an accurate correlation between the separation of ch2 stretch frequencies and the hch angle in...

SpectrochlmlcsActa,Vol.26A,pp.420 to440. PergunonPreaa 1070. Pr‘intedinNorthemIreland

An accurate correlation between the separation of CH, stretch frequencies and the HCH angle in molecules containing the

Kc= gronP

J. L. DUNCAN Department of Chemistry, University of Aberdeen, Old Aberdeen, Scotland

(Received 24 Augwt 1969)

Abstract-It is demonstrated that an accurate correlation can be made between the separation of the asymmetric and symmetric CH, stretching frequencies and the HCH angle in molecules containing the H,C= group. Care must be taken, however, to take into account any Fermi resonances present, or to avoid these by considering isotopically substituted molecules where the resonance is absent. In conjunction with BERNS-‘S relation [l] between the averaged CH, stretching frequency and rs(CH), the correlation described here is used to predict the CH, group geometries, rs(CH) and as(HCH), in a series of 12 molecules containing the II&= group, including butatriene and butadiene. The results are presented in Table 2. The accuracy of the predictions, &O-O03 A on rc and &lo on as, are comparable with those of conventional estimates of structural parameters. The correlation also reveals a number of mis-assignments in the CH stretching region, which are corrected.

INTRODUCTION

IN 1962 BERNSTEIN [l] demonstrated by second-order perturbation treatment of the secular equation that an accurate correlation could be made between the averaged CH stretching frequency, 5, of a molecule and its CH bond length, r,(CH). Theoreti- cally, this was justified by observing that the averaged cf element is always given by Q = ,!&i + ,ec, so that, within the limitations of the 8pproximstions, variations in 3 %e entirely from variations in the averaged CR stretch force constant, PC,. This can easily be shown [l] to be equal to fCH, the CH stretching valence force constant, which determines the strength of the CH bond and hence its length. The usefulness of such a correlation is obvious in cases where the CH bond length has not been determined, or cannot readily be determined due to the size of the molecule. Al- though subject to some extent to the undetermined effects of Fermi resonance, (generally small though, as it is the average of two or more frequencies which is required), the validity of the predictions has been amply justified in the case of allene-predicted ro(CH) = l-086 A, experimental T,(CH) = 1.087 A.

By analogy, (although by no means so rigorously), in the situation where all the CH stretch symmetry force constants are equal over a series of molecules, it is

snticipated that the symmetric and asymmetric CR stretching frequencies, ye and Y&, should reflect variations in the respective a elements. The latter arise only from different trigonometric relations involving the HCH angle, a, e.g. in methylene group molecules, Go&m) = pn + 2p. cosz (a/2), &&asym) = ,!.& + 2c(C sin’ (a/2). Thus, for such series of molecules, in the approximation that the CH stretch vibrations may be separated from all others, and that the CH stretch-stretch

[l] H. J. BERNSTEIN, Spectrochim. Aota 18, 101 (1962).

1 429

430 J. L. DUNCAN

interaction, f,.,., may be neglected*, the separation of asymmetric and symmetric CH stretch frequencies, Av, should be a sensitive function of a(HCH), in the absence of Fermi resonance. While Bernstein’s relation (constant G, variable F) is applicable over the whole range of sps, sp2, and sp hybridised states of the C atom, the new relation (constant P, variable G), should be applicable to those molecules belonging to each of the sp3 and spa hybridised states in turn, for which reasonably constant values for the CH stretch symmetry force constants are anticipated. (It is of course not applicable to the 8p acetylenic CH state for which there is no HCH angle.) The spa saturated CH, state is fraught with difficulties arising from the variable and generally undetermined Fermi resonances between the CH stretch vibrations and combinations and overtones of the deformation vibrations, while there are few enough spectral investigations of small molecules belonging to the corresponding saturated CH, state to merit a study. However, the ap2 ethylenic CH, state is amenable to test, since in many cases any Fermi resonances are apparently negligibly small, and in others where Fermi resonance does occur (almost always between

vou,(sym) and v o_c + vaei) it can satisfactorily be allowed for, or avoided by considering partially deuterated molecular species (see below). This paper attempts to demonstrate that an accurate correlation can be made in molecules containing the H,C= group between the separation of the asymmetric and symmetric CH, stretching vibrations, and a,(HCH).

