Normal coordinate treatment and assignment of fundamental vibrations of vinyl chloride and the seven deuterovinyl chlorides

JOURNAL

OF MOLECULSR

SPECTROSCOPY

27, l-16 (1968)

Normal Coordinate Treatment and Assignment of Fundamental Vibrations of Vinyl Chloride and the Seven Deuterovinyl Chlorides 11. ZAKI EL-SABBAN*

AND

BRUNO ,J. ZWOLINSKI

The assignments of the fundamental wave numbers of vitlyl chloride and the seveu deuterovinyl chlorides have been reinvestigated on the basis of a normal coorditlate treatment with a valence force type potential function. A six-colrstallt ollt-of-plane and a 25.constant in-plane pot,ential function reproduced the observed fundamental wave numbers very satisfactorily. The presellt calculations remove the violations to Rayleigh’s rnle in the hitherto adopted fundamc~ntal assignments and give reliable estimates of the urlcertait) 01

lurohserved fundamental wave numbers. INTRODUCTION

The infrared absorption spectrum of gaseous vinyl chloride (l)-(

5)

and the

1Caman spectrum of the liquid or gas (I), (4j, (G)-(9) have been the subject of several investigzkions that started as early as 1930. Similar data also have been reported more recent,ly on all the partially deut’erated isotopic species (9)--( II) as well as on the trideuterated derivative (IO), (12). A partial normal coordinate treatment, \\-ascarried out for the in-plane (13) as well as for the out-of-plant (I,$) vibrations of vinyl chloride. Also, a normal coordinate treatment MM carried out for trideuterovinyl chloride (Id) with a Urey-Bradley type field. This treatment predicted a value for the lowest, hitherto unobserved, in-plane vibration. I.at’er, the reported Raman spectrum for this derivative (IO) showed that t,he predicted value was t,oo low. At the time of the present investigation, no normal coordinate treatment was reported for any of the partially deuterated members of the series, and the existing assignment of the fundament’als of these molecules was based on the available experimental data. This invest,igat’ion w-as undertaken to reexamine all the available vibrational data and reassign the fundamental wave numbers on t,he basis of a detailed normal coordinate calculation involving all eight members of the series.

* Preserlt address: IY. Y. Bureall of Mines, 13’38, Bartlcsville, Okla,homa 74003.

Bartlesville

Petroleum

Research

Center,

Bus

EL-SABBAN

‘2

AND

ZWOLINSKI

While the present investigation was in progress, a paper on vinyl chloride and its deuterated derivatives by Enomoto and Asahina (15) appeared. The main purpose of that investigation was to show that certain reactions would lead to a selective preparation of some isomers of the partially deuterated compounds. As a part of that investigation, the authors carried out a simple normal coordinate analysis for certain compounds of this series using a Urey-Bradley field. These authors did not obtain a satisfactory agreement between the observed and calculated wave numbers. Furthermore, they did not settle the question of t’he complete assignment of t’he 72 in-plane and 24 out-of-plane fundament,als of the eight compounds of this series. Recently, after the present investigation was completed, Kukina and Sverdlov (16) published the results of a normal coordinate treatment for the present series. Inasmuch as their assignment, based on the results of their normal coordinate treatment, is fundamentally different from ours in many respects, it was still felt worthwhile to report the results of the present investigation. OUT-OF-PLANE

VIBRATIONS

1. NORMAL COORDINATETREATMENT All members of the series belong to the C, point group, having only the plane of the molecule as a symmetry element. Each molecule has nine in-plane and three out-of-plane fundamental vibrations, all of which are allowed in both the infrared and Raman spectra. The three o.p. vibrations for each molecule could be described roughly as CHCl wagging, CH2 wagging, and C=C twisting modes. The corresponding internal coordinates for these three vibrations may be taken as (see Fig. 1 for numering of the atoms) : RI = Ar,

(146),

Rz = A-Y,

(2351,

AT, represents the change in the angle between the CHCl plane and the C=C bond; A-r,, the change in the angle between the CH2 plane and the C=C bond; and AT, the change in the angle between the CHCl and CH2 planes. The G-matrices have been calculated with the molecular dimensions given by Kivelson, Wilson, and Lide as a result of their microwave work (17) and with masses of the atoms based on carbon-12 (18). The F-matrix of the o.p. vibrations is given in Table I. With the six independent potential constants we managed to obtain a least squares fit of the 24 o.p. calculated wave numbers to the observed ones. We started by tentatively assuming the nine assigned fundamentals of CHz=CHCl, CH-CDCI, and CD2=CDC1 to be fairly reliable [see Ref. (10) for summary of these assign-

