Studies of the Infrared Spectra of Unsymmetrical Molecules Citation Zumwalt, Lloyd Robert (1939) Studies of the Infrared Spectra of Unsymmetrical Molecules. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/4nt1-c125. https://resolver.caltech.edu/CaltechTHESIS:01062025-234118673 Abstract No abstract. 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): Unknown, Unknown Thesis Committee: Unknown, Unknown Defense Date: 1 January 1939 Record Number: CaltechTHESIS:01062025-234118673 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:01062025-234118673 DOI: 10.7907/4nt1-c125 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 16946 Collection: CaltechTHESIS Deposited By: Benjamin Perez Deposited On: 13 Jan 2025 22:40 Last Modified: 13 Jan 2025 22:45 Thesis Files PDF - Final Version See Usage Policy. 21MB Repository Staff Only: item control page

by lop~e . ~P - 4-10 I) . An Ab~ox~pt.lou Batld ot' li'oI•rn;aldex:~ t:>P· 12 - I 4 C• Dubetltut.ea Ale oho.ls. !OP· lb - 53 E• Propositions pp. se-bl ) at A 95'72 • The Banq._Envelopes ot.· Uns;(_mrn.etrica l Rotator Molecul es._. I l! Qalc ,~ lation o:f...!Jl! Theoretical Envelgpe~. 4 NOVEMBER, 1938 JOURNAL OF CI-IEMICAL Printed in U. S. A. PHYSICS VOLUME <> The Band Envelopes of Unsymmetrical Rotator Molecules. I. Calculation of the Theoretical Envelopes * RICHARD M. BADGER AND LLOYD R. ZUMWALT Gates and Crellin Laboratories of Chemistry, California Institute of Technology, Pasadena, California (Received June 14, 1938) Since the majority of molecules of chemical interest are too heavy to per~1it resol~tion of the rotational structure of the infra-red bands, it is of interest to find what rnf~rmat10n can be derived from a study of the band envelopes. Considerations of the type which Gerhard ~nd Dennison have made for symmetrical molecules have been extended to the unsymmetrical rotator. By the use of an approximation method the envelopes of the three elementary types of band have been calculated for nine different sets of molecular parameters. INTRODUCTION T ' HE number of molecules with moments of inertia small enough to permit the resolution and analysis of the rotational structure of the infra-red bands appears to be rather limited. In the majority of cases of interest to the chemist it is an idealization to speak of the bands as consisting of lines, since the spacing of the theoretical lines is less than their breadth must be under the conditions of experiment. Gerhard and Dennison 1 have considered the unresolved bands of symmetrical rotators and have shown that useful information can be obtained from the separations and relative intensities of the maxima. They have calculated a number of band envelopes which we have found very useful in qualitative comparisons. However, the majority of molecules are unsymmetrical and their calculations are inapplicable since with even moderate asymmetry the appearance of the bands is materially modified, especially near their centers. * Contribution from the Gates and Crellin Laboratories of Chemistry California Institute of Technology, No. 653. 1 S. L. Gerhard and D. M. Dennison, Phys. Rev. 43, 197 (1933). We have recently observed the spectra of a number of moderately heavy unsymmetrical molecules and have found that the bands may vary considerably in appearance and frequently exhibit distinctive features. For example: In some cases there is only one broad maximum, in others there may be as many as five peaks of unequal intensity. The significance of these features has not always been immediately obvious but their variability suggests that useful information may be obtained from the shapes of the band envelopes alone. To make this possible the theoretical envelopes for various types of molecules must, of course, be known . The discussions of the unsymmetrical rotator bands which have been given in the literature are quite inadequate for our purposes. Both Dennison 2 and Nielsen 3 have presented diagrams giving the positions and intensities of a few lines as functions of asymmetry, but these plots can give no idea of the intensity distri_bution in a band since only lines of very low J value are included. Aside from this fact they are restricted 2 D. M. Dennison, Rev. Mod. Phys. 3, 2 (1931). a H. H . Nielsen, Phys. Rev. 38, 1432 (1931). ~ f 5. 712 • R. M. BADGER AND L. R. ZUMWALT to planar molecules. The elaboration of such diagrams to the point where they would be of general use is not practical owing to the amount of labor involved in calculating every line of appreciable intensity. Since we are not interested at all in individual lines it seems more sensible to follow a procedure similar to that used by Gerhard and Dennison for the symmetrical molecule. Even this is difficult in the unsymmetrical rotator case, but we have devised a method for calculating the intensity distribution in a band which can be carried out with a reasonable amount of labor. The method involves a number of approximations but the errors should not be excessive and the results are indeed justified by satisfactory agreement between calculated and observed band envelopes. In the unsymmetrical rotator case one finds a number of complications which are not present in the symmetrical molecule. Two of these concern us at this point. In the first place it is comparatively seldom that the bands are of any simple type. If symmetry elements are entir~ly lacking the electric moment or change of moment FIG. 1. The energy levels of an asymmetric rotator for may have components along all three principal J =8 plotted as a function of S, with (a-c) and b kept axes of inertia. It is convenient, however, to constant. The continuous lines represent the levels given by exact theory and the dashed lines indicate those given consider any band as being built up of the three the by approximate Eqs. (1) and (2). A horizontal line through elementary types of structure which would be the center of the figure would represent the energy 2 expected if the electric moment were parallel to Wb=J(J+1)h2b/8,r • the minor, intermediate or major axis in tum. CALCULATION OF THE BAND. ENVELOPES We shall follow Nielsen in designating these Our first step in the calculation of the band structures by the letters A, B and C, respectively. There has been no consistent usage followed in envelopes was to find approximate expressions the literature but it is convenient to adopt the for the energy levels of the asymmetric rotator convention that the three principal moments o( . which are sufficiently accurate for our purposes inertia shall be designated by the same three and at the same time of a convenient form. solution symbols and always in the order A <B < C. The The~ were obtained by an approximate of the secular determinant of Wang 4 using secondreciprocals, designated by small letters, will conorder perturbation methods. sequently be in the reverse order: a>b>c. An In any particular case the secular determinant "A" band shall be one in which the electric may be written in three different ways. To obtain moment or change of moment is parallel to the reasonably accurate values for the energies with minor or A axis, etc. only second-order perturbation methods, it is In the second place the energy levels of the necessary to use different forms depending on the unsymmetrical rotator are arranged in a most energy ranges with which one is concerned. Forinconvenient fashion and it is not possible levels with energy greater, or less, than Wb accurately to represent the positions and in- =J(J+l)h2b/81r2 the appropriate forms are tensities of the rotation lines by simple functions those in which the diagonal terms are the same 4 S. C. Wang, Phys. Rev. 34, 243 (1929). of the moments of inertia. 