In the first part of the paper, molecules are considered whose geometries and CH, stretching frequencies are accurately known in order to derive the correlation. In the second part, the CH, geometries of a series of 12 molecules, including butadiene and butatriene, are confidently predicted. The accuracies of the correlations- Bernstein’s for r,(CH) and this one for a,(HCH)-appear to be roughly comparable with that expected from the best microwave, infrared, Raman, and electron diffraction estimations, i.e. fO-003 A on r,, and &lo on ao. Care must be taken, however, to account for Fermi resonance effects. In Bernstein’s relation an un- accounted for resonance generally gives rise to only a small error in 0, being the average of a number of frequencies. In the relation derived here, it is the separation of frequencies, v, - v, = Av, which is required, and this of course is much more sensitive to any resonance effects.

CORRELATION BETWEEN AvCH, AND a,(HCH)

Seven molecules involving at least one 8p2 hybridised terminal methylene group were used to determine the correlation. They are cyclopropane, ethylene, allene, vinyl chloride, vinylidene fluoride, ketene, and diazomethane. In all cases the CH, group geometries are very well determined with maximum errors of &0*003 A on r,(CH) and f0.5’ on a,(HCH). The CH, stretching frequencies are all well established, and any Fermi resonances can be adequately allowed for, or avoided by using data from partially deuterated molecules, as explained below. Small differences in

* This is necessary for the above argument to apply. However, it is not essential: all that is required is thst f,, is B constant in the series of molecules considered. Then, instead of all CH stretch symmetry force constant being equal, there will be two constent force constants, EtOH(sym) and 3’&x~yrn). This is more physically realistic, end the correlation with variations in the a elements and hence in a(HCH) still holds.

Correlation between the separation of CH, stretch frequencies and the HCH angle 431

Table 1. Separations of asymmetric and symmetric CH, stretching frequencies and CH, group geometries for a series of molecules containing the H&I= group

Molecule CH, stretch frequenoim

Va V, Ref.

Av= ‘0 (CH) a,,(HCH) Ref.

(va - vs)

1. Cyclopropane-H, 3101.7, 3082 -3030”. 3024 [6, 61 65 l-084 f o-003 118.2 f 0.6’ [8, S]

2. {$S$Y 3106.6, 3102.2 30264,3020* w1 80 3096 3019 1121 >

76 I.086 f O-003 117.6 f O-6’ [I9

3, {aging; 3086.6 3016, 3006.7 [14, 161 3084.4 3012.8 w1 76 >

12 I.087 f 0.003 118.2 f 0*6’= [I41

4. {g$z;g 3124 3038 [l?. 181 86 3122 3036 w1 87

> 1.084 f 0.003 119.6 f 0*6O [20]

6. H&F, 3140 3066 I211 86 l-082 f O-003 121.0 f O*b” [2, 231 6. H,C=C=O 3166.1 3070.6 [241 94 l-079 f o-003 122.2 f 0-6O [24] 7. H,C=N=N 3184.6 3077.1 [261 108 l-076 f O-003 126.0 -J= 0.6’ [26]

* Estimated unperturbed value after Fermi resonanoe taken into amount; me text.

the cis- and tram- CH bond lengths in vinyl chloride are averaged. Vinyl fluoride, the geometry of which is accurately known [2, 31, is not used, as the infrared data on CH,==CHF and CH,=CDF [4] are incompatible with each other, and the former data imply a significant Fermi resonance between Y, and vcho + vdei which cannot be corroborated. The frequency data are thus considered to be unreliable. The data used for the correlation are sumnmrised in Table 1, and details outlined below. The correlstion between ve - v, = Av and a,(HCH) for H,C= group molecules is given in Fig. 1. The Bernstein correlation between r,(CH) and P for the series of

[2] V. W. LAURIE,J. Chem. Phye. 84, 291 (1961). [3] D. R. LIDE and D. CHRISTICNSEN, Spechochim. Aota 17, 665 (1901). [4] B. BAK and D. CHRISTENSEN, Spectrochim. Acta 12, 355 (1958). [5] J. L. DUNCAN, J. Mol. Spectq 26, 451 (1908). [6] P. M. MATFLU, G. G. SHEP~RD, and H. L. WELSH, Can. J. Phy8.34, 1448 (1950). [7] J. L. DUNCAN and D. C. MCKEAN, J. Mol. Spectry 27, 11’7 (1968). [8] W. J. JONES and B. P. STOICHEFB, Cum J. Phy8.&&2259 (1964). [9] R. W. SCHWENDEMAN, G. D. JACOBS and T. M. KRIOAS, J. Chem. Phy8. 40, 1022 (1964).