1.INYL

H'(3)

C(6) \

H*(l)

H"(2) FIG. 1. The virlyl chloride

molecule

ments]. We then obtained the set of potential constants that reproduced very closely (within about 2 %) these nine wave numbers. This same set of constants was then found to reproduce equally well the other fifteen wave numbers of the remaining five members of this series as assigned by de Hemptinne et al. (IO, 11) . This result shows that this set of constants is appropriate for the o.p. vibrations and also justifies the assignment. The perturbation program then was used to refine this set until a reproduction error of much less than one percent wa,s achieved. The calculated values of the fundamental wave numbers of vinyl chloride are given in Table II, together with all the observed values. A most probable set of fundamentals based on these data also has been selected and included in the

EL-SABBAN

4

AND TABLE

THE

F-~\~ATRIX FOR O.P.

ZWOLINSKI I VIBRATIONS

OF THE

VINYL CHLORIDE SERIES

TABLE oBSl~;RVl:D, C.4LCcL.4TED, AND

PROBABLE

NUMBERS

OF

II

V.4LUES

VINYL

Raman (liquid) y-

Y,O

0.P.

FUNDAMENTBL

VW

KB

EB,

903

915

909

908

901

614

605

610

620

623

-

WAVE

CM-'~

IR (gas)

W;1:’

-

VI1 VI2

OF THE

CHLORIDE,

WU*

TTg

CTh

935

940

942.5 941

910

895

896.8

896

617

622

-

620

Calc.

PVk

3

943 897

944 1897

943 897

tw ulp

620

621

621

WI

GiYa

Vi

values are rounded off to the nearest cm-l. * M. Pestemer (6). c W. West and nl. Farnsworth (7). d T. Y. Wu (1). eK. W. F. Kohlrausch and W. Stockmair (8). f J. C. Evans and H. J. Bernstein (9). g H. W. Thompson and P. Torkington (2). * A. Ii. H. Cole and 1~. W. Thompson (a). These values are the Y,,‘s as ralculat,ed rotational analysis of these bonds. i C. W. Gullikson and J. R. Nielsen (4). j G. Varsanyi (5). k Probable values. 1Based on the calculated PET>; tw = twist; w1 = (CHCl) wag; ‘w: = (CH,) wag. a Calculated

TABLE OBSERVED,

CALCULATED, Wavy

____

AND

NUMBERS

Raman (liquid) Hb-^

VI0

VI1

VI”

730 690

PROBABLE

III VALUES

OF

OF CDFCDCI,

IR (gas)

from

THE

O.P.

FUNDAMENTAL

CM+

Calc.

PVd

Moded

730 683

i31 689

730 690

W2

491

491

491

tw + Wl

H*

NC

730 690 491

(1Calculated values are rounded off to the nearest cm-‘. b nl. de Hemptinne, G. Germain-Lefevre, R. Van Riet, c S. Narita, S. Ichinohe, and S. Enomoto (12). d See footnotes k and 1 of Table II.

and D. Lenaerts

tw

(10).

Y10 VI1 II?

__

882 717 494

__ IR(g) _

900 804 587

IR(g) _I__._

_ ___~

R(1)

720

--

905 803 590

R(1)

881 717 492

Calc. .__

882 717 494

PV

__

900 803 ,590

___

CD2=CHClc

___

899 802 590

~__

(Cl + IW 2,’2 (11: + WI

___ Mode

_

2(:2 illr w1

__

MO&

846 686 564

.-___ R(1)

____

803 510

._.

K(I)

___-

940 815 511

-.__-__-__-

937d 8l.j 511

830 690 567

JR(gj _~~ 832 689 568

Calc. I__ 850 690 367

PV

CHD=CDCl(lraas)’

_~__

937 815 511

CHD=CHC~(~WS)~ __.___ TK(g) Calc. PV __ _ __-._ __

TV

1Ol

ll’? tut + uj, 101 + t7o

____ Mode _ I___I---

111~ +

fW + 1c1 U’2

Mode ~_~__ _.