6. BAND ENVELOPES OF MOLECULES 713 as they would be for symmetrical molecules with the reciprocals of the two like moments of inertia equal to the mean of band c, or of a and b, respectively. If one makes an approximation regarding the interaction terms by replacing (J - u) (J - a+ 1) X (J+u)(J+u+l) with [J(J+1)-u2]2, one obtains general solutions for the two cases mentioned above, which may be written as follows: is not greatly different from Wb. On the scale to which the figure is drawn the levels calculated from Eqs. (1) and (2) cannot be seen to deviate from the actual ones up to the point at which the splitting becomes appreciable. From this point on they diverge along the dashed lines. Fortunately the failure of both equations in the transition region is not very serious. In the first place, only a small fraction of the energy levels are concerned. In the second place, the transitions p(S-3S)(l+S)] involving levels in this region are the weakest in W""(h 2 b/ 87r 2 ) { J(J+l) [ 1-- - - - the cases where the predicted frequencies are 8(3-S) most seriously in error, namely in the t::,.J = ± 1 branches of the B type bands and the t::,.J = 0 branches of the A and C type bands. In the remaining cases where the transitions are strong the approximation is not so poor. In a rough first approximation of the band envelopes we have assumed that the transition p(l 7 + 14S+S2)} -K" 2- - - - - (Eq. (2)) for W<Wb, probabilities are the same as those of the symmetrical rotator, using of course the rules which 8(3+5) will be appropriate for the levels given by the where p=(a-c) / b and S=(2b-a-c) / (a-c), two equations, respectively. This will lead to and K' and K" are integers with maximum considerable error only in the "intermediate" value J. region , as has been discussed by Dennison. 6 We prefer to take Sas a measure of the sym- Since our energy expressions are of the same metry of the molecule rather than Wang's b, form as those for the symmetrical rotator the since the latter quantity is not uniquely defined procedure which Gerhard and Dennison 7 have but may take three different values depending on worked out is directly applicable and it does not how the determinant is written. It will be noted seem to be necessary to give further details of that S takes the values 1 for the symmetrical our calculation except to mention two modificaplanar molecule, -1 for the symmetrical spindle, tions which must be introduced. In the first and O for those molecules which as regards place, two sets of calculations have to be made arrangement of the energy levels we may regard in each case taking account of the two regions of as least symmetrical. energy levels separately. In the second place, In restricting Eqs. (1) and (2) to their appro- some changes have to be made in the limits of priate domains we may make use of an approxi- integration to take account of the fact that the mation suggested by an equation given in the lower limits of K' and K" are s' J and s" J, second paper of Kramers and Ittmann. 6 For the respectively. lower limits of K' and K" we may take s' J and Although this first apprQximation just des" J, respectively, where scribed gives a reasonably satisfactory representation of the intensity distribution in either the s'=(2/7r) tan-1 [(b-c)/(a-b)J½ t::,.J = 0 or the t::,.J = ± 1 branches of a band, the ands"= 1-s'. The upper limit in each case is of envelope obtained by combining the two may course J. be considerably in error. It is easy to show that As may be seen in Fig. 1, our approximation of the sum of the transition probabilities between the energy levels is entirely adequate except for 6 Dennison, Ginsberg and Weber, Phys. Rev. a: small "intermediate" region where the energy 52 , Randall, 160 (1937). + H. A. Kramers and G. P. Ittmann, Zeits. f. Physik 58, 217 (1929). 5 7 The expressions given by Gerhard and Dennison contain several typographical errors and should not be used without careful examination. T 714 R. M. BADGER AND L. R. ZUMWALT 0 s--1/2 p ---1 l I I I I l/3 I I I I I - -- , NONEXISTENT I I I 0.5 1.5 FIG. 2. The A bands (electric moment parallel to the minor axis of inertia) for eight different sets of parameters. The absorption coefficient is plotted as a function of x. One-half the band is shown , with the origin a t the left . For further description see text. levels of a given J val~e is independent of the symmetry of the molecule. Co,1sequently this sum for any unsymmetrical molecule is the same as for the symmetrical rotator. A similar rule applies to transitions between levels which have J values differing by unity. In our approximation these rules are violated, though the ordinary sum rules are obeyed. This has the result that in the B type bands the branches with t:,.J = 0 are robbed of a considerable fraction of their intensity while the t:..J = ± 1 branches are augmented by the same amount. In the A and C type bands the errors are in the opposite direction and are less senous. Since the symmetrical rotator intensity expression must hold fairly well for transitions between the highest and lowest energy levels, respectively, it is evident that these errors must arise from a serious failure in the intermediate region. Besides the failure with respect to the normal transitions there are of course additional transitions which have no analog in the sym metrical rotator case. We have found it difficult to estimate the total contribution of these, though general considerations seem to show that it cannot be large. We shall assume that it may be ignored, which seems to be justified by the observations on the rotation spectrum of water vapor. Out of a total of well over two hundred lines of sufficient intensity to be observed only eight could be identified as due to anomalous transitions, and none of these was very strong. 6 Considering this assumption to be justified it is possible to apply a simple correction to the BAND ENVELOPES OF 715 MOLECULES NONEXISTENT 0 .5 1.5 FIG. 3. The B bands (electric moment parallel to the intermediate axis of inertia). band envelopes which takes into account the errors resulting from our approximation regarding the intensities. Actually of course we must expect that the symmetrical rotator expressions fit fairly well for the highest and lowest levels but fail more and more badly as one approaches the " intermediate" region. To compensate for this precisely would be difficult but it is simple to calculate two limiting envelopes between which the theoretically correct one should lie. In the one case one may assume that the intensity expressions are adequate except in the very center of the "intermediate" region where they abruptly fail, in the other case that they fail uniformly throughout. In the former case the deficit or excess of the . sum of probabilities for any set of transitions (J__,,J') may be accounted for by attributing it all to one transition in the very center of the "intermediate" region. Correction envelopes may then be calculated in a very simple manner, which have to be added to or subtracted from the envelopes obtained in our first approximation. In the latter case the correction may be made by multiplying the probabilities of any given set of transitions by a constant factor. Since this factor is independent of J, one needs merely to multiply the ordinates of the t:,.J = 0 and the t:,.J = ± 1 branches by the appropriate constants before adding them to obtain the total envelope. It turns out that the corrected envelopes obtained by these two different procedures do not differ materially. This is, of course, to be expected since in any given set of transitions the probability changes rather rapidly from one line to the next and a small part of the total set is 716 R. M. BADGER AND L. R. ZUMWALT --7 0 I I -7 I I I I I I I I I I I I x0,5 1,5 1.5 FIG. 4. The C bands (electric moment parallel to the major axis of inertia). responsible for a large part of the intensity. Consequently we have been satisfied to calculate the envelopes by the second method and believe that they deviate less from the ideal theoretical ones than observed bands will normally do, owing to A the nonrigidity of real molecules and other factors which we have not taken into account. In Figs. 2, 3, 4 and 5 will be seen the three types of band envelopes for nine different sets of parameters. To save space only one-half the B C -, I I -7 I I I I I I x1.5 FIG. 5. The A, Band C bands for a molecule with S= - ½and p = ¾. 10. BAND ENVELOPES OF -0.7 -0.8 717 MOLECULES ' -0.6 -0.5 -025 O +0.5 +I .. \ \ ·, \ \ \ \ NONEXISTENT \ MOLECULES \ \ \ \ \ \ 8 I 7 ·/ SYMMETRICAL SPINDLE MOLECULES -l◊.t A/B-- 7 0.15 0.2 0.25 0.3 FIG. 6. Lines with constant Sand with constant p plotted in a field with the dimensions a/band c/b. The sca.les provided are in units of A/B and C/B rather than of the reciprocals. band is shown in each case, with the origin at the left. The absorption coefficient has been plotted against x, where x= (v-v 0)1r(2B/kT) ½, so that the figures are adaptable to molecules with any absolute moments of inertia and to any temperature. The