that slici ng experi ments cannot de·~ermi :1 e a u nique d i stributio:1 for the rods i n a fiber . O ne must understand a specific r.nechanism for or ientation before he can put confidence into the s licing experi m e nt as a means for dete r m i ning a d i s tribution parameter. 185 R EF E R ENCES 1. J. D . Ber nal a n d J .. ~ranku ch e n, J. G en . P hy siology , 25 , 111-1 46 (1 94 1). 2. J. D . Wat son, B i o cbi1.'"!'1 . e t B i o ph y s . A c ta , .!l• 10-1 9 (1 9 5 4 ) . 3. D . L . D . C aspar , Na t~1re , .!22.• 928 (1 95 6). 4. R . E . F ra nklin , Natur e ,~· 3 79 (195 5 ); ~· 2:..2}_. '~29 (19 56). 5. A . H er shey a nd E . Burgi , J. Mol. B i ol., ~· 14 3-152 (1960). (Th i s i s r e f erenc e t o br eakage by s tirring .) 6. A . D . Kai s er, J. Mol. B ioi., .!• 27 5- 28 7 (1 962). '7 . A . D. Kai se r,~, 2 8 5. J. ·~vei gl e , priva t e co mmunication. 186 P ROPOSI TI O N VI The six parameter problem for the resolution of two Gaussians i e presented below. The three parameter problem for the r esolution of two equal Oaussians ha s been solved and a computer program w ritten for the least squ ares analysis of the problem. I t is proposed that the latter analysis be e m ployed for the treatment of data from density g radient. sedimentation equilibrium experiments which have been used to look for strand separation of DNA. The general problem of the resolution of two Gaussians is o£ interest to people carrying out density gradient, sedimentation equi librium experiments. It has been shown that ma cromolecule s of h omogeneous density and m olecular weight will band with a Gaussian distribution about a buoyant density position in a three component system ( 1). ~ The band width i s proportional to 1/(/N~"f- where M is the molecular w eight of the macromolecule. The question of two species has often come up i n density gradient studies. (In many cases there i s also the problem of more than two species.) For certain conditions the resolution of two Gaussians with arbi trary amplitudes and band widths has been considered and solved (2). were considered. Two crite ria for resolution One condition wa s that the respective maxima of the two Gaussians be distinct; the other that the distribution has at least four inflection points;.!.:.!:..:, one Gaussian manifests itself as a shoulder. 187 Although a system is " unresolved" by our cl"iteria, if one ha s a system in which he knows that there are two specie s , t hen the general re solution of the respective Gaussians is in princ iple s olvable. I have con sidered the problem in detail and present the results below. 1 w ill outline the general six parameter problem (two amplitudes, t\vo band widths , and two position s ) and show how it is solvable in principle, but in practice I have not been abl e to find a convenient solution . A solution for the case of equal band w i dth;; , but different amplitudes a n d positions is outlined below. can be found. I t is very lik ely that a better method The ca s e of equal amplitudes and band widths , but dif - ferent positions , has been s olved and a generalized least squares analysis carried out. I have written an IB M 7090 computer program for this la 3t case and will gladly leave it with anyone who is interested in the problem . The last case is particular ly useful for density gradient s tudies of "strand - separation" for DNA. If one treats DNA with a strong base, at pH 11, most of the thymine and guanine hi the molecule will be titrated (3). The hydrogen bonded structure will be disrupted. To the extent that each of the two strands !