_ R(l)

923 790

__ R(1) 923 790 573

.___

WI + Izo

Si3

866 726/ 506

866 722 506

Calc. __

866 722 506

PV

20% 201 + tu, 10; $ tw

___-. Mode ___.__

fW + W1 Wr

Mode ~_~ ~

922 790

CHD=CDC~(C~S)~ IR(g)

921 790 573

CHD=CHCl(ris)< -__ Calc PV IR(g)

~;iderc~tl~ a probable

and

value

of ii2

mm1

for pI1 of CFTD=CDCI

is ubtainetl.

0 Calculated valllcs are rotlllded olT to t,he nearest, cnl-I; 1 = liyllid; g = ga.5; for the meulling of other symbols see footnotes 1. 1of Table II. 6 J. C. Evans and H. J. Bernstein (9). c 11. de Hrmptinnc, (;. CernG-Lefevre, R. Tan Riet, and D. Lenaerts (10). d This is a. very strong balid; furl hcrmorc, ii lies very c~l~)seto the cc>mbinatjion (of cis Cl11 )=CHCl; investigated sample cout,ains by the present calcldations (see Table X) would a mistllre of the two isomers) Y:, + vl: = 936 cm-l. A lower value of I I , as favored bring the value uf 111is combitution still lower. The valr~e of the observed band at 937 cm-’ may well be inflllenred by this very close combitlation band and hence a higher value for t)he unperturbed flllldamcntal uIu , closer to the calculated value, seems likely. ehl. de Hemptinne, R. Tan Riet, and ,4. T)efosscx (If). .{ This is a nrak baud. It is also close to ~~0 of C!U~=CDCl (730 cm-‘, see Table III), which is prrseut ill the sample as all impurof ihe two fru~dwmentals. Thtls WIIity (10). 0~ may nell collsider, thercforc, i hr vnlur of the ha1111 :lt i26 (,nW1 as al, avrragc

_

VI0 VI1 v1r

_____

CH.J=CDCl* I__-__ Calc. PV _____

TABLE

6

EL-SABBAN

AND TABLE

ZWOLINSKI V

OUT-OF-PLANI:FORCECONSTANTS FORTHE VINYL CHLORIDEP

VlD

(943 cm-l)

VI1 YI?

(897 cm-l) (621 cm-l)

0.3919 0.0840 0.5760

0.0271 0.9974 0.0009

0.7165 0.0235 0.2868

a The numbering of these o.p. fundamentals follows that of the i.p. ones. To save journal space, only the diagonal elements are presented.

table, together with the approximate mode of vibration for each fundamental, as determined by the calculated potential energy distribution. Table III lists similar data for CDFCDC~, whereas Table IV includes data for the remaining partially deuterated species. The final set of force constants for the o.p. vibrations, together with the corresponding standard errors, are shown in Table V. 2. POTENTIAL ENERGY DISTRIBUTION

The assignment

of the torsional

been in dispute. Thompson

fundamental

and Torkington

(2))

in the vinyl halides always has Gullikson

and Nielsen (4)) and

assigned this mode to the lowest o.p. wave number (621 cm-‘) in vinyl chloride. Potts and Nyquist (19)) on the other hand, assigned it to the highest wave number (943 cm-‘). In the present investigation, we have calculated the potential energy distribution for vinyl chloride as well as for allother deuterated members of the series. The calculated PED for vinyl chloride, shown in Table VI, clearly favors Potts and Nyquist’s assignment that the 943 cm-’ mode is preponderantely torsional. This seems to hold generally true for the vinyl halides hitherto studied. Potts and Nyquist (19) and Scherer a,nd Potts (do) Narita et al. (Id)

VINYL

CHLORIDE

ASSIGNMENTS

7

assigned the highest o.p. fundamental mode in vinyl fluoride to the twist,ing mode. These latter authors also carried out a normal coordinate analysis for the o.p. vibrations of vinyl bromide (21) which showed again that the highest fundamental (941 cm-‘) should be assigned to 6he t’nisting mode and not t,he lowest, as has been believed heretofore. This is not always the case, however, with the deuterated members of the vinyl chloride series, as may be seen from Tables ITI and IV. IN-PLANE