frequencies are to be expressed in reciprocal seconds and B (the intermediate moment of inertia) and kin the usual units. The continuous lines represent the total envelopes while the dashed lines indicate the t.J = 0 and the t.J = ± 1 branches from which they are composed. In the A and C type bands the area of the dashed rectangle at the left represents one-half the amount of intensity in the collected "Q" branch. fo the approximation to which we worked this branch should appear as a line of zero width. Actually this will not be the case, but in our experience the observed central branches have a width which is mainly due to the stretching of the molecule and to the difference in rotational constants in the normal and excited states and is much greater than would be expected for a rigid molecule with no interaction between rotation and vibration. In most cases this central branch can be well represented by a Gaussian function with width about 0.166x at half-height. Our calculations have been confined to highly unsymmetrical and consequently little elongated molecules. These have been least investigated and seemed to us most interesting. The envelopes of spindle-shaped and slightly unsymmetrical molecules have become familiar through the investigation of several good examples. Since one may wish to compare our curves with the envelopes of the "perpendicular" bands of the symmetrical rotator calculated by Gerhard and Dennison it may be worth while to call attention to the following facts. As S approaches + 1 the A and B bands degenerate into perpendicular bands, which is likewise true of the B and C types when S ·approaches -1. In both limiting cases when S= ±1, pS= -(3, where (3 is the parameter which Gerhard and Dennison have used to describe the symmetrical molecule. Figure 6 may be of some assistance in the rapid estimation of the parameters S and p in any actual case. The lines of constant S and constant p are represented in a field with the dimensions a/b and c/b. For convenience the scales attached have been given in units of A/B and C/B, rather than of their reciprocals. Some molecules whose moments of inertia have been determined with some precision are located on the plot. It is of interest to note that in the extreme right portion of the figure the parameter S varies rapidly with the moments of inertia. In a paper to follow we shall show how our calculated band envelopes have been of assistance in the interpretation of somt: observed bands. An Absorption Ib:nd of Formaldoxime at 'A 95.zg. rz . APRIL, 1939 JOURNAL OF CHEMICAL PHYSICS VOLUME 7 Printed in U. S. A. An Absorption Band of Formaldoxime at i9572* LLOYD R. ZUMWALT AND RICHARD M. BADGER Gates and Crellin Laboratories of Chemistry, California Institute of Technology, Pasadena, California (Received February 13, 1939) The third harmonic of the 0- H band in formaldoxime vapor has been found to lie at >.9572 (10,444.1 cm-1) and under high dispersion has been resolved and found to resemble a parallel band of a symmetric rotator. Owing to the weakness of the lines near the center of the band a definitely unique rotational analysis could not be made but the harmonic mean of the two larger moments of inertia appears to lie between the limits 73.3 and 76.6X 10-4o g cm 2• The hydroxyl hydrogen does not rotate freely and indeed its torsional oscillation appears not to have a very -low frequency. It is not possible to locate this hydrogen uniquely until other parameters of the molecule have been determined by electron diffraction. The possible effect of resonance on the 0- H frequency is discussed. EXPERIMENTAL T H E trimer of formaldoxime was prepared in the manner recommended by Scholl. 1 On heating the substance to around 100° it yielded the monomer in the vapor state. The formaldoxime vapor was confined in a ten-foot Pyrex absorption tube at about 100° and one atmosphere. Exploratory spectrograms were first taken with a glass spectograph of moderate dispersion to locate the 0- H band. In the resolution of the rotational structure a 21-ft. grating was employed * Contribution from the Gates and Crellin Laboratories of Chemistry, California Institute of Technology, Pasadena, California, number 681. 1 R. Scholl, Berichte 24, 573 (1891). which has a dispersion of about 2.SA per mm in the first order. Eastman 144Q plates sensitized with ammonia were used and the wave-length calibration was made by means of iron lines in the third order. EXPERIMENTAL RESULTS As may be seen in Fig. 1, a single O-H band was found at },.9572 (10,444.1 cm-1) with a simple structure apparently identical with that of a parallel band of a symmetrical molecule. In Table I are given the frequencies of the observed lines. These are the average of two independent sets of measurements. In the case of some of the 13 , 236 L. R. ZUMWALT AND 10420 10440 R. M. BADGER CM- 1 10460 • FIG. 1. Microphotometer curve of the O-H band at >.9572 in formaldoxime vapor. The water vapor spectrum in the same region is shown below. weaker lines the error may be as large as 0.1 cm- 1. The separation of the maxima of the P and R branches is 31.0 cm-1 . The extreme values of the means of the two larger moments of inertia are those given by assignments 1 and 2 of Table I. They are, respectively, as follows: D"=73.3Xl0and 76.6 X 10- and D' = 73.6 X 10- and 76.8 X 10There is a slight uncertainty in making the extrapolations but it appears very unlikely that the actual values of the moments of inertia should lie much outside the limits given. 40 DISCUSSION OF THE RESULTS Formaldoxime (H2CNOH) appears to deviate rather little from being_a symmetrical rotator both from considerations regarding its structure and from the appearance of the band here described. Consequently the spacing in this band will, for all practical purposes, be determined by the harmonic mean of the two nearly equal and larger moments of inertia. It should be possible then to evaluate this mean moment of inertia for both upper and lower vibrational states by making the same combinations which would be appropriate for a parallel band. With the help of a Fortrat diagram J values were assigned to the lines. It was not possible to do this uniquely and in both P and R branches there are two assignments which appear to be equally plausible as shown in Table I. The combinations can consequently be made in four different ways. In obtaining the rotational constants from the combinations t:!.. 2 F'(J)=R(J) -P(J) and t:!.. 2F(J)=R(J-1)-P(J+l), it was found convenient to plot t:!.. 2F"(J) / 2(2J + 1) against (J+½) 2 since the effect of the stretching of the molecule with rotation is quite appreciable, and the extrapolation to the rotationless state would otherwise have been difficult. 40 40 40 , TABLE I. • Frequencies of lines in the formaldoxime band at >.9572. ALTERNATIVE J ASSIGNMENTS > (CM- 1) No. 1 No. 2 ALTERNATIVE J ASSlGNMENTS > (CM- 1) No. 2 P branch P branch 10,411.12 11.75 12.49 13.33 14.13 14.91 15.58 16.32 17.10 17.83 18.59 19.35 20.13 20.88 42 41 40 39 38 il7 35 34 33 32 31 30 29 43 42 41 40 39 38 37 36 35 34 33 32 31 30 26.88 27 .67 28.46 29.23 22 21 20 19 22 21 20 19 3 I.IS 31.86 32.61 33.42 34.21 17 16 15 14 13 17 16 15 14 13 36 No. 1 10,435.66 36.44 37.21 11 10 9 11 10 9 Q branch 44.13 R branch 55.31 56.00 56.64 57 .27 57.92 58.58 59.18 15 16 17 18 19 20 21 16 17 18 19 20 21 22 61.41 62.01 62.65 63.28 63.88 25 26 27 28 29 26 27 28 29 30 66.12 66.67 67.28 67 .91 68.50 69.07 33 34 35 36 37 38 34 35 36 37 38 39 14. BAND OF FORMALDOXIME THE STRUCTURE OF FORMALDOXIME Although it is not possible to determine the structure of formaldoxime from the data at present available, some interesting conclusions can be drawn. One of these is quite certain; the others may be somewhat in doubt and await further investigation for their confirmation . The appearance of the band at )1.9572 seems to excl~de completely the possibility of the free rotation of the hydroxyl hydrogen. The band appears to be simple in structure, and if there are any superposed bands arising from absorption from excited levels they are certainly quite weak. It appears reasonable to conclude that the 0- H torsional vibration is not extremely low. When hydroxyl hydrogen, though not free to rotate, may be found in more than one position of potential minimum, the 0- H frequency appears to be considerably different in the different positions unless they correspond