[lo] W. L. SETH and I. M. MILLS, J. Chews. Phys. 40, 2095 (1964). [ll] M. E. JACOX, J. Chem. Phy8.86, 140 (1962). [12] B. L. CRAWFORD, J. E. LANCASTER and R. G. INSKEEP, J. Ohem. Phye. 21,678 (1953). [13] H. C. ALLEN and E. K. PLYLER, J. Am. Chem. Sot. 80,2673, (1958); J. M. DOLLING and

B. P. STOICHEFF, Cm. J. Phy8.37, 703 (1959). [la] A. G. MAKI and R. A. TOTH, J. Mol. Spectry 17, 136 (1965). [la] S. BRODERSEN and E. H. RICHARDSON, J. Mol. Spectry 4, 439 (1960). [lS] D. R. EATON and H. W. THO~ON, Proc. Roy. soo. A%O, 39 (1959). [17] C. W. GULLIKSON and J. R. NIELSEN, J. Mol. Spectq 1, 158 (1957). [lS] S. ENOMOTO and M. ASAHINA, J. Mol. Spectq 19, 117 (1966). [19] J. C. EVANS and H. J. BERNSTEIN, Can. J. Chem. 33, 1792 (1955). [20] D. KIVELSON and E. B. WILSON, J. Chem. Phys. 8f& 205 (1960). [Zl] H. W. THOMSON and P. TORKINQTON, Tram. Famday Sot. 41,236 (1945). [22] J. R. SCEERER and J. OVEREND, J. Chtm. Whys. 32, 1720 (1960). [23] V. W. LAURIE and D. T. PENCE, J. C7wm. Phy8.88, 2693 (1963). [24] C. B. Moo- and G. C. PI~NTEL, J. Chem. Phys. 88,2816 (1963). [25] C. B. MOORE and G. C. P~ENTEL, J. Chem. Phy8.89, 1884 (1963); 40, 329, 342 (1964).

432 J. L. DUNOAN

I I I 1 I

115 I20 I25

a,(HCH), deg

Fig. 1. Correletion between separation of asymmetric and symmetric CH, group stretching frequencies, Av, and HCH bond angle, a,,(HCH), for a series of molecules

containing the H,C= group.

I 1 I I I I 3050 3100 3150

F* cm-l

Fig. 2. Bernstein correlation between the averaged CH, group stretching frequency, 9, and the CH bond length, r,,(CH). The curve is drawn so ss to be also

consistent with the (off-scale) points for methane and acetylene.

Correlation between the sep8ration of CR, stretch frequencies end the HCH angle 433

molecules and also benzene [l] and HDC=CDF [4] is given in Fig. 2, where the curve drawn is consistent with the points (off-scale) for methane and acetylene. In all cases gas-phase frequency data are used, and all geometries are for the ground state.

1. cyclvpropa?M

The observed frequencies are ye = 3101.7, 3082; vs = 3038, 3024 cm-l [5, 01.

The Raman active 8,’ band at 3038 cm-l is in Fermi resonance with 2~~ and 4vll [6, 71, and the unperturbed frequency is estimated to lie at ~3030 cm-l. The observed separation of asymmetric and symmetric CH, stretching frequencies is thus Av = 66 cm-l, with a probable error of i-4 cm-*. The best geometry, from the rotational Raman spectrum [8], and by analogy with microwave data on cyclopropyl chloride [9] is r,(CH) = 1.084 & 0.003 8, a,(HCH) = 116-2 f 0.6'.

2. Ethylene

The observed frequencies are 3106.6, 3102.6; 3026.4, and 2989.7 cm-l [lo]. One might wonder why the two symmetric stretch frequencies are so widely different when the two asymmetric ones are almost identical. The answer is to be found in the possibility of Fermi resonance between vi1 at 2989 cm-l and Y, + viz, evidence of which is to be found in the infrared spectrum [ 111, and from which yil unperturbed is estimated to lie at ~3020 cm-‘, giving an estimated Av = 80 cm-l. A direct estimation of Av may be obtained from the two CH8 stretching frequencies of H,C=CD, where, owing to the lowering of the C==C stretch and CH, deformation frequencies, the Fermi resonance is no longer significant. The two frequencies of 3095 and 3019 cm-l [12] give Av = 76 cm-l. This emphasizes the importance of taking Fermi resonance into account, or of avoiding it by considering partially deuterated species. * A value of Av = 78 f 2 cm-1 is used. The CH, geometry is r,(CH) = 1.086 f 0.003 A, a,(HCH) = 117.6 f 06’ [13].

3. Allene

For allene-H,, the observed frequencies are 30866; 3016, and 3006.7 cm-i [14, 161, while for allene-1,1-D, they are 3084.4 and 3012.8 cm-1 [16]. In neither case are there any Fermi resonance complications, and the isotopic species give Av = 76 and 72 cm-l. A value of Av = 74 f 2 cm-l is used. The CH, group geometry is r,(CH) = 1.087 f 0.003 A, aJHCH) = 118.2 f 0.6" [l4].

