J . Phys. Chem. 1988, 92, 3302-331 1
3302
Vibrational Optlcal Activity in Deuteriated Phenylethanes Sergio Abbate,? Henry A. Havel,* Leo Laux,s Vaughan Pultz,l and Albert Moscowitz* Department of Chemistry, University of Minnesota, Minneapolis, Minnesota 55455 (Received: March 15, 1988)
Infrared, Raman, and vibrational circular dichroism (VCD) spectra have been recorded in the region 3100-2000 cm-’ for (S)-(+)-l-phenylethane-l-& (S)-(+)-l-phenylethane-l,2-d2,(S)-(+)-1-phenylethane-1,2,2-d3,and (S)-(+)-1-phenylethane-J,2,2,2-d4. From these spectra we have been able to assign fully the aliphatic CD and CH stretching vibrations in all four molecules. Using a harmonic force field which fits the observed frequencies, we have calculated the dipole and rotational strengths of these modes on the basis of the charge flow model. These calculations show that this model underestimates the VCD intensities of these stretching modes. However, the model can be improved through the introduction of polarization terms. Generally applicable analytical expressions for such terms are derived. When applied to the phenylethanes, they lead to the correct orders of magnitude for the rotational strengths.
I. Introduction
To test the validity of theoretical models for the interpretation of vibrational circular dichroism (VCD) spectra, it is particularly useful to compare calculations with experiments in a series of chiral molecules which differ only by isotopic substitution. The four optically active phenylethanes, (S)-(+)- l-phenylethane-l-dl,
(S)-(+)-1-phenylethane-1,2-d2,(S)-(+)l-phenylethane-l,2,Z-d3, and (S)-(+)-1-phenylethane-1,2,2,2-d4,Idesignated generally as Ph-C*HD-X (X = CH3, CH2D, CD2H, and CD3),serve this goal. Their structural formulas are given in Figure 1 . In such a series, the force fields for the ethyl and phenyl portions have been very well characterized.24 In addition, from infrared (IR) intensity studies of paraffin molecules5-* and of b e n ~ e n e one ~ ~ ’is~able to obtain a set of parameters which can be used in the charge flow model” for the calculation of rotational strengths. In section I1 we discuss our general experimental methods. In section 111 we discuss the assignments of the aliphatic C H and C D stretching modes; the corresponding normal-coordinate calculations are given in section IV. In section V we present the VCD spectra of the four molecules in the CH and CD stretching regions. Sections VI and VI1 are devoted to the calculation of the rotational strengths: In section VI the unmodified charge flow (CF) model is employed; in section VI1 the polarizability of the phenyl group is addressed explicitly within a CF model framework. 11. Experimental Section
were used as solvents. As suggested by Holzwarth and Chabay, we also recorded the spectra with the sample in the “absorption base line po~ition”.’~ All the VCD spectra reported in this paper are the differences between spectra taken in the sample CD position and spectra taken in the absorption base line position. The rotational strengths were evaluated by using the calibration scheme described in ref 15, and integrating the frequency-weighted area under the VCD curves. 111. Vibrational Assignments of the Aliphatic v(CH) and v(CD) Modes
The IR and Raman spectra between 3000 and 2000 cm-l were used to assign the fundamental aliphatic C H and C D strengthening vibrations of the four molecules. The spectra are shown in Figures 2-9. In all four molecules the bands above 2980 cm-l are due to phenyl CH stretching modes. The isolated stretching modes of the C-H and C-D bonds attached to the asymmetric carbon are readily assigned respectively to the broad band centered at 2910 cm-I in the spectrum of Ph-C*HD-CD3 (Figure 2) and to the similarly broad band centered at 2150 cm-’ in the spectrum of Ph-C*HD-CH3 (Figure 3). We will denote these modes as v(C*H) and v(C*D), respectively. The broadness of these bands may be attributed tentatively to the presence of many rotameric forms of the phenyl ring. (See also: Cavagnat, D.; Lascombe, J. J . Chem. Phys. 1982, 76, 4336.) Having assigned u(C*H) arid u(C*D), one finds it easier to assign the other aliphatic C H and C D stretching modes in the remaining six spectra. In the spectrum from 3100 to 2800 cm-I of Ph-C*HD-CH3 (Figure 4), the broad band at 2910 cm-’ is easily recognized as v(C*H). Three aliphatic fundamental C H stretching vibrations remain to be assigned in this spectrum.