1. EXPERIMENTAL

VIBRATIONS

DATE

The st’atus of the in-plane fundamental assignment of the eight members of this series, prior to t.he undertaking of t’he present, investigation, has been summarized by de Hemptinne et al. (IO, 11). This is the assignment suggested b> t’hese authors and also adopted later by Kukina and Sverdlov (16). As it stood then, the assignment was in violation of Rayleigh’s rule in a couple of instances. This rule (22) states that an increase of the mass in any part’ of a vibrat,ing system causes a decrease or maintenance of all t’he normal frequencirs. The violations t,o the Rayleigh’s rule in de Hemptinne’s assignment are 1. C-Cl

stretch,:

for cis CHD=CDCI

(674 cm-‘)

> for trails CHD=CHC‘I

(667 cm I ) ;

2. CH, deformation: for CD2=CHCl (903 cm-‘) > for cis CHD=CHCI (SS7 cK’i. The first of these cases is a part of t,he general confusion in the C-Cl stret,ching range in the spectra of these compounds. This confusion is due to the presence of impurit,ies of one or more of t)he other members of the series. A similar result of this general confusion is the unacceptabln C-Cl stretching assignment of the t,rideuterated compound. In the infrared spectrum, this is assigned by Narita et al. (12) to the band at 663 cm-‘. This assignment is in violation of Rayleigh’s rule since the corresponding fundamental for CD2=CHCl lies at 655 cm-‘. Again, the explanation of the high infrared value is the possible overlap by t,he CY--(‘l stretching bands of other members of t,he series present as impurities in t,hc CD2=CDCl sample; in this case, cis CHD=CDCl with C-Cl stretching at ca. with C-U stretching at about 667 cm-‘. or 660 cm-l, or tram CHD=CHCI hoth (see Table X). The second case of the violation t,o Rayleigh’ s rule in de Hemptinne’s assigrlment, could not be accounted for readily. De Hemptinne et al., realizing this irladequacy of the assignment,, suggested later (11) that t’he 857 cm-’ originally assigned hp them (IO) be reviewed in order to be compatible with Rayleigh’s rule.

S

EL-SABBAN

AND

ZWOLINSKI

2. NORMAL COORDINATETREATMENT The normal coordinate treatment for this series was carried out with a valence force type potential function. The internal coordinates used were the changes in the five bond distances and the four X-C=C angles, the equilibrium values for which are shown in Fig. 1. To start with, t,he general quadratic potential function was simplified with the assumption that all interaction constants between the C-H stretching vibrations and the C-Cl stretching and C=C-Cl bending vibrations were negligible and hence could be set equal to zero. This assumption is well justified because of t#he relative magnitudes of these vibrations. A perturbation program then was used to effect a least squares fit of the calculated to the observed in-plane wave numbers of the eight compounds of this series. Only gas values were used in these calculations. Fundamentals for which only liquid values were available were not used in the adjustment of force constants (see Table X) . The only exception to this rule is the case of the lowest fundamental vg. Since gas values for this fundamental were reported for only vinyl chloride and CH,=CDCl, the liquid values for all the remaining members of the series \vere used in the force constant adjustment. Throughout these calculations, observed fundamentals were given a weight of l/Xobs , whereas unobserved or uncertain ones were given zero weight. During the course of t,he perturbat)ions, further co&mints among the force constants were made. The three interactions between the C-H stretching and the C=C st,retching coordinates were rather skongly correlated and hence were constrained as equal. As such, t’his con&ant became insignificant (error > value of the constant,) ad \vas removed from the perturbat,ion with no noticeable ill effects. The corresponding inter&ions between the C=C stretching and both t,he C-Cl stretching and C=C-Cl bending were found to be ill-conditioned, and t#herefore they were constrained to zero. The interactions of the C=C stretching with the remaining three C=C-H bendings proved also to be insignificant in the perturbation. One of these interactions was constrained to zero and the other two were constrained equal and, as may be seen by reference to constant 22 of Table VII, even then assumed a value only slightly exceeding the standard error. Constant, 22 could have been constrained to zero xvithout not,iceablg affecting the final result. Other reasonable simplifying assumpt’ions of constraining similar kinds of force constants equal and eliminating other ill-condit8ioned ones, made as the calculations proceeded, may be seen from the definitions of the final 25 constants in Table VII. This table lists also the values obtained for the force constants and t,heir standard errors. The general picture of this set of force constants looks and in particular, the values of the diagonal constants look satisfactory, very reasonable.