to equivalent or very similar confi urations of the molecule. The fact that only one 0-H band is observed at )1.9572 may be taken as indicating that in the great majority of molecules at least the hydroxyl hydrogen is to be found in only one definite position, which one would consequently expect to correspond to a rather deep potential minimum. Since the molecule is most probably planar, it is of interest to speculate as to which of the two geometrically possible plane con figu rations is the -more probable. In both models the 0-H bond makes a considerable angle with the minor axis of the molecule and if the change in electric moment is more or less parallel to this bond it is a little difficult to see how either can g;ive rise to hydroxyl bands so predominantly "parallel" in character as the one observed. However, the one represented in Fig. 2 in which the hydroxyl hydrogen is farthest removed from the carbon atom seems definitely to be more probable. The moments of inertia of the molecule would be of assistance in locating the hydroxyl hydrogen if the other parameters were known. Some of them can be estimated with sufficient accuracy but since there seems to be some possibility of resonance in formaldoxime one hesitates to make 237 a guess as to the C - N and N - 0 distances. The latter is particularly uncertain, and the assistance of electron diffraction measurements must be awaited. H FrG. 2. Possible configurations of the formaldoxime molecule. The less probable location of the hydroxyl hydrogen is shown by dotted lines. If the N -0 bond does have appreciable double bond character, one should expect the 0-H frequency to be somewhat affected, probably lowered. An effect of this sort may well be responsible for at least a part of the lowering of the 0- H frequency in the carboxylic acids and in nitric acid. Indeed it is possible that the frequency lowering might serve as some measure of the importance of the resonance and it is unfortunate that internuclear distances are not available in any cases which might serve for calibration. However, it is doubtful whether any simple relation exists owing to the presence of numerous other complicating factors. The third harmonic 0- H band of formaldoxime has nearly the same frequency as the analogous one of phenol. In the latter molecule the "mportance of resonance has already been suggested. 2 In both cases the frequency is indeed slightly lower than in the primary alcohols but may still be regarded as well within the normal range. Consequently it appears unlikely that the N - O and C - O distances in the two molecules, respectively, will be found to be much shorter than the normal single bond dist~nces. E lectron diffraction measurements will, however, be awaited with interest. 2 L. Pauling, J. Am. Chem. Soc. 58, 94 (1936). Inve .s tigation. of the 'l'hird Ha.ri:nonic Q::.H Lci!ldS of Substil,uteg !lC ohol§..!_ ~mvest~ga~~o.n e t' 'tl1e t,h~rd Ha:rraonie 0-!i, it,utEJd .Alcolw lth .~Band~ .- ., et.· .. .B:nbst = ·.~ ~ ......... In t l\(1 fol lov,ir.z p ax•,1~,gr.d;lis w.d.11 be de~<::ribrcd a s i>ecU"o• .sr a phic .lnv0~t.1gati.on wh :;.ei.. def' irute 1¥ c GHllS~ in tht1 uor11a4n ot t o bt~ nztl(;h too <-'o.uipli<>lt~d. t ·o 'be given a c1u~it.ut1ii it;icch~nical t.l'€-~ tlUETft in G:t"dt~:t• 'tc c or::r-'e l >:.tt.e tb.t, de;t~.1.11s 0t' tl:i:e: {:fjl.li•e r,re<l i.t; about. tlie 1M1me as the ()-H :trequency oi: phi&nvl w:td..le in th~ c ~'UHs of' t.t-.1.ttr t'irt1rt c 1.:, 1.ct'ig,~Jl• ~tio:n t-he O• Fi fi•equenoy i~ ~ome• ato1u wlar11 n~ar t,he el€ctron@gative Qblo;.dn(f at.ot.n will i.mdf;t•go an at:trQctl ve int~rac ti~:n, i• e . :t'Gr1:11 a h,ydf•ogfl:n L,_,:. n.-a , tWd tl1i.s has tl:it1 6!'1"ect o:f' lowerir)g the 0-11 vibrational :t.·:1:~e(~ency . f) Badgez· and l~auer... in c ontiiider:i.i::g t~l'l~ doublet b~d ch1a-:a:•·a c:tei•• the ab£SOl?p tio.n SiHtCtr:a iner·t. $(.l'lVEU:l t©- • :,..u1ct, Qf ~-ut•e: l i(,iU.lcis a nct\t,heir etd.,. .iti'11LS ill in t.b(z liq uid l.';Uit~ 0:ne will have 'Whlc:n 'lfl.lsft> cit' t ht: p1•1Js,<.r tice. 4gli..i.1<.1e b is,d 1cu 1 J.IKiex 01' t•1;;;fractiou ot' • .0° n 20 ~J ,- ;t J...4i3o. This c.HJ£¾,f)tn.u1d \<:\·ae ,h .$-t,ilJ.e·d und.e1· t•ectu.ced pre~eui·e ,ind tht: ,'511dGle tr;t;tctitm ~·a~ u :t ~d • in t .bfE iii,p f:CU"<)SCO£d,e a p.1.. oduct of thij Met':foro Che~r~ic al Co ., 'lffH 'i, 0 ill. d i~-'t illed 'to ilin~ 1>0 in.t of 1.:d 4 • l ( COl'' l'•~c: t.ed t o 760 ltil.1.) • pbtr:wl O:,a$t1"11an) u~e-d i u th<& f.LK;,:-~-r-L'U€:.Ut~ :Sina hud Th$ O•chlot·o ... . ,./ 1? ,...o l?i! ' b ,:,) i.l~d at .L ,,:-• .::. '- 4-~~ This ir.1.ve-stige.tion w,H. s ca,r r iecl out with ·thB u se of a Li ttrow glass spectrograph with a dispE.rsi 0n ot· about '70 A per mm. at /I 9000 . 'I 'hb V,E:i.lues :fo11nd :for the frequencies o:C the centers of t he absorpt ion bands ax·e accurate to about oc: cm•l • Som€ ui:1c_ertai nty ar ise·s t:n the estimx t.ion of the true. ma.xir:r.a of the ba.nd.s, il1 m~.1.king c o;npErator· A t h r a:e me ter Py:t•ex ;:1bsor-ption cell wh ich ·was heJa ln- a res is t ance :fu.r:th.ce co:n€, i 1;ti:ng of a sh eet .metal tube wra:s,p ed fti.rnace was of somewhat ~-r eat.er length than the cyli narical absorption cell and h ad one lE;ns at €< ach end p l aced it.tter·m~diate betwee:r:i the end of the i 'urma.ct and the cell. The .pr·essure of the v :ai;,or in th€. cell was r egula:ted. b.1 f 1.xing th.0 t€c:aipe1...ature of a tra_p wh ich held an E: xcess of the liquid and v1-hich wa.s cora:i.ected to the b ottom of the absorption cell at ~nd . using tlH:, same appar.atu~ tbE: entro.:.· ies of' v ai;,, 01•1.. at the boili:ng point , of· pl1€nol (r-E:agent q uality) a nd .P-chlorop hE:1101 ( Eastman) were ev;:.:i. luat ed ae 24 .7 and 24.:4 c a l.lde~ .mole K Note: 1:>ne, r> 6sp ectively. ot' t;h{ii l tct4• Q platq;~s ch"' .'i. n~es Vf:!z~y tnl-t.t"ked.l,,, t; i tll wa~•{;; ... le1:1gt:ti in thiz l'.'€agion) -t-tUd tiau.s th<; b itCkgr s:: i-u nd b li±ic.:kC"nir~ Cl.'.:d.l'i~t-S C t:itl,• Table I A.boo~ption max..1.ma -·----------i~~::L g1,hyltne c l:d. oi• ohy cir>111 •Et hy l£ne 10 , 318 bromohydr.:1.n 10 9 4'70 10,53.7 Metbyl c€:llo.solve l 0 , 3i~1 l0, 472 l0, 638 'i'r ime tt.yl ene chlorori.ydr in Tr i rr1ethy leuec l 0 ,4.70 10 , 629 ' brOi?lO!tydx• irt Pl"o:r:·y lenft chlorobj'·dl· in 1•(.;illoro-2-propanol 10,ase Sy in• .iJlv'Cerol 1, 3• die n.loro2•p1--opanol 10, 243 10; 325 dic.hlorohy dr1:n 10, 400 2-CHLOR0~ETHAN0L I,3-D ICHL0R0-2-PR0PAN0L I I I I I CH 2 CI CH 2 0H CHeCICH0H C~CI 2 - METHOXY-ETHAN0L I I 1-CHL0R0-2-PR0PAN0L I I CH.,0CHaCH.0H I I 3-CHL0R0-I-PR0PAN0L I I I CH~CI CHaCH~0H 2-BR0M0-ETHAN0L I I - - / CH 1 Br CH1 0H CH 2 CICH0HCHa 159° ' / -I ,0,200 10,400 Fig ure 1. -- I · 10 600 l . -- - - - "\ ----- ~ 10,100 t . t t r t0,4O0 10,E>0O 101400 / to,?.o,o 1O,t>00 Micr ophotomet ~r curves of the 0,H third h ar monic abso~pt i on ba nds in th 0 vapors of s ix s ubstituted alcoh ols. The temp era t ur e of the vapor is marked on t he ci..ll'ves. _, cm. N- PROPYL ALCOHOL I I I I I I 103° / .t- \0,300 Figure 2. 10,500 - \0,700 Microphotometer curve of the 0-H third harmonic absorption b and of n-propyl alcohol. Th€ dashe d line indi- cates the trend of the b ackground bla ckening. If' we. eon4,:,&re th~ above data ,on etbyl~ne chl,oro}~rm• :u.1., ethylel'.Ht trc-,!f,)hydr..1.n ~nd 2-meU,t<,~l' ..,etha,nol w-1t,h t.btl t'b:tii ' ot • cha1•,acte1t·is-t ic or no:t-illiil alc•..:ih ola (d:ieplac ed to tJl.J.i'h,tly hightr ft"eq,u coo1es); however, \'¥e also have a nil\w bw:1d appearing_ new band vwulcl thi~m to rArise t'r cm a situatlo:n ar,~~logou.s to ti1~t, occurrii~ in orthochl(;;;i1•ophmlol. dist,i;i.nces , but l t \:r :Ju.ld eet~m probable thhltt. an .intrtA.iuolecu.iar hydrogen bond c 0u.l.d be .:t'or~led bt;tVie{,.n the chlo:r.'it.. e at.om and tiorJ.S ot.' etll;Yl~:na d.1.l.orohydrin is lower tha n ti'Hli: oor ttA1 0- E f1•equency becaw;Hs ot· the a ttract,1v ~ int.c:r-ae:t.i0n of tLt L_ydl:-OXJ-1 baud cor-re$ponds t.o o onti.gurations ot: thtii _;1m , le<n.tle in :v-;tiich Uit't l:iyoroxyl ~TCfUf) i t:.t ll.'} a .s.lti...iat.ion s-linl.lt<i.t" to t.h~t. in w.aicb it find& i taeli' in- the- i.ln~ubsti:t.ut eo. alc.H::>hol. Th<:; :n,liture of the O•H barlds i ll t-hG c a:1.s~e oi: {t:tii.;fl@.ne b:Pomohydr.i:n and 2-me'tlu.'