>as a different density, the strands w ill move to their corresponding densiti es. The s ingle Gaussian di s tribution for the native molecule will now broaden a nd become a sum of t.lte two Gaussia n s characteri stic for each strand. Each strand should be essentially the same in molecular weight and the ultraviolet absorption for each should be almost identical. Thus the two new 188 Gausai ans have equal band widths and equal amplitudes. I n order to carry o ut a least squares analysis for this experi ment, th e o riginal D NA must be very homogeneous and breakage of the str ands by a ction v.Ji th base must be minimal. T -7 DNA is h i ghly homogeneous ( 4) and could very well be an ideal materi al to look f or s trand separation with the k ind of analysi s discussed above . The non -interacting Ga ussi ans are written as (x-a ) 2 · {x-a ) 2 1 2 + G( x ) O ne w ay to generate si x i ndependent equations for the s i x parameters, a , a , a , ct , A , and A , is to evaluate i ntegrals of the type 1 1 2 1 2 2 for n = 0 to n = 5 • Defi ne I n co 1 = n J-co x G(x) dx Then , I 1 = alA lal + a2A 2cr2 ? 2 2 2 1 2 = Alcrl ( crl ... + a l ) + A2cr2 {a 2 + a2 ) 1 3 = Ala l 0 1 ( 30 1 1 2 2 2 2 + al ) + A2a2° 2 ( 302 + a 2 ) ? 2 4 4 2 2 4 =A 1a 1 (3a 1 ~ + 6cr 1 ~a 1 + a 1 ) + A 2cr2 (3cr 2 + 6a2 a 2 + a 2 ) '1, 1 15 1 =A lalal ( 1 ..:>0'1 4 + lOcrl 2 a l 2 + al 4) + AzalJz( 1 .)crz 1 + l Ocr2 2 a2 2 + a24 ) r: 189 I t i s di ffic ult to s olve these six equations s i multaneo usl y for the Another forrn f or t..~e sum of the two Gau ssi a n s may six parameters. be written G (x ) G(O) = -p 1 + p 2 Then + + p 2~2 ' 2R 2 2 G ( - 2) = P l R ? 1 PR ·" + Q 2 ..22 I t is also difficult to solve for P ' s , (i ' s , a nd R ' s from these equations . By usi ng the fir s t three s i mpl e equati oo.1.s of each kin d , one m ight hope for an easy solution . But the transcendental rela ti onship between P ' s, :l ' s , and R's and the A's , cr' s , and a ' s a s implifi c a ti on . S-co does not afford The gener al rel ati onship 00 (x -x ) o n G(x ) dx + . • . +( -l)r n ! (n -r) ! r! =I n - nxo I n - 1 + n (2.ni -1) x r I o n -r + ... + I n X 0 0 may be useful . A c h oice of x odd power of x ' = (x - x 0 ) vani sh . I t i s not obvious . however , which of 0 '~ 2 2 . 2 can make one of the i n tegrals w i th an . the three odd power i ntegrals will affor d a simplifi c a tion by choosi ng an 190 x 0 such that I' n+l 2 r =. eo - co 2n+l (x -x ) 0 G(x) dx = 0 , for n = 0 , l , or 2. This last possibility has not been belabored . For the ca se of o 2 = o , a considerable simplification is 1 i n troduced. · The integral expressions now become I 1 I 1 = (A 1a 1 + A 2a 2 )cr 2 = [A 1a 1(3o2 + a 12 ) + A 2 (o 2 + a 2 2)1 o 3 = r A 1a 1 ( 3o2 + a 1 2) + A 2a 1 ( 3o2 + a 2 2) b We may also use the relation ships I 1(x O) =I 1 - xOI O I ( x ) =I - Zx I + x ~ 2 0 2 01 0 0 where .f co - co (x - x )n G ( x ) dx • 0 191 T h en I /x: ) = (A - A )acr , whe re a= a = - a • 1 1 0 2 2 I (x ) =(A + A )cr 1 2 0 2 3 +(A 1 + A )a 2a 2 = I 0 (a 2 + a 2 ) 2 2 J (x ) = ( 3cr + a )(_A 3 0 = I t<::-: ) (3cr 2 0 If x 0 2 - A )acr 2 2 +a ) c an be determined, then the s olution for a , 0', immedi ate . a 1 2 a nd a • A 1 , and A 2 is Fron"l I (~-c ) and t (x ) we may ea s ily get expressions for 3 0 2 0 4 4 2 2 We then substitu te i n to I (x ) I ( 3a + 6a cr +a ) for 4 0 0 = 2 2 a , cr expressi ons . The result i s + 6 [I 3 (x 0 )I 0 - I 2 (x 0 )I 1(x 0 )JOI 2 (x 0 )I 1(x 0 )- t (x 0 )t 0 1 3 + (31 (x )t (x ) -I (x )I l 2 0 1 0 2 0 0 3 B y subs tituting the l n (x )• s wi th the polynomial expansions in x and 0 0 I ' s , w e ge t a si xth orde r polynomi a l i n x • 0 n "t'ifi th the appropriate root, then, the param e t er s a , cr, A , and A can be d eterrni ned. 1 2 The analy si s of the two Gaussi ans w ith e qual ampli tudes a n d ban d w i d t hs i s now present ed . center of gravity position i Since the two G aussi ans are equal, the will be the o ri gi n of the system s uch that 192 ') ') •;> -(x' + a) .... /zcr'-' G(x') = A[e where x ' =x - x . 