VINYL

CHLORIDE

ASSIGNMENTS

VIII

3134 3036 1608 1355 1271 -

715 -

3134 -

3036 1614 1035

721 402

-

1602 1355 1271 -

709 396

-

Wu

WF

P

703 396

3078 3027 1601 1360 1271 1024

KS

Raman (liquid)

706 396

3112 3079 3027 1603 1363 1274 1025

EB

719 394

3121 3086 3030 1607 1368 1279 -

GNb

719 724 -

1610 1370 1280 1030

1615 1390 1300 ( )d 398

3120 3086 3037 1608 ca. 1371 cu. 1279 1021” 1038

GN

CM-~"

IR (gas)

3096 -

TT

CHLORIDE,

3130 -

Wu

VINYL

720 398

3125 3089 3037 1612 1374 1281 1036

V

728 393

3127 3081 3034 1612 1380 1283 1038

Calc.

724 396

3125 3086 3037 1610 1374 1281 1036

PV

(5) (6)

(2, 3) (1) (2, 3) (4) (8) (7) (8, 9)

PEDc

a For meaning of symbols, see footnotes to Table II. Calculated values are rounded off to the nearest cm-r. b Gas values. c This could be a PR branch band; alternat.ively, the peak at 1021 cm-r could be interpreted as 621 + 396 = 1017 cm-l, in which case 1038 cm+ would be assigned to ~7 d This is a very strong band t,hat was reported by these aut,hors as four peaks at 710, 716, 723, and 731 cm-l. This fundamental was not used in the adjustment of force constants. e This column gives the force constants, following the numbering system of Table VII, that correspond to the predominant parameters in the calculated potential energy distribution.

Y9

Y8

TABLE

OBSERVED, CALCULATED, AND PROBAI~LE VALUES OF THX IN-PL.\N~ FUNDAMENTAL WAVE NUMBERS OF

1.INYL

CHLORIDE

ASSIGNMENTS

11

3. DISCUSSION Table VIII summarizes t’he experimental spectral data on vinyl chloride. It also includes the calculated values of the fundamentals as well as the recommended probable values. The last column in this t,able shows an approximate description of the mode of each vibration based on the calculated potential energy distribution. Table IX contains similar information for CD2=CDCI, whereas Table X shows a comparison of the observed and calculated fundament,al wave numbers and the modes of vibration for the remaining partially deuterated species. It is seen that the calculations reproduced the observed fundamental wave numbers very closely except in some cases of the loA-est fundament,al vy . This is most probably due to bhe fact that we had to use liquid rather than gas values of t*his fundament’al for most of the compounds of this series. Although the t’ables are self-explanatory, a few important points need to be discussed in more detail. As is seen from Table IX, the present calculations have cleared up much of the uncertainties in the assignment of CD,=CDCl. This is particularly so for the C-Cl stretching fundamental VS. The present calculated value favors the lowest wave number in the series of bands reported in this region by both Narita et al. (12) and de Hemptinne et al. (IO). Other accompanying bands in this narrow C-Cl stretching region of the spectra of both authors must be due to the presence, as impurities, of one or more of the other deuterat’ed compounds of this series (see Table X) . The results for CDFCHCI deserve a couple of comments. De Hemptinne et al. (11) assigned vq , the C=C stretching fundamental, to a strong band at 1.557 cm-‘. It seems now most likely that this is due to a CHD=CDCI impurity ( see Table X), since the present calculated value, 1538 cm-‘, is much lower. It is very probable that this band could not be detected because of its close proximity t’o this strong impurity band at 1557 cm-’ as well as to the band at. 154.5 cm-l (11) which is the C=C stretching fundamental of CDFCHBr (23) present also as an impurity. The second case that deserves comment in the spectrum of CD2= CHCl is t.he fundamental v7. The calculated value for this fundamental seems too low for the infrared value reported by de Hemptinne et al. (11). It should be noted, however, that this latter value does not correspond to t’he position of the Q-branch of the band, but rather to the mean of the PR-branch positions. This may jvell explain the relatively high reported value of this infrared band. Alternat,ively, one may consider the band at 915 cm-’ (assigned by de Hemptinne et al. to the R-branch of v7) as due t’o v10 of CHD=CDBr (23) which is very likely present as an impurity in the sample. This would then leave the band at 900 cm -’ (considered by de Hemptinne et al. as the P-branch of ~7) to be convenient,ly assigned to ~7. In any case, and whichever point of view one may take, it seems that the calculated value of v7 favors a value closer to the lower Raman value of 90.3 cm-‘. Finally, the calculated value of v6 favors the reported Raman value. The infrared band for t’his fundamental is very weak, as shown by the tracings