4. Vinyl chloride

From two independent investigations, infrared CH, stretching frequencies of 3124 and 3038 cm-l are obtained for H&=C!HCl [17, 181. For H,C=CDCl, the corresponding values are 3 122 and 3036 cm-l [ 191, implying that any Fermi resonance frequency effects are negligibly small. This conclusion is supported by the appearance of the liquid Raman spectra for both isotopic species [19]. The accepted values for the separation of CH, stretching frequencies is thus Av = 86 f 2 cm-l. A microwave estimation gives for the CH, geometry r,(CH) = 1.084 f O-003 A, a,(HCH) = 119.6 f 0.6’ [20].

* The uncorrected frequency eeparetion for ethylene is Av = 95 cm-1 which is quite iu- compatible with the known geometry of the CH, group.

434 J. L. DUNCAN

The data of THOMPSON and TORKINQTON give 3140 and 3065 cm-l for the two frequencies [21]. The data employed by SCHERER and OVEREND [22] in normal coordinate calculations is incorrect in that they use the band at 3103 cm-l as ua. This band is undoubtedly due to Y o-c + Ydef as assigned by THOMPSON and TORK- INQTON. (In both vinylidene fluoride and chloride the asymmetric CH, stretch is a weak absorption.) Because of the low resolution of the spectral data employed and of the possibility of Fermi resonance between the 3103 and 3056 cm-l bands, a frequency separation of Av = 85 f 8 cm-l is used. The average of two independent microwave studies gives for the CH, group geometry r,(CH) = 1.082 rf 0.003 A, a,(HCH) = 121.0 f 05’ [2, 231.

Table 2. Predictions of CH, group geometries of molecules containing the H,C== group from the averaged CH stretch frequenoy (Bernstein’s relation) and from the separation of the asymmetric

and symmetric CH, stretching frequencies

M&O& CH, stretobiug frequencies

Va VS Ref. Av= $ r,(on) a,WoH) Va - Va

1 ’ H#Z=CHBr 3113 3027 [17* 281 H&=CDBr 3110 3020 WI

88 3008 1.083 f 0.003 120.5 f 10

; z;-s;: 3138 3122 3046 3037 1271 H&&FC!*

WI 92 85 3092 3080 1.080 I.082 f f * 0.003 0.003 121.6 120.0 f lo 10 4. 3166 w3060t [21,30] 96 3107 1.070 f 9003 122.0 f 1.60 6. H&=CH(CN) 3126 3042 [311 83 3084 1.081 f 0.003 119.6 f lo 6. H,C =C(CN), 3140 3037 ~321 103 3088 1.081 f 0903 1246 f 1.6O 7. H&EcH(CCl,)* 3116 3049 [331 76 3087 1.081 f 0.003 118.0 f lo

8 ’ H,C=CH(SiH,)* 3067 2904 [361 H&=CH(SiD,)* 3067 2006

;:;;

72 3040 1.088 f 0.003 117.6 f lo

9. H&==CH(SiCl,)* 3081 3002 79 3042 1.087 f 0.003 118.6 f lo

lo ’ H,C=CCl(CH,) 3121 -30367 H,C=CCl(CD,) 3120 -3040t

;::; 82 3078 1.082 f 0.003 119.2 f lo

11. H,C=C=C=CH,$ 3080.3060 2996, 2994 [3Ql 77 3032 I.089 & 0.003 118.2 f lo 12. H,C =CH.CH =CH, 3102.3101 3014, w3010t 1401 87 3066 1.086 f 0.003 120.6 f lo

* Reassignment of observed frequenoiea; see text. t Estimated unperturbed frequencies eftm Fermi resouauoo token into acoouut; 888 text. $ The frequencies quoted ore the gaseous iufmmd cmd liquid Raman of MILLEB end MATSUBARA [39]; SW text for

e&mation of AV = 77 cm-‘.