>x.y ... t \U -i.E.14-Uo l 1e thought to 'be ~uite the Bame as in U1e caee •of' ttl:iylen.e chlcrobyctr1i1~ 'tbt lOifo t're• quency band co:r1"~S_p1.itlda , ill ~ach int'/t.n'"ree , to a form ot' u1e molecule which i& etelatErta. In eth;}'..lene bl•omohydr.i.n a li;tdrojtll a l-l.}fdroten '·bond Joi11~ ther.., t\'i1'.'.l o~tg~u a t. 0.~.s,1a oi' tl:1€ iuol,e.<:t.ile. As. is $ho.wn in ]tig . 1 tlic z• (.l t,z:tive iute n~ itite. -of the ba:11c:la of' the t.hree bW.b9t.i tuted tl:'tb,it'l.Ol tiit <.:ha11ge r~l?kedl.J \~itl1 d~cr~ases ~ith ·t~rap~1" atu1~e , t1hile t..11~ ixrt-(llnei t;; o:r t htu dou.blet io1;u1d inc1~1&a!Ht(i w.i th ~mr,1er ~;1.t.ure . I Ac <:OL'-di.ng to .Bo.l:t. 1&maJ;1 n s p:t' .U').r-.i.ple ,the high enex·gy etate-e becom~ more popula.t.~o !!le the Tr1is principle when appliE:'-0 to the above ob&ti.':l'>vt.:t.tion imiicates that the !:t ioleeul-,tt· 1·0:rms col''• rei>pondi:.r;g to the lo'i'c frGJ ;,;,_ uenc~r 0-H ba.nd bf,rVe a lo\,; e:e i Ot~rrt.ial band . We might well expect th.ts ,for ,1n &<H'ier .:1 1, tlH;: :t' ;:;1•~1:ii! ation ot"" a l:V-dl"'og~n bond 1rrv 0lve2 a pot~.:ntlal E:nU,Zi d<-:::c:t"fJ.•.;tfH\'. ot' s,everal kiloc~tl.Ol"ies PU" ,'.U Ol.e . The chi~mge , WJ.th te.mp~,r a.tur~ , i:n the reL,tive int€rae.1tits o:t" th:~ bands of theirn th::.•fHi sn.fb~t 1tut.e d ~th~n:o..l.s . vm ulo ru l e out tr1a, idea that th~ n£•w b;1.nd &;;•fHl'r }l.:.r ing in the ~ubst,1. t uted the U € V'I b~nd or 1ginat(td t':r o.m a l·0\'-1' I.J·i:ug e~C i .~ fit".i st~t(J of the n1olecule , tb.e irrten$1 ty of' this b;ind would incre'.l.ae wi t.h t.em. p-e1~atm"e, however• , the irrt~niS :l.:ty of this b mnd actually decreases cor1"ee;f.JOrtciir1g t o th~i: ~i~ :in b E.ind, a lov'i f'r~ que,ncJ vibr•ation J.s t::)l{cited. ph1an1omen i.:.>rh 4 . J!etnyl acet;yie:ne .tur--nii.3 t1ea {'a.fl cx&tt~l).J,Vi ot C •• • - ·> '\ 0 > < ·tnl.e • I n -s uch a cr,.:i.s e, howevu· 11 the .i.:r:rt.~ns .... t.i ol' t.he b<1nd 1,,-w fr•e quency /irwl"E'. l;'.i.SE:·$ wl ti..: temp6J? . : . t u.re , and f 'u:::·tl:H.,:rm.o:.t·t a. cor1t11es,p ondir\g to el ,:bel,~rti :Jn occur$ at a .lower :t"t•e,~ueney in U.1e c,.;,.$e ot' et.hyl~~le bromohydrin tbru1 in th~ C :$t;;;£ o!' etti.y lene .. . tion h ands wi th max.b na at l0, 243 t;.nd 10 ,3h~5 CI.u-J. a u.d , PJZI•.b ;;;i ps , tion ~~he:re the by,.'ll:'o.ayl gr·oup t'o:rm& a x~·ctrog(i!:n bond Wl. th one ot the chlorine at. (. :;~ s ,'ii'l:d.1~ tl:ut 10,243 cw"" 1 baud cor:resp onds to a co1".i.f'igut>(1t.tion where th@ hydr-oY...yl hydrog€•.n is able to In t:ht latter situation atructural arrar}itmerrts with. resp ect to 2:"'Eil~tive r ctat.io:t1 about. the C• C b 0nda; so in discu.si~ing thta etructur•e of a ioolecule by hand d. The h-c 011figuratio11 corres yonds to the situation · where the orienta tion of ea ch c .2irbon a to:n is such tha.t. a p lane passing through the bo1id connecting a pair of carbon atoms and passing through one of the rema ~nirJ!s tetra.hsdral bonds of one of the carbon atoms 'Will pass through a tetrahedral bond of" the other car·bon. atom. •rhe d-config1..tration corresponds to the rnolec1,.;.lar form obtained :from an h-conf'igura tion by ma.king a rotation of 30° about each carbon-carbon bond. The distance between the oxygen and chlorine atom for a . given c,:mf'igura.tion of trimethylene chlorohyciriu s hould have an important bearing on the strength of a hydrogen bond between these atoms. F'or _examp lE~,chelation is entirely imp ossible in the case of the h-co n:figuration of trimet hylene chlorohydrin y.;here the 0:1\ygen, chlorine and the t:hree c ,irbon atoms all lie in a p lane because the oxygen-ch lorine distance ( 1.68 A*) is . so small th,:?lt only a repulsive interaction c ould occur. The oxygen-cLlorinB distance for othE r forms of th€: molE:cu.le which C(mform to the h-c onfiguration is too great for one to expect l'1yd.rogen bond formation. A twisting abollt the C•C bonds, which supposedly lead& to a potential energy incr€ase, -would te required to bring the chlorine .and oJcygen to a distance more f',.ivorable for hydrog a1 bo :.:.d :t' ormation. In the d-co.nfigu- ration,the; oxyge n-chlorine distance ( 2 .53 AK) would se Em to be a little small for hydrogen bond formation. The distance K Internuclear distances calculated assuming the tetrar.1.edr•al bond , m gl.es a nd the normal single bond covalent distances. in the case of o-chlorophenol, where we h ave a relat ively strong hyd.roge:n bond, is 2.98 A. One wo ... ld c erta.:Lnl.y .expect the oxygen-oxygen dista nce i'or a str·oug hydrogen b vnd . to be le6S than the oy..y·g en-chlorine distance i'or an e qua.11y st1~ ur:;g hydroge n bond since the chlorine: atom h as a t ~r·ea ter radi us than the oxygen at om. In dimeric formic aeid,where we have strong hydrogen bondirig, the oxygen-oxygen distance is 2.67 A0 • It would see1n th3t an oxygen chlorine distance of 2 ~ 53 A is too small for a good hydrogen bond, A twisting about tile carbon-c arbon b ond will lead to a more :favorable oxygen-chlorlne distance ,tut this may ha ve the e:ef'ect of counter, balancing the decrea se in the potential energy of the molecule due to for.ma• tion o;t· a stro1-.iger hydrogen bond by tending to increase tl1e potentia l energy on ac count of' rotation about tlle carbon-carbon bonds. The increase of~ ene1~gy due to t wi sting would not a.i11ount to rnore than three or f our kilocalor;ies per mole; hence such a n strained" chelated co:n:figuration should not ha ve an energy much higher than that of other p oss ible c un:figurations. The chelated molecules should ther €fore have an a_pprE.c.iable exista.nce at ordi nary temperatures and sho~ld s how up in the absorpti on s p~ctrum p:c ovi ded the fr 1;1 .ction of c h ela t e:d c,. mfigurations rela tive to all possible con:figur &ti ons is not. too small. Although there will be a greater nu;nbf;r of c cnf'igur·~ti ons wh€rein ther• E, is no ch€la ti on r e lative to the number of' configurations where there is cl.uslation in the c tw e of the tr1.methy lene h :ilogenohydrins thd.n ther€ wi ll be in the c :,.s e o:f the subs ti tJ.ted alcohols / previously discussed, it would seem that thE:re: should te an appreciable fraction of' chelated f'orms in the 1""ormer case. According to the above it might be antici patt:d tbat onG '\i\'.D Uld obtain spectroscopic ev J.dence of chelation t o form a six-membEH'€<.1 ring in the c as € of' triraetJ:1ylene chlorohydrin Ll. .nd tri.ra«:thylene br omohyd.r in. The micr~opl:,.otometu· curves, however, du not give evidence of an additional co:nponent O-E tand 01· somewh at lower frequency than the normal u,.,ublet band. A photometric investigation of the e1~fect ot· cl.H.:i.I'.lge in temperature on ths. b c1r.lds of normtal propyl alc oh ol, ethylene chlorohydrin, and orth.ochlorophenol was made. menta l procedure is t he t ' ollO\'<' ing. rhe experi.. 1 The t.e,iuperatUl'e of' the absorption cell was held constant by fixing the voltag:e across the resista nce furnace and the temperature: was r·ead from a. ther~mometer inserted in a 'IJl,ell at the midsection oi' the absorption cell. It is estimated that the corrected thenno• meter reading gave the tempEr ::tture of the absorbing vai.,or within tr.i.reE:. or four degrees •. F..aving t'i>::ed the temperature of tlie vap or of' the absorbing sub~tance 1 tht- absorption sp€ctrun1 of this c c,mpound v,;;;.s taken at a series of diff'erent v 1_por densities of the substance. The pressure of the vapor was fl.xed by maintaining the temperature of the trap connected to the absorption tube at a constant value. This temperature was ~lwa.ys lovier than the temperature of the absorption cell and an excess of li quid v.:~).S he:.ld i:Q. the trap. With this arrang ement whenever equilibrium is established one .knows that t11e pressure of' the v.e.por in the absorpti on cell is equal to th t vap or press.ure o:f.' the liq uid i .r:. the trap. The sy stem was allowed to stand ;:.,t a fixed temperatWI~e :t'or over an hour before an exposure W i.'l.S m:ide in order to insure the attainr.nt.nt of equilibrium. In the case of' the o-chloro- phenol experiment's the temperature of the liquid in the trap • was fixed by employing a v-;ell agitated oil bath whi ch could. be kept at a. temperature which w~s constant within two .. tenths of' a degree., The f'irst pa.rt of the series of" exp osures, each of which corresporlded to a de!.. inite va por density, w:,s taken with the , temperature of the vapor in the absorption cell a little above the temperature corresp onding to the