12

EL-SABBAN

AND TABLE

Osse~v~cu,

ZWOLINSKI IX

C.~LCUL.~TED, .~ND PR~B.LBLIC ~.\LCISS or' THE IN-PLANK WAVE NUMRICRS OF CD,=CDCl, CM-'~

Kaman (liquid) H* 23j7 2303

2224

1531 975 813 ( 6470 1654 349

IR (gas)

Calc.*

FUNDAMENTAL

PEDC

Hb

SD

2337 2315& 2305 I2296

2360 2313d

2356

2357

(2, 3)

2296 2244”

2297 2243

2296 2244

(1)

1 I2220 (1545’ \ 1528 1046 994 817 650~ i 662 I 674 (253)”

1527 1048 985 814 644

1530 1046 984 815 647

(4) (8) (7, 9) (5, 8) (3, 9)

( 2226 (2216 1530 1040 984 815 647~ I 657

i !

(2, 3)

349

u Calculated values are rounded off to the nearest cm-‘. The values of t,he fundamentals Y3, VP, and VRwere not used in the adjustment of the force constants. The fundamental Yewas involved only in the last stages of the refinement of the force constants. * These symbols have the same meaning as iu Table III. c See footnote e of Table VIII. d These two authors adopted a mean value of 2305 cm-l for this fundamental. The present calculations favor a lower value, that of the peak at 2296 cm-l. The band at ca. 2314 cm-1 may be ~3 of trams CHD=CHCl present as an impurity (see Table X). e These two authors adopted a mean value of 2226 cm-’ for this fundamental; the present calculations favor a higher value, that, of the peak at ca. 2240 cm-l. The band at ca. 2220 cm-1 could be assigned as ~4 + ~~1 = 1530 + 690 = 2220 cm-l. f These authors adopted a mean value of 1537 cm-l for this fundamental. The present calculations favor a lower value, that of the peak at ca. 1530 cm-l. This agrees with the assignment of de Hemptinne et al. The band at 1545 cm-’ could reasonably be assigned as Y, + ~~0 = 815 + 730 = 1545 cm-l. y De Hemptinne et al. assigned these two bands to C--Cl37 and C-Clx stretching modes, respectively, whereas Narita et al. assigned their three peaks to a P&R-type band centered at 662 cm-‘. The present calculations favor the lower value in each case, that of the band at ca. 650 cm-l. The band at ca. 65.5 cm-l reported by de Hemptinne et al. could be the C-Cl stretch of CDa=CHCl, whereas the bands at 662 cm-l and 674 cm-l reported by Narita et al. could be the corresponding fundamentals of cis CHD=CDCl and trans CHD= CHCl, respectively, all of which are anticipated to be present as impurities in the spectrum of CDg=CDCl (see Table X). h Calculated (12).

\‘INI’I,

C!IILOI:II)E

ASSIGNMENTS

14

EL-SABBAN

ANI)