[26] J. R. SCHERER and J. Ovnmwn, J. Chem. Phy8. Us, 1081 (1900). [27] F. WI-R and D. 0. Hcmm~, Spectrochim. Acta 23A, 1839 (1967); F. WINTEER, private

communication. [28] P. JOYNER and G. GLOCKLICR, J. Chem. Phy8. a0, 302 (1952). [20] J. C. EVANS, J. Chtvn. Phys. SO, 934 (1959). [30] D. E. MANN, N. ACQ~STA and E. K. PLYLIFR, J. Chem. Phy8.23,2122 (1965). [31] F. HALVERSON, R. F. S~AMM end J. J. WEAUZN, J. Ohem. Phy8.16, 808 (1948). [32] A. ROSENBERO ad J. P. DEVLM, Spectrochim. Acta 21, 1613 (1966). [33] E. R. SHULL, J. Chem. Phy8.27, 399 (1957). [34] D. R. LIDE and D. CHRISTENSEN, J. Chews. Phys. 85,1374 (1961). [35] S. G. FRANKISS, Spectrodim. Acta 23, 296 (1966). [36] J. M. O’REILLY and L. PIIQRCE, J. Chem. Phys. 34, 1176 (1961). [37] E. R. SHULL, R. A. THURSACE and C. M. BIRDSUL, J. Chem. Phy8. B&147 (1066). [38] H. HUNZIKER and H. H. G~TEARD, Spectrochim. Acta 21, 61 (1966). [39] F. A. MIUER and I. MATSUB~A, Spectrochiwa. Acta 22, 173 (1966). [40] R. K. HARRIS, Spectrochim. Acta 20, 1129 (1964).


6. Ketene and diazomethune

The high resolution infrared studies of MOORE and PIMENTEL [24,25] yield accurate A, values for these molecules and their deuteo isotopes from which the CH, geometries are: ketene, r,(CH) = l-079 f 0.003 A, a,(HCH) = 122.2 f O&‘; diazomethane, r,(CH) = 1.076 f O-003 A, a,(HCH) = 126-O f 045“. From the same studies, the CH, stretching frequencies are accurately known, and are : ketene, 3166-l and 3070.5 cm-l; diazomethane, 3184.5 and3077.1 cm-l, giving Av(ketene) = 94 f 2 cm-l, Ay(diazomethane) = 108 f 2 cm-i.

CH, GROUP GEOMETRY PREDICTIONS

In this section, the CH, geometries of some 12 molecules are predicted. The results are summarised in Table 2. Several mis-assignments are corrected, and these and all relevant comments are outlined below under each molecule in turn.

1. Vinyl bromide

The CH, stretch frequencies of H,C=CHBr, 3118 and 3027 cm-l, and of H,C= CDBr, 3110 and 3020 cm-l [17,26] give average values of AY = 88 and ? = 3068 cm-l. From the two values for the symmetric CH, stretch, any Fermi resonance effect is expected to be very small. Consequently, a CH, group geometry of r,(CH) = 1.083 f O-003 8, a,(HCH) = 1204i f lo is predicted.

2. Vinylidene chloride

Infrared gas-phase CH, stretching frequencies .of 3138 and 3046 cm-l have been recorded [27], their liquid Raman counterparts being at 3129 and 3035 cm-l [28]. Fermi resonance between the 3046 cm-l band and raEc + Yd& at 3000 cm-l is probably negligible, since the latter is only 12 cm-r lower than the sum of the two fundamentals, and a discrepancy almost exactly equal to this (attributable to anharmonicity) is found in other molecules where any Fermi resonance is negligible. Also, the liquid Raman spectra reveal no evidence of the combination band on the low frequency side of Y, [29]. Values of AY = 92 and F = 3092 cm-i are found, which predict r,(CH) = 1.080 & O-003 A, a,(HCH) = 121.5 + lo.

3. Vinylidene bromide

CH, stretching frequencies of 3122 and 3037 cm-l [27] give values of Av = 86 and t = 3080 cm-l with little likelihood of significant interference from resonance effects. A CH, group geometry of r,,(CH) = l-082 f O-003 8, a,(HCH) = 120-O f lo is predicted.

4. l-JEuoro-l-chloro-ethylene

THOMPSON and TORKWJTON give 3140 and 3055 cm-l for the two CH, stretching frequencies [21]. More accurate date are available from M_4NN et al. [30], but their assignment is undoubtedly wrong. The 3016 cm-l band which they assign as u, is due to yc=o + vdef = 3039 cm-l, while the 3166 cm-l band that they dismiss as a fundamental on account of its low intensity, and ascribe to a ternary combination, is ve. The strong band centered at 3068 cm-l is r,, and not Ye. In this case, Fermi

436 J. L. DUNCAN

resonance may well complicate the issue. If the customarily found anharmonicity factor of 10-16 cm-l is allowed on the combination band, then the actual band is still some 10 cm-l lower in frequency. If this further lowering is due to Fermi resonance with Q, then the unperturbed symmetric CR, stretching frequency is estimated to lie at ~3060 cm-l. From this, we predict Av = -96 and ti = ~3107 cm-l, giving r,(CH) = l-079 f 0.004 A, a,(HCH) = 122 f l-5’. Undoubtedly this geometry is not so well determined.