2 -(x ' - a )'"'/ 2cr · +e 1 Therefor e , we fir s t l oc ate the origin~. 00 X \' xG(x) dx .., -co : 00 J G(x) dx -ro a.nd define the new coordinate x' =x - x. We next solve for a fir st approxima tion of the parameters A, a, a nd a. 1 1 2 = Aa(O' 2 + a 2) =I 0 (cr 2 + a 2) 4 4 2 4 =Aar3(cr 2 +a 22 ) .. 2a l =1 [3(Izli ) - za 1 0 0 In = AO 1 00 r .l -oo x'n. G( x ') dx' =I r:t. / VI zllo - V~\· 1- 3(1 2 / 10 ) 2 - 1 4 / I 0 l. T he s ubscripts zero refer to first order appr oximations. 'N ith the para m eter s app roximated to fi rs t o r de r , we now 193 proceed to a generalized lea st squares analysis ( 5). A con v enient for m f or the overall . di s tributi on func tion G( x ) i s = P R x 'z (Q -x ' + -..1 +x'> y where =Ae p 2 2 - a /Zo ; Q = e a/ a 2 ; R = e -1/ 2o 2 To first appr oximati on -1 / zo =e Let 2 0 n be the number of n"leasured ordered pair s , (X Y i ) (i = 1, 2 , • •• , n) . 1 x Then Fh 2 -x =y h - PR h h +Q (U +x h ) = 0; h = 1, 2 , ••• n , where yh and xh are the c a lculated points for the determined param . eters P , Q . and R . Let x. = X l i - Vx i y. =Y. - Vy. p = p .~ = .:. t o - q .R =R l 1 0 0 Now we Taylor expand F ' l - p - r h about x ., y. , P , 1 1 ~. and R . Then 194 oFh !~ V yi + oy.1 i (j' Fh \ I i DFh + r; P · P Vx . + 0x . 1 1 1 uF ' -oQ 1 q N e approx i mate h ~ F ~ y p i - 0 R X. 0 -X . 1 ( .") '""0 1 +X. + , ., 1 ) ....:0 - .... h ~ 0 By least squares , = 2: W· re s 2 6 ~ 6 or s = L: wv 0 v = 0 • T h e variations of the re s idual s , expans i ons above . p , q , and r . i ,_-F i = q = i ( )'·' ..-. ~ 0 ~p i oFi r = (L' F 0 By usi ng La Grang e 's mul tiplier s w e solv e f or -;-pI ~ ~ 'F i 'L ) • l -1 t, 11 + ( T' . .. ~<' - 0 -1 1 ' 1 w-v- -'" 1· -1 I L i ) 6 l, 2 + ( r F 0 v~ i -1 /Li ) 6 2 , 1 + ( ~ Fo ~ / L. ) 6 3 1 + ( l: F o u.. oFi i i ~Fi 0 8Q 3F i -ay + i i:. F i -1 ~ ) t, l , 3 1 . 1 / L i) 6 1 , 2 + ( L F O -1 6 "'BR") 1, 3 i oF i - 1 6 oR ) 3, 3 -1 f)Q"" /Li) 6 3 , 2 + ( L. F 0 '· k' v_ where L. Taylor The sol utions are: ( "~ ·rL ;- 0 p o V , m ust sati sfy the n &Fi 195 and Wx i and W y i are the weights f o r t.."le cor r e sponcling points X i , Y i . -1 The t:... are the inve rse matrix elements oi the 1-natrix 1J I: - 1 L. JF 2 _ i ) ( ·-·F i = l: r vP oFi (p (} ,:J aF /Li DF. 1 /Li ~ ~/L. I: ()Q l:)p aF 1. aF oR () .\; ( <. F i 2 ~.Q ) /Li C1F . 1 1 1 DR - oR oP 1 &Fi OQ "'DR"" / L i (J W' ~ /Li /L. c:nt I:"_! (.. F. i;Q 1 cF.1 E_! 1 c; _ /). E aF.1 . 2 1 I: { BR" ) /L . 1 The standard deviations of the parameters a , a , and A are c alc ulated frorn the i nverse matrix e le ments in the usual way . F>.>r the compute r prog ram 1 ha ve assumed that a first approxi- c;a tion is adequate for the l east s quare:2 a naly s i s . If n. s econd approxi .. rna ti o ;:l i s neede d , then th e data are probably too crude ! or t he det.;<.iled. analy 3i s above . R Eif'ERENCE.3 1. Cf. J ohn E . Hea r st a nd Jerome Vinogrc:..d , Pr o c . Nat. A c aC.. ; ci~ , .!!.· 999 -10 25 ( 1961). 2. ·.i.J . H uber , R . 3te wart and J . V i nogr ad , u npubli s hed wor k . 3. J . 1\t!orris , J . Vi11ograd , N . D avid s on at'1.d '-l{ . I ) ove , P r o c. Nat. A cad. S ci., in pres s . 4· . J. Vino g rad , p rivat e c ommunication • . 5. W . E . D emi ng, Statistical Adju s t men t of Data . J ohn Wiley & S o nG , I nc. , New York, 1943 , pp. 4 9-5 8 . .'. . ..· ":.