ZWOLINSKI

kindly provided by Professor de Hemptinne. Furthermore, the liquid Raman value fits better with both the sum and product rules. For these reasons we favor the liquid Raman value of 1023 cm-’ for w,. A comparison of the calculated and observed fundamental wave numbers of CHFCDC~ looks very satisfactory except for the fundamental Q, . This fundamental seems to be exhibiting a Fermi resonance interaction with the combination vll + ~1~= 803 + 590 = 1393 cm-l( a’) [see ref. (9) and Table IV]. This apparently leads to a corresponding shift of both the fundamental and the combination away from their unperturbed positions to the presently reported values of 1358 cm-’ and 1406 cm-l, respectively. This seems to be the plausible explanation for the relatively too low reported value of v5as compared to the calculated one. The main important features of the remaining four, partially deuterated species, namely CHD=CHCl (trues and cis) and CHD=CDCl (trans and cis) , are the following. The present calculations reversed de Hemptinne’s assignment (10) of v5and v6between the two isomers in each of these two compounds. These calculations also established the value of VTof cis CHD=CHCl at 923 cm-l, i.e. just about coinciding with the corresponding fundamental of the tram isomer. This result removes, therefore, the apparent violation to Rayleigh’s rule referred to earlier in this paper. The present calculations gave also a value of 839 cm-’ for the corresponding fundamental v7 of cis CHD=CDCl. The proximity of the two strong infrared bands of other fundamentals at S21 cm-’ and S50 cm-’ accounts for t,he failure to detect it. The final case that needs consideration is the lowest fundamental vg of tmns CHD=CDCl. The present calculated value of this fundamental is 351 cm-’ (Table X) which led us to assign it t’o the strongest band in the spectrum of this molecule, at 349 cm-l. It is worthy of note that de Hemptinne et al. (IO), being guided only by the experimental data, considered this band at 349 cm-‘, despite it being the strongest in the spectrum, as due to a CDFCDCI impurity whose vg fundamental happens also to be at 349 cm-’ (see Table IX). Instead, these authors adopted the band at 362 cm-l for the fundamental vg of tram CHD=CDCl. It is clear now, as a result of the present calculations, that these assignments should be reversed, and hence that the band at 362 cm-l in the spectrum of CHD=CDCl is in fact due to a cis CHD=CHCl impurity. One final comment based on the result of the present investigation. Clearly, it is highly desirable that the spectra of very pure samples of the compounds of this series should be reinvestigated with spect)rometers of high resolution. The results such a reinvestigation, together with the present results, should establish quite accurate and reliable values of the fundamentals of these molecules. Table XI contains the results of the product’ and sum rules as applied to the present series.

(trans)

CHD=CDCl (cis) CHD=CDCl

(cis)

CH -_CHCl CHz==CDCI CHD=CHCl (kzns) CHD=CHCI

0.277 0.143

0.270

0.27:’

0.274 0.141

0.269

0.272

0.520

;5‘2 1

0

0.516 0.528

Calc.

0.+518 0. ,529

Ohs.

TABLE

SVIII SVII

SVI

SV

= 5748 3371

= -5,725

= 5698

= 6099

SI = 6421 811 = 6052 8111 = 6066 SIV

XI CHLORIDE

ANU T~IE SEVEN

DEUTERATED

+ VI) 5 ;79;

jc(IV

= 11423 “(v

+ VII i1) = 11423 :) -

X(11

+ V) = x(111

+ V’

= 0

+ VI)1 = 6

+ VIII)J

= 11792 j&I + VII) - X(1 + VIII)J = 8 = 11800 = 12169 I~t,rrr + IV) - X(1 + VIT)J = 4 + I\') = 12165

+ VII) + VII)

=$;;V++‘;/)

Z(V

X(11

x(III

X(11 x(I

cc.1 + VIII)

Sum Rulea cm-1

THE SUM RULK TO VINYL ISOTOPIC SPECIES

AND

zvi

RULE

n H. J. Bernstein and A. 11. E. Pullin (24 a). III these sums, contribrtt.ions from hydrogen and deut,erium stretching wave numbers have been omitted (25). Theoretically, the ditl’eretices shown shordd be zero if the sunI rule is fulfilled exartly. The agreemetit is excellent Similar very good agreement, has beet1 attained with the xv2 sum rule (24 b). In these calculations, gas values were used; when not available, the ralctdated valttes rather that1 the liclttid valttes were used; see, however, footnot,e e of Table X

CD,CDCl VII VIII CDFCHCI

VI

V

IV

I II III

PRODUCT

Product Rule

RMULTR OF APPLIC.~TION or THK

16

EL-SABBAN

AND

ZWOLINSKI

ACKNOWLEDGMENT The authors wish to thank Mrs. Lesley J. Clague and Mrs. June M. Husbands for their valuable help in the literature search, the Data Processing Center of Texas A&M University for the generous allotment of computer time during the early part of this research, and the Bartlesville Petroleum Research Center of the Bureau of Mines for the key punch facilities during the latter part of this investigation. Thanks are also due Dr. Donald W. Scott of the Bartlesville Petroleum Research Center for very illuminating discussions. The authors wish also to thank Professor de Hemptinne for kiudly supplying the infrared curves aud Raman spectrograms of CD-CHCl. This work was supported in part by the Thermodynamics Research Center Data Project (formerly the Manufacturing Chemists Association Research Project) and the National Burearl of Standards Office of Standard Reference Data. RECEIVED:

Xag

9, 1966 REFERENCES

1. 2. S. 4. 5. 6. 7. 8. 9. 10.

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