5. Acylonitde

The infrared CR, stretching frequencies are 3125 and 3042 cm-l [31], with apparently little or no Fermi resonance complications from the evidence of the liquid Reman spectrum. Values of Av = 83 and ii = 3084 cm-l lead to predictions of r,(CH) = l-081 f 0.003 8, a&HCH) = 119.5 f lo.

6. Vinylidene cyanide

Here the CH, stretching frequencies are quoted as 3140 and 3037 cm-1 [32], again with apparently no resonance complications. In this case, Av = 103 and f = 3088 cm-i, so r,(CH) = l-081 f O-003 8, a,(HCH) = 124.5 f l-5’, and the addition of a second cyan0 group apparently leads to a significant opening of the HCH angle, with apparently little change in the CH bond length.

7. 3,3,3-trichloropropene

On the basis that the symmetric CH, stretch vibration seems invariably to be the strongest CH stretching Raman line [17, 19, 28, 29, 311, the data of SHULL [33] give as the two CHp stretching frequencies 3116 and 3049 cm-l, from which Av = 76 and + = 3087 cm-l. A CH, group geometry of r,(CH) = l-081 f O-003 A, a,(HCH) = 118.0 f lo is predicted. On the basis of Shull’s assignment, Av = 116 cm-l, predicting an HCH angle of ~130”, which would seem most unlikely when the angle in propene is known to be 118.0 f 0.3” from microwave measurements [34].

8. ‘vinyl &lane

By the same argument as for the last molecule, the data of FRANXISS [35] give as the two CH, stretching frequencies 3067 and 2994 cm-l for H,C=CH(SiH,), and 3067 and 2995 cm-l for H,C=CH(SiD,), giving Av = 72 and 0 = 3040 cm-l. A predicted CH, group geometry ofr,,(CH) = 1.088 f 0.003 A, a,(HCH) = 117.5 &- lo, may be compared with that of r,(CH) = l-097 f 0.005 A, a,(HCH) = 1195 & 1” calculated from microwave investigations on only two isotopic species [36]. From Frankiss’ assignment, Av = 105 cm-l, which predicts a,(HCH) = 125’.

9. Vinyl trichlorosilane Again, the data of SHULL et al. [37] must be reassigned to give 3081 and 3002 cm-l

as the two CH, stretches, from which Av = 79 and 0 = 3042 cm-l, predicting a CH, group geometry of r,(CH) = l-088 f 0.003 A, cr,(HCH) = 118.7 f lo. The original assignment gives Av = 111 cm-l, implying an HCH angle of ~127~.

[In the last three cases, and also for acrylonitrile, there is a weak band, (polarized in the liquid Raman spectra), lying ~40 cm-l lower than the symmetric CR,

Corrolatiou between the separation of CH, &r&oh frequenoios and the HCH angle 437

stretch absorption. The only reasonable assignment for this absorption is that of the comb~ation baud p*c + Q~. This band is almost certainly in Fermi resonance with the symmetric CHa stretch, but from the very large difference in intensities between the two bands, the effect should be small. Possibly the symmetric CH, frequencies should be ~6 cm-1 lower, after allowing for this Fermi resonance. This would imply an increase in the HCH angle of ~1~ in all cases. It is this weak absorption that the previous workers have consistently assigned to the symmetric CH, stretch vibration, assigning the stronger absorption to the lone CH stretch vibration.]

The data of HUNZIKER and G~IJ‘NTHBBD [38] give for the CHI stretch frequencies of II+C=CCl(CH,), 3121 and 3026 cmf, and of H@==CCl(CD,), 3120 and 3013 cm-x. The large difFerence of 12 cm-l in the symmetric stretch frequencies with deuterium substitution of the terminal methyl group is not expected (see the analogous case of vinyl silane) and almost certainly arises from Fermi resonance. In the two molecules yoXc + vda is calculated to occur at 3069 and 3042 cm-l. Allowing 10-l& cm-l for anharmonicity, the observed bands at 3064 and 3067 cm-r in the spectra [38] oan be explained with Fermi ~onan~_ shifts on the ~mb~ation bands of ~10 and ~27 cm-l, leading to values for the unperturbed symmetric CH, stretch frequencies of -3035 and ~3040 cm-l which seem quite reasonable considering the approximate nature of the corrections. Prom the speotra in [38] the resonance is much strouger in the trideutero molecule, ss predicted from the above corrections. Indeed, if they are at all valid, in the trideutero molecule, it is the band at 3067 cm-l which contaius more C?I& symmetric stretching character, and the band of approximately equal intensity at 3013 cm-l more combination band character, in which case the Fermi resonance shifts are ~17 cm-r in the opposite dire&ion to those in H&===CCl(CH~), i.e. vs at ~3040 cm-l is raised to 3067 em-l, while 3~._~ + vdef at ~3030 cm-l is lowered to 3013 cm-l. After correcting for Fermi resonance, values of Av = 82 and 8 = 3078 cm-l are found, predicting a CHsr group geometry .of r,(CH) = 1982 f 0.003 8, a,(HCH) = 119.2 j, lo.