boiling point ofi the substance. Then exposures were taken with the temperature o'f the vapor seventy-five or one hundred degrees higher. All of the exposures were taken with an equal exposur~ time alld with equal intensity of the light source. When the temp6ra- ture of the absorption cell 1/i ,"'s brought :from the lower tempera• tur·e to the higher temperature, there was a tendency :for the. part of the optical syst-em which Vias held ir1 the re{;).iJstance furnace to become slightly displaced on accou.nt of thermal expansion. This nee es s i ta ted a compensating adj ustrn<L,nt of' the :mirror directing the beam of light to the slit oi' the All exposures of any such series were taken on the same photographic plate. This is important because then all exposures of a series are made on a photographic plate of' the same sensitivity and ar·e subject£d to ide ntical c ondi- tions of photo&,"'!'a,Jhic developm, nt. The e.qual exposure times, equal intensit.Y of iL.umination o1' the slit, equal c ur:.ditions of sensitivity and development lead to a uriif .:,;r mity in the photographic image of the s pE- ctrum which is essential for the photometric method em:ployed., Microphotometex• cu1"vE-rn oi.' the absor.. ption spectrum. corresponding to eac h of these exp osures were obtained .ke eping t.hemicroph.otorneter sensitivity and zero settings th '-- sarne through - out. The microphotometer employed was a Kr\iss instrumer.i.t of The goal of uniform exposure vn:LS not. comp letely' attained, a.e the: backtT0und blacke rd :n g was shown by the mierophotometer to var ':/ som€what. This was probably largely due to the fact that in readjustment of· the mi r ror af'ter the b€t.Un had been. slightly displaced the slit was not illuinin a ted exactly the same a. £ It is believed that before. the dif:ference in backgr ound blackening in a giv€n series of exposures is not great enougli to 1nvalida.te the :photometric method which will be described in thei next s ection. ----------Photometric Studies Figure 3 gives a ty·piea.l pair o:f' rnicrophoto.mete r· cui·ves which show the efi'6' ct of.' cha.nge in temper :;l,ture on the int.ensi ty of the third h armonic O-H absorption bands of o-chlo:r-cphe:nol. We will now describe the photometric method of studying the effect of temperature on these bands. The photoriietr ic experi- ments are carried out as desc:r•ibed above. Eat:h exposure on the pld.te corresponds to an absorption spectrum of o-chlorophenol v a t, or which is at a given :pres.sure and at a given tem- per;,i.ture. The microphotomtter deflections corresp ondi r.g to each of the two abs0rption bands (A band at 10,443 cnt 1 and. B band at 10,189 cm'"" 1) are measured fr 0m the microphotometer trace of ea.ch absorption spt:ctrum photograph. 'l'he measure.. 0-CHLORO-PHENOL . l0,500_ Figure 3. tm- 1 Microphotometer curves of the 0-H third harmonic absorption bands in the vapor of o-chlorophenol at tvrn d.if'f erent temperatures. me.nt of the microphotometer deflection c 0nsists o:f measuring on the mi c:r·ophotometer tra.c e the he 1.ghth of the peak of' the < \ absorp tion band above the line cer:respor.iu.1ing to backgl•ound glackening (no absor·ption) .. The miero.;phot. . . o mettH". <lef'lections . • ' ,· . ·' (DA) Ti and (D1)T corresponding res1:iectively to the· A and B 1 bands, for all tlie exposures made whe:ri the o-chloropheilol vapor was at the temperature 1r 1 are plotted on the same gr·apl'l against An example of such a plot is given the pressure of the vapor. in F'igure 4 •. Let (DA)Ta· and (DB) Ta be values of the mi<!rophotometer deflectio ns for an exposure. t aken when the o-cr.i.:lorophenol vapor was at the temperature T2 3:~ let PJt be the pres~'l4'"e· wh.i ch corresponds to the va lue (DA) T 1 ;: (Dp) 'r~ on t.b.e (pA;)T curve plotted from data obtained. at T1 • 1 pressure Likewiee let Py be the pressure which corresponds to the value (D.B)T 1 ·.::;. (bB)T 2 on the (DB)T - pre.ssure curve plotted. :from data obtained at T.1. • ., ' 1 . If certain reasonable assump.· tions hold 1 then I it :follows that ~ E.'0 ::.: TT PX :goA·. • -13 Tl'~. . :;i ~ 'R l n...-:• Tt •T,:~- - py ( l) where a E.0 is the dif't'erence in the thermodynamic molal internal e:nergy at standard conditions of the two molecular f 'O:V-ill5 cor ... res pondi:ng to the A. and B bands and where n is the molal gas constant. By finding the values of Px and Py fr om the micro• photometer traces correspondi ng to exposures t aken at T1 and T2 and using formula (1), I). E0 was evaluated. The principal assun1ption upon w.Lich the above formula is b.:.i. sed is thS1.t the microphotometer deflection corresponding to either one oi' the bands for a series of exposures taken on I 0,189 BAND 6.01------l---,----+-------;-----,---------. D 2,0 400 600 (mm. Hq) Figure 4. Plot o:f' the microphotometer deflections correspond- ing to the A band (lo, a43 cm- 1 ) and the B band (10,189 cm- 1 ) in the vapor of o-chlorophenol versus thE total pressure of' tre vapor. The data was obtained from a series of exposures taken on the sa11e photo~--raphic plate and during each eAJ) osure the vap or was at a constant temperature T1 • the same pla te is solely a !'unction of the number of molecules in the absorption cell which are :in the conf'iguration correspond• ing to the band under con.si derati0r"" ThE. micz•ophotometer deflections should be independent of the intensity et: · the source of' radiation, length of pa th of absorbing va;)or, illumina• tion of the slit and the exposure time since these possible varia bles a re held constant thr,)ughout a series of ex,posures. Since all exposures are taken on the sarne photo&Taphic pL:.ite, there should be uniform sensitivity of~ the emulsion and uni• formi ty in the developmu1t or the photogra phic iraa.ges cor- r·esponding to the absorption spectra. l:i'urthermore in obtQn... ' i1.1g microphotometer 'traces of the absorption bands the zero and the sensitivity of tl:Le microphotometer is ltErpt constant while obtaining the re·c ords of bands for the entire aeries of exposures on a g;iven plat11;. As a result, the bellavior of the ,:nicroph otometer sh Juld be unchanging and the position of the recorded i.ina.ge of the quat"tz fiber of the microphotmneter elec;t.rometer should only depend on the dem~i ty of silver in the photographic image o:t· the absorpti.011 spectt•um . A quantity which can affect the observed rnicrophotometer deflection is te111fHllr~-ture,for,ii' an absorption band becomes broader at a higher teinp~.rature of the vapor but retains its original intensity, it wi ll h ave a smaller microphotornete:c deflection, i.e. the vertical distance on the .micr0photo:11ete r· curve from foot to the peak of the band will be less. It is believed th:,:. t th.is e:f'fect ie small enough in our exfl E:,l"'iments to be ignored. The _situation being ae described, the only quantity ,uhich will det\frmine the m.agni tude of the microphoto~eter def'lections corresf ondin.g to a given band is the number of' molecules in tl'.le absorption cell a t the time oi' e:xpuure_ which are capable of absorbing light of the f~e quency oo:r"'resp onding to the ban.d. A mathemdtieal just if ieation o:f equation (1) will no"', be g.i.ver.i. Let n A = No . of molecules per cc. in state A (trans form) of o-chlorophenol. n B = :No. of molecules per cc. in sta te E (cis form) of' o•chlorophenol. DA -= micronhotomete.r deflection corr€spondi ng to r the A band D5 =- microphotomete r deflection corresponding to the B band. By assumption: These expressions mean that for a given series of photo• graphs o'f the: absorption spectrum ther E is an. unchanging tune• tional relationship betw~;en the rnicrop;t1otomete:i:· deflection ·and the concentration of molecules ·w hich corres1-1ond to a given absorpti on band. This functional rE:lationship depends on the behavior of the photographic plate at the frequency in question, upoz-.i the shap e and width of the band and up on the transition p robabi l ity corresp ondiri..g to the b ..1r...d- as th{, intE>nsi ty of the l i ght s ow:·ce, illumination of the slit, setting of the microphotometer .: lr (: held c _,nstarrt. Dependence on the photographic proc.eS:s is eliminated by the u c e ot· a single photographic plate for a g iven series of' e:,:posures. Let P :::: total pressure-: of o-chloro;phe:nol vaf or. To the approximation that o-chlorophenol vapor obeys the perfect gas