The gaseous infrared and liquid Raman data of MILLER and MATSURBAnA [39] give an average value of Av = 76 and ii = 3032 cm-l. Close examination of their infrared spectra leads to the assignment of the band centre of the type-B perpen- dicular band as close to 3074 cm-l. Along with the band centre of the type-A parallel band at 2995 cm-l, this leads to Av = 79 cm-l. Since the CH, groups are separated by a considerable distance and three carbon atoms, one would expect the corresponding gaseous Raman frequencies to be closely similar to these. Aocordingly, Av = 77 cm-l is assumed, and is probably accurate to f3 em-l. A CEIa group geometry of r,,(CH) = l-089 f 0*003 A, aO(HCH) = 118.2 f lo is predicted, which is essentially identical to that of ethylene and allene. lMiller and Matsubara calculate a value of A o = 4,786 f 0.01 cm-1 from the rota~on~ analysis of the infrared active wagging vibration. Although this band is in strong Coriolis interaction with the

438 J. L. DUNCAN

infrared active rocking vibration* (as in ethylene and allene) a combination difference analysis for the ground state is still valid, since it is the upper state which is the perturbed one. The geometry derived here predicts a value of A, = 4.788 cm-l, in perhaps fortuitously close agreement with experiment. It appears that the slight lowering of the A, value compared with ethylene (A, = 4328 cm-l) and allene (A, = 4.807 cm-l) is caused by a slight lengthening of the CH bond, rather than by an increase in the HCH angle, as assumed by Miller and Matsubara.

12. Butudiene

From the data of HARRIS [40] the four CH, stretching vibrations of tram+ butadiene are observed at 3102,310l; 3014 and 2985 cm-l between the infrared and Raman gaseous spectra. As remarked by Harris, the 2986 cm-l B, band can Fermi resonate with both the vLc + vdti combinations of B, symmetry, calculated to lie at 3041 and 3028 cm-l. This almost certainly occurs, since the two symmetric CH, vibrations would be expected to be closely similar, as are the two asymmetric ones. If the observed infrared absorption at 3066 cm-l is due at least in part to the combination(s), then the unperturbed frequency of the symmetric CH, stretching vibration would be raised considerably, a value of ~3010 cm-l being quite reasonable and compatible with the other symmetric frequency. Consequently, a value of Av = 87 cm-l is assumed, which should be accurate to better than &-6 cm-l, and 9 = 3066 cm-l. A CH, group geometry of r&H) = l-086 f O-003 rf, a,(HCH) = 120.5 f 1” is predicted for butadiene. Although the carbon-carbon bond lengths and angles in butadiene have been accurately estimated from rotational Raman and high resolution infrared data [41], the only estimate of the CH, geometry comes from an electron diffraction study [42] from which r,(CH) = 1.082 f 0.01 A, a,(HCH) = 120.4’ (no error quoted), on the assumption that all CH bond lengths and CCH angles are the same. From the CR, group stretching frequencies the CH, group geometry is confidently predicted to be r0 = l-085 8, u0 = 1205’.

COMMENTS

Provided adequate care is exercised, it appears that accurate estimates of the H,C= group geometry may be obtained from the frequency positions of the asymmetric and symmetric CH, stretch vibrations. The correlation given here is based entirely on gas-phase data, and might not give quite such reliable predictions from frequency separations obtained from liquid or solid state spectra. In the cases which can be checked, a fairly constant downward shift of 10 cm-l on both frequencies is to be expected on going to the liquid phase, so liquid phase separations used in conjunotion with the correlation in Fig. 1 should give reasonable estimates of the HCH angle.

* This can be eeen from the manner in which the & branches in each band degrade strongly away from each other, and in the very large difference between the ground and upper state A values in the band analysed [39].

[41] D. J. MARAIS, N. SFIEPPARD and B. P. STOICHEFF, Tetmh&on 17, 163 (1962). [42] A. ALBTENNINUEN, 0. BASTIANSEN ctnd M. !~AETTENBERQ, Acta Chem. 9canrl. 12, 1221

(1958).


As a corollary, in cases where the geometry of the H,C= group is known, the anticipated separation of the CH, stretch frequencies may be an aid in assignment work, particularly when other CH groups are present. A good example of this is the molecule isobutene, whose infrared and Raman spectra have been the subject of two recent investigations [43,44]. In both cases, observation of the gaseous infrared and liquid and solid state infrared and Raman data shows that although the band assigned as Ycn,(asym) moves down by 8 cm-l on going to condensed phases, the band assigned as Yon,(sym) is !rc&ed by 9 cm- l. No Fermi resonance complications can be found to cause this effect. Consequently, the gaseous frequency separation of Av = 106 cm-l predicts a,(HCH) = 125', while the liquid frequency separation of Av = 90 cm-l predicts a,(HCH) = 12 lo, compared with the microwave estimation of a,(HCH) = 118-5' [45]. This incompatibility between the gaseous and condensed phase spectra can be resolved when it is observed that the highest of the methyl group stretching vibrations occurs in the Raman liquid spectrum only 10 cm-l below the band in the infrared gaseous spectrum assigned as the CH, symmetric stretch. Accordingly, it is proposed that the band observed in the infrared gaseous spectrum at 2981 cm-l is due to the highest stretching vibration of the methyl groups and that the symmetric CH, stretch vibration (strong as always in the liquid Raman spectrum) is hidden under the R branch of this stronger infrared band. Once the possibility of Fermi resonance between the symmetric fundamental at 2989 cm-l and vkc + vdaf at 3019 cm-l in the liquid Raman spectrum is accounted for, the anticipated frequency separation of ~80 cm-l is closely predicted.

In the case of propene, the well-established geometry from microwave investigations [34] of r,,(CH) = l-086 & O-003 AL, a,(HCH) = 11&O f O-5" leads to the predictions G = 3050, Av = 76 cm-l, and thus v, = 3088, v, = 3012 cm-l. These correspond almost precisely with the bands observed by LORD and VENKATESWA~LU [46] at 3089.7 and ~3013 cm-l (observed at 3010 cm-l as a strong polarized Raman line in the liquid), although the authors assigned the latter band to the lone CR stretch vibration. The band at 2991 cm-l which they proposed as due to the symmetric CH, stretch is probably a combination band in Fermi resonance mainly with the methyl group vibrations, the highest of which has been unequivocally located at 2974 cm-l by WINTHER and HUMMEL [47], the other two lying at 2954.4 and 2931.9 cm-f.

Acknowledgment-I am indebted to Dr. D. C. MCKEAN for most helpful discussions and for a critical reading of the manuscript of this paper.

Note added in proof

In a private communication, Dr. F. Winther, University of Kiel, has supplied the following information on two further methylene group molecules: H,C=CBrCI-v, 3130.3 (g), 3120.0 (1); us 3039.6 (g), 3027.8 (1); from which Av = 91, 4 = 3085 cm-r; r,(CH) = I.081 f 0.003 A

[43] W. L~TTKE and S. BRAUN, Ber. Bwmenges. Phya. Chem. ‘Xl, 34 (1967). [44] C. M. PATIZAK and W. H. FLETCRRR, J. Mol. Speotq 31, 32 (1969). [46] L. H. S-PEN and V. W. LAWIIC, J. Chem. Phye. 39, 1732 (1963). [46] R. C. LORD and P. VENKATESW~RLU, J. Opt. Sot. Am. 43, 1079 (1953). [47] F. WINTRER and D. 0. H UMNEL, Spectrochim. Acta 25A, 417 (1969).

440 J. L. DUMXN

a@CH) = 121.5 f lo. H&=CCl(CN) from whiuh AV = 89,$ = 3082 om‘-’

-Q 3136.9 (g), 3127.3 (1); V, 3047.0 (g), 3038.6 (1); ; r&H) = l-080 f 0*003 A, a,(HCH) = 121*0 f lo. ltn the

above,(g) and (1) signify gaseous 8nd Ii&id phase infrared frequencks respeotively. For both mol- saula the symmetrio CH, stretoh fmqueuoy, Y*, suffers at worst only weak Fermi ~nance, so the correlations are oonsidered valid. The author is indebted to Dr. W&her for providing this inform&ion, and 8180 for providing more accurate frequency data for H&-CCI, and H&GC!B~,, which have been incorporated in the paper.

an accurate correlation between the separation of ch2 stretch frequencies and the hch angle in...

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