laws we have, at the temperature T1 , that: nA :: cAP wl1ere c A and c 8 are constants at th e given nB :: c pP .c, temperature SuppoEie (DA)m Pa and. (DB)T·2, P· a are the microphotometer de:t'leetions • .1.2 , for the A and B bands co:r·respondir:i.g to :a.n absorpticn· s;pectrum of the vapor taken at the temperature T2 and the pressure P.2• Then using th-e curves obtained from absorptiol'1 q'.i ectra 1;hotoe;;-raphed with the vap or temperature was T1 ( see F'ig. 4) one (D ) .. Since A Ta ,P.a • That is, the number finds t h e pressure Px at -which nA = 1.'A [DA]then ( nA7T 1 ,Px. = of molecules in the absorption cell in state A when the temperatUl·e is T1 az:1.d thE. pressure is Px is equal to the number of molecules in state A when the exp osure is made. at the tem• The concentration of mole ... perature Ta and thi: pre.ssure P:a• cules in tht absorption ce·ll in configuration B .:it temperature T2 and pressure P2 is given by ( n ..b,)T27 p ~ = C~·,Py·~ whert Pvis .ti> i. the ·p ressure corresp onding to the v alue (DB) T1. ..: (DB) Tz ,P,:i on the DB-pressure curve (Fig. 4). The concentration of' molecules in f'or·m B .c:. t the temp 0r .x ture T1 and ;iressu.re P x is given by ( ..... ell x B)T1 P ' X ( n A) n n ~ra ,P.Q :::. p .By C ( f\ A) p cB.P ~ ~ --- X n BT1,Px Let us cunsider the reaction o-chlorophenol o-chlorophenol • ois form tx.. ans f c;rm (corresponds to b band) (corresponds ;to • A band) L.aploy ing the thermodynamic s yirib"ols used ty Lewt~ and Randall we can write /1 V - 0 thus it follows that also ( Q.1.!l.15) d P T :::. 0 Furthermore 1 oln K) P ;;. \ d 17T thus (1) In the employment o.f the above described method for the evaluatio n of t!:i E0 , there are quite a. few :p1a<:es v;here -errors can creep iti. The illumination of the slit may not have been quite the same for all exposures, t~i e photographic plate may not have been sensitized or developed t1uite uni:t'orraly or th:e microphotometer ,lfi,~Y have shown a slight cha nge of behavior with time. A large unc-ertainty a.rises in the measurement ot: the rnicrophotometer de!lect,iou on the microphotometer plates . On account of th€ irregu.lal'' nature of' the mlcropboto-meter cllrve, d.ue l a1~gely to gra.lniness and irregularities of the photograpl1ic plate, it is difficult to decid.e upon the true height.' of the peak of am absorption cu.rve above the f"dot of the cu1·ve. A band. 'l'hi 1.: :- is particularly true in the ca~e of tl:16 weak The accuracy of measurement of tEe m.:i.crophotometer def'lection corresponding to ,the A band is de·cisive in determining the accuracy of evaluation of C1 E-Q . The error may be a s much as twenty pe:rcent. The difference :ln the free energi ~s of the t wo 1"orms o'f o-c l;.lorophenol may also be evaluated if, for tht series of ex1Josures previously d(eSCribed, thei f'unctional re;l a tionship between the rnicrophotometer deflection and concentratio11 of molecules corresp onding to a given bt:U1~is identical for the This ou.ght to be true if the f olJ.ov'l'ing conditions hold: ( 1) the behavior of the photograr,hic plate is the: same at both band fre quencies (2) the shape and vi'idth of eaeh band i s· tlle same (3) the transition probabilities of both bands a.re the same. The first condition is fairly well. satisf'ied because Z plates whose sensitivity is practJ..cally constant with wavelength in th.is region, ·were 'i.lBed. A cousi• deration of the microphotome 'i:, er curves of ·t he third har;oonie 0-H band of o-chloropb.enol obtained by Badger and Bauer2 indi ... r cates tha:t the second c ,;)ndi tion h c lds to a f'a.ir a 1:. .,proximation, The studies ot· Wulf and Lido.el7 on the sec ond harmonic O•H b-a.nds of o.. chlorophet1ol dissolved in CCJ.4 seem to indicate tha t the transition pr-obabili ties .tor the A and B bands a.re about e qual. I:f this also holds for· the third harmonic bands , then ., the third condition is satis fied• It is seen that ~e have reasons :t'or believing that the functional relationship betVhU'l the microphotometer de::t'1ection a.."ld concentration of .molec... .1€s corresp onding to a given 1:'-..and is approximattly idem... tical for tl1e A and B bands of o•ch lorophenol. In the ideal Et .i.tuation, wti.er€: t he functional relationsh i p s are ident i ca l, suppose s equals th€ factor by which the absc i ssa of the DA curve must be reduced so that the DA curve will c oincide with the n13 curve (see Fig. 4); thens will eq ual the ratio of the concentrati ons oi' the two rnole:cul'il" spec i es. LE':t us consider a n1,:1thematical justif'i cation of' the last Now s ta teine nt . nA :;: :f [ DA ) ·( 2) where f.' in each equation denotes n B ;:;;: £ LDB·1 ( ~3) the same function. Let NA = mole fraction of molecu h s in the trans form N - ;nole f'raction of molecul(~S in thE- cis form ~B PA - pressure corres p,):ndir;g to DA = DA on the DApressure curve (Fig, 4) PE• ::.: press-..1re correspondL:;g to D ~ D' ;B -. 'E in the DB- pres s:.1re curve. n A = 11 B OCC O l'" ding but/ to the perf' ect gas laws pt nA and n,._ b ::: k = Boltzman's constant _JlN kT1 A T 1 = absolute te:mperature Pl = kT1 ~~B _; of' vapor when absorp- ;'-T tion spectra. were photographed but pt A s - pt ~13 !{ow accordi ng to thE:rmodynamics • • A J:i'O :;;; R'f' ·-, 1n' but - -1 . ,,• (4) ·we repeat that e is the :factor by which the abscissa of the curve corresponding to the 10 443 crn"'" 1 band must te reduced 7 in order that this curve coincides with t he ctJ.t•ve corresponding to the . 10i189 cm-l barid (see Fi&,'Ure ♦). . ·b. 1,o0 is the di:ff'erence in standard :fre:e e11ergies of the trans and cis f orms ot· o-chlorophenol and :11 is thE gas c onstant. Employing equation (4) one can easily calculate D. :F'0 fr o.ru the photometric data plotted as in Figure 4. This :mtthod of calculatlng Ci I•' 0 involves additional aS$Umptions besides those made in the c a lculation of A E0 , but the previously men... tioned uncertainty in the v :1lues of the microphctometer deflections probd.bly outweighs any of· the other uncertainties. E~perim.enta l Results of' the Photometric S.tudy-2.f.·. Qrthochlorq• Three preliminary photometric exi )e;r-iments I, II and III and two more exte nsive experiments 1V and V were at:.ide on o• chlorophenol. The data and experimental results ar-t i g.iven in Table II• An Average o:f &:everal e:x:per.l.m.ents gives for o-chlorophenol Table II I -~;;--r -! 8 • 56 o .?3 o.83 64 2 o .16 :-:-:7e-~;-~~ ., ~ I 459 ! 5_o_ _______i _.__ 539 _ _l___ .... .... _ ----- ·-· ~ : ., 457 o.9o 2s1 i l o .49 i ____ _ __ !__3.5 _L_2 ,_6 1 - 146 -. 458 282 458 334 i : - I I l i 540 -,------r--~-· ~ ' \ 8 . 41 460 1 i ?S.3 i l :60 o. sa A • 63 4 . 20 o.a? 4 ::i l 201 462 638 I ·1 .. ,. --~··---· :___ _____.,,. ____ : r ------- •·•r·--------------"·'" ·---- ..... ~- r·~····-··-··-····•· . -i 1. b'~ .t..00 i 22 . ti 0 . 48 ! l t Lx.pE,rim€nt IV .. ·),_, • 2·· ---- ·-- i , ----l -:::: - l--::: -,- --::: -r----,-·· -·-·-·- 1 x-J-) e- :.~ u .4 o 11 4 •3 l o. 94 o. 56 4 10 I b xperiment I I • l r.· • o 0r· r- 4') I_,. ,I .J v . ,:;i , - - --~ - - - - - - < - - - - - - -~ /_____________ I o . 96 1_1._ ; 453 2~~---,....------------- --- 4.8 l I -I Table II (continued) D A DB cm. cm. p 'l' 0 K LP kcal :run Eg mole ! :L.xp €r iment V ! ! 0 . 30 1 . 75 0 . 50 3 . 10 0 . 62 4 . 42 451 0. 91 6 .39 4 50 1.60 A5.1 \ l 450 450 I I .I l FO kcal mole .. ~.--..,. - ·- 36 . 7 78 . 5 166 l Il ! r l 314 lI 676 !I 0 . 70 3 . 25 537 4 .5 I o.Go 2 . &'7 f:>37 4 .6 o . 58 3 . 14 537 l :i ~ 'i I 3 .6 I I I I 1 Ii D.\ .i:-L 2.7 _.,~--- = MicrophotomE:ter d €:f lee ti on cor res p onci.i ng to band a t , -1 . .Y . :, .) C.u1 1 0 ' ,t14,:, - MicrophotomEte:r deflection corre sponding to band at 10 , lS-~ cm-l T -= Tc:mp eraturl? of o-chlorophenol vapor in absorption c ell P = Pre&S,i.lr·~ of o- c11lorophenol vapor in a ·bsorption cell ' 1 6 E0 = 3.~ kcal./mole and fl F' 0 :: 2.8 kcal./mole (at 180°C) where these are: energy differences between tht. cis. (che lated) and trans (norl-chelated) forms of the molecule. As previously discussed the accuracy in measurement of D is not V€ry great; , . • A p~ consequently the uncertainty in th~ above values may/a.a much as twenty percent of their given va lue. ~.Qj&metric .Study of N•PrOP,t'l Alcohol and Etgylene Chlorqh;:Ldrin It was found in the study of n-propyl alcohol that the change in the r atio of the intensities of the doublet band was within the uncertainties imposed b_y thEt n.1ture of' the experiment. F'rom this it may be estimated that the u pper l imit for 1 E0 • f'or the t·wo hypothetical c 01.figurations 2 is about 0.8 kcal./mole. Ethylene chlorohydrin was studied in a rnar.J1er similar to o-chlorophenol. In this case, one must co:.nsi_d er t hre ~ m.iero- photomet er deflections DA, DB and De which correspond respectively to the .maxima of the doublet band at 10,546 cm· 1 and 10,485 cm.. 1 and to the band at 10,367 cm.. 1 • 'l'l1e difference in the energy of the molecular con:figura tions corresponding to the normal doublet band and the configuration cor·respo:nding to intra.molecular• hydrogen bond f ormation was cal culated. The data and results of two photometric expt:rim€nts on etbylene chlorohydr i n are listed in Table III~ An average value of This v alu e is subject to an uncer- tainty of ,perhaps,twenty :percent. TablE III ~r Photometric stud:; of etr:y1enE chlor-ohydrin D,\ c~ . I D-- cfil. l Experiment I I T 0 K - - - - - -- ---- p u1m • I . ll.? ------ ---·- --·--------- ·-·---·-- r 1. 00 1 . 61 2 . 87 425 I 490 1 . 22 1 . 8\) 3 . 2~ 425 I 646 425 ) I l 2 . ~6 2.05 1.42 I 4 . 90 2 . 22 2.GO i 5:;1 ; i kcal mole Hg I I I 1048 i I ! i I / ; ! ------ l . '0 -·-··· T~ Exp er im€11t -1 A - • • - - -- 1 . 00 1.72 2 . 87 -- 420 i 417 I i : ?Of; iI 1120 ! I 1. 65 3 . 99 2 . 40 42 1 ; 2.29 o . 8? 3 . 42 1 . ~12 5 . 12 ! l 1 . 70 421 5 16 !I I ! 2.1 DL\ = Micr-ophotometE.:I· cie:flE,ction corres _ pond.i..ng to absorption . . -a maxirm..:u:i at 10, 546 cm- 1 D-. - Microphotometer def lee ti on c:01Tesr;or::.d.1.r.g to absorpt ion ,t:'; maxirnu.u1 at 10, 485 cut 1 De ;;;; Microphoto:neter dE::f'lec ticn c orrEsponding to absorption maximum at 10 , ::;67 cm- 1 T - '.L'empera.ture oi' eth;,rlE:11€: chloroh,yc1riu vap or in absorption Cell P - Pressure of the va 1.ior in the absorption cE:11 . Di§~ion gf the. H~sults o:f the Tem12.§.rature E:t'f'E:ct :::,tud:i,e_§ The value of .1 FP for o-chlorophenol ,which corresponds to the ener gy of the i11tramolecula.r hydrogen b c,:nd :formation, appears to be related to the frequency dif'f'erenee o:f the two bands obsel~ved/in the· mar.mer which one would expect f'ro.111 the relation betwten fre quency shift and interaction €nergy pointed out by Badger and Bauer8 . This relation also seenii, t o apply to c a.se of eteylu1e chlorohydrin ,al though A E0 in t 1a s case involves the dif'fere11ce in the c -Cl and c"".'o dip ole interactions as well as hydrogen bond energy. It is a little di:f':ficult to be certain concerning this p :.:• int but it appears that the oxygen-chlorine hydrog~n bond is in the case of o-chlorophenol than it is stroriger/in the case of ethylene chlorohydrin. One might exp ect the hydl"ogen bond to be stro ~ er in the i'brmer ca s e tecaus,€ in o-chloro~:J1enol WE h ave a quantum mechanical resonance which tends to increas e the .:i.onic character o:f' the 0-H 'bond. c~mtributio11 fr 0m the res~nane: e form should especially enhance the electrostatic interaction between the hydrogen and chlorine a.toms. The vaJ_ue of A l<' :.: 2 .8 kcal/mole ( 180°C) is to be c ompared with A F = 1.4 kcal/mole calculated by Pauling1 f'rom the data of Wulf~ and Liddel6 on the second h armonic bands of' o-chlorophenol dissolved in c arbon tetrachl oride. Since t.b.e O•E in the trans position will have a slight interaction with the solvent molecules one might expect the 0 A 1'1 for o~chlorophe,uol in solution to be a lit t le lE:ss than in the vapor, hov;ever,, the difference in the two values S<Eem;Si a bit l arge. to microphotometer curves of Badger and Ba uer2 the A band appears to be a little broader than the B band. 'l'his should have. the 0 effE,ct of m1:1king our estimated v aluE: o:f A Ii' a little high. The v ~1.lues of 11 E0 =- 3 .9 kcal/mole and A li'0 = 2.8 kcal. /mole f'or o-chlorophenol give the entropy difference as 2 .4 entropy units .. 'l'11is mtans that the trans configuration of' o-chloro- phenol has the h1.gher entro py v alue. When one co:nsJ..du·s the plot of the potential energy of the molecule against rotation of the hydroxyl hydrogen around the C•O bond, a sha.llo\ver and perhaps broader potential minimum compared with the minimum for the cis form seems reasonable :for the trans :f'orm of the molecule. Applying the ideas 01· stt.atistical mechanics i:n a qualitative wa;y .,we decide that we would ex9ect a greater entropy to be associa te:d with the trans form of the o-chloro phenol li'urthennore the interaction o:f the h.rd.:i:•o1¾'tl hydro- molecu.le. gen with the chlorin~ atom rnay increase the C• Cl bending This would tend to , :further . increase the _entropy frequency. o1" the trans form \\i th 1·espect to tht cis form. Q . ~ of Im2ottant Point~ Points of lrnportance 0 1· interest a.rising f'r0m this research. 1. Evidence :for intramolecular hyd:rog€n bonds has . . beE:n found. for s everal substituted alc0hols . 2 Badgcr and Eau.er , J. Chem .. Phys. 1, 711 (1836) 3 Ba.rcl1ewi tz and FrEymann, Compte rendu. ~ , 1728 ( 1937) 4 Herzberg, Pat at and Ver leger , J. Phys . Chem. il, 1:2:3.. 32 ( 1937) 5 wulf', Liddel and Hendricks, J. A. C. S. 2.§, 2287 ( 1B35) C 0 L . Pauli1ig and L. o. Brockway , Proc. Nat. Ac:ad . Sci., gg, 3:36 (1934) 7• '.f,.U 1-P :i. 8 -.en d L,l.u.ae • . •, 1 , d.... • A • C. • C ~ • i-·7 1464 (1835) f?...., nadger and Bauer , J. ChE:m. Phys. Q, 87-~9 ( 1837) Slllll1B¥Y . In the paper entitled The Band Envelopes of' Un$y:~'Unetrical Rotator It{olecules . I, Calculation o:t' the 'l'heore.t ical Enve- lo:pes,,,:. the env:clopf;, S of the three elementary types. of band h a ve be en calcul1.ited by an appro;.:.J.mation method for nine di:ff'erent sets of' molecul. :. r parameters . Thi£, wo:rk cons titut,es t he f irst calculation of' the theor .; :,tical envelopes oi' unsymmetr i cal :uo lt-Cu.le s. The calculated envelopes arE o:f' a~sistance in interpreting the observed bar.d b of heavy unsymmetrical molecules. A rotational anal.isis o:f the third harmonic 0- H bai1d in f ormaldoxime, vapor was m.ade in the ...r:ubl ication ~--------~ An A.bsor·o+ i on ..... Banc!. of F·ormaldo,xiu.1.e at ;... 9672. T-he information,thus obtained, regarding the moments o,f inertia o!" th1:: molecule whl n combined with data obtainE:d :from t'lectron diffraction measur·emefits will probably be oi' assistance in locating the position of' the hydrox,,-cl hyd:rogen in the molecule. Th€ a ppearance of' the absorption ba:nd indicates that the 11,ydroxyl hydrogen doe.s not r otate i'reely about the N-0 bond .. 'I'he Investigat1:.2n of t h e Th ird E.,u•mo.rLLC O=IJ Band Qi" Sub- _ sti tuted ____ .......,..__ Alcohols _.,.,_"~-....._._gives succtrosconic ... . evidence i'or intramolecula r g;:'ilce s hydrogen bonds in thE: c a se of~ several substituted alcohols. A chr1.nge 1J.i th temperature of the r E: lative ll1t€nsi- ties of the two bands o:f o-chloro.i, ,henol wa s ob20r~vEd. f'o:r the :first time. Th€ direction o:i"' the chfu:;.g·e is in dgr;;:ernent with the exp lanation (b~ L ... nus })ciuling) for these tw c, bands. The photometric st~dy oi' th£ effect .oi: temper .~~ture on th€-. 0- H bands of ethylene chlorohydrin and o-chloropl1enol i~i\/;.':.;;, thE; correspondtng €nergies of intramolecl.lL:tr hyd:r-ogen b0nd i' ormation and also th e entro ,.y differenc€ of the cis 3..nd trans forms of o-chlorophenol. .la,SB strongl; i.n the b.f'.l.loger1at0d file ide o!' erit,H:1.ne~o. a<d.,l t:rtret:i jftli thl-il'.l 1:n tht non•lH!'.lor:r-e1Ja,I,; .,_A a,,,, 'i ,,i,, ~· '-"'...,_.V .~ ...... ~~ 1 ,;, -~·"'"' '{ ","" '~,;·.: .,...·1_,··• ,,,:,,t -.. ·, ~., ') ,;; "''' ·" 'I" r~•!>,.• <',, ,.,,,...,1 .. -~· :;~t.;v u ... ~ 1:-t~. WJ.. ~~;p_..t ~ • · .fJ the 6 a~eous fil.tate. A slt.ght. ex:t~11e-ion ot J'a:i;::-bx•e:the:r ' a"'' tr~t~.t ment int:lic:~®;t,tis th~t is r1ei£-r.t:t1ve 3 :t:'o.l" iliftseoue. ii' (d)""/~):re HCl tJ:tGn (ar/dr) re iG po~i tive for HC l i:n a olu:tion. 1 . 15B;t~,. nsv .t. 4 9 , ~i1s ( 1&36,. A -v I v w111 be proportion;il to tbe enE.:r_gy of ir-,teI-act.i<.u1 for a epfi:cial i.'o:r·1n ot: I) but 1n gener,Ta1 ntHtd .not bt: ♦ . . :f 1 ln-r1N1 ,.;:: 2r.~ } [{· '" ,.., ~ -1 i T + {· ,.,. }'j ~ p T 2. SJ~ ;i,i ·~ t.hus acc t)rd.:i.2~ t o th~ 1,! irsky ...,Pau .i..ing.a pieture of oen"',.t.uration whid'i in bot.:h the upper ;:1nd. lo'trer S;t, ::a.t es , cor re.epondir~ to the Jl• H b&nd ,a low; fre quency vibration is exc 1ted.