The Raman scattering instrument used was a JEOL-JRS-1 spectrometer which is equipped with a 90° scattering system, a double grating monochromator, and a photomultiplier tube detector. A Control Laser Corp. Model 551A Ar+ C W laser was used as the excitation source at 488 nm. The excitation power was 1.3 W and the spectral resolution was 6.8 cm-I. Samples were measured as neat liquids in sealed 1-mL ampoules. In addition to the infrared transmittance spectra recorded with the VCD instrument, we show IR absorption spectra taken with a Perkin-Elmer 283 spectrometer. These spectra were measured for dilute solutions in either CC14 or C2C14in cells of known path length. The VCD spectra were recorded with the apparatus described in earlier works.I2-I4 In the C H stretching region (3100-2800 cm-’), the spectral resolution was 13 cm-’, while in the CD stretching region (2250-2000 cm-I), the resolution was 9 cm-I. The number of scans recorded for each spectrum varied from 4 to 16 depending upon the signal-to-noise ratio. A 7-s time constant was used in all instances. As with the IR spectra, CC14 and C2Cl4
Neto, N.; Scrocco,M.; Califano, S. Spectrochim. Acta 1966, 22, 198 1. Kakiuti, Y.; Shimanouchi, T. J . Chem. Phys. 1956, 25, 1252. Mills, I. M. Mol. Phys. 1958, I , 107. Heicklen, J. Spectrochim. Acta 1961, 17, 201. Meyer, W.; Pulay, P. J . Chem. Phys. 1972, 56, 2109. Gussoni, M.; Abbate, S.; Zerbi, G. J. Chem. Phys. 1979, 71, 3428. Spedding, H.; Whiffen, D. H. Proc. R. Soc. London, A 1956,238,245. (IO) Kovner, M. A,; Snegirev, B. N. Opr. Specktrosk. 1961, 10, 328. Akiyama, M. J. Mol. Spectrosc. 1980, 84, 49. (11) Abbate, S.; Laux, L.; Overend, J.; Moscowitz, A. J . Chem. Phys.
‘Permanent address: Instituto di Chimica Fisica, Universita di Palermo, Via Archirafi 26, Palermo, Italy. Present address: The Upjohn Company, Kalamazm, MI 49001. 8 Present address: Lockheed Palo Alto Research Laboratory, 3251 Hanover Street, Palo Alto, CA 94304. Present address: Department of Chemistry, Northeast Missouri State University, Kirksville, MO 63501.
1981. 75, 3161. (12) Havel, H. A. Ph.D. Thesis, The University of Minnesota, Minneapolis, MN, 1981. (13) Pultz, V.;Abbate, S.; L u x , L.; Havel, H. A,; Overend, J.; Moscowitz, A.; Mosher, H. S. J . Phys. Chem. 1984, 88,505. (14) Chabay, I.; Holzwarth, G. Appl. Opt. 1975, 14, 454. (15) Nafie, L. A,; Keiderling, T. A,; Stephens, P. J. J . Am. Chem. So;. 1976, 98, 2715.
0022-3654/88/2092-3302$01 S O / O
(1) (2) 117. (3) (4) (5) (6) (7) (8) (9)
Elsenbaumer, R. L.; Mosher, H. S. J . Org. Chem. 1979, 44, 600. Schachtschneider, J. H.; Snyder, R. G. Spectrochim. Acta 1963, 19,
0 1988 American Chemical Society
Vibrational Optical Activity in Deuteriated Phenylethanes
The Journal of Physical Chemistry, Vol. 92, No. 11. 1988 3303
H D
u
Hw X
11
\
H
neat
H
X
5
C H 3 , C H Z D , CD2H , C D 3
Figure 1. Absolute configuration of the four optically active (S)-(+)-1phenylethane-1-d, isotopomers. I
I
1
3100
1
I
3000 2900 Av(cm-’)
2800
0 0 4 2 M/CCI&
IW
1
\
60
€ neat
-
% 0
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5100
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3000
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iL , 2800
A v (cm”)
501
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111
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L
Figure 4. Raman (top) and IR absorption (bottom) spectra of v(CH) modes in Ph-C*HD-CH3.
>
c v, z W
I-
z
w 0
a W I-
tV v)
Figure 2. Raman (top) and IR absorption (bottom) spectra of v(CH) modes in Ph-C*HD-CD3.
neat
>
e Ln z
c/;;..
3100
I
1
1
3000
2900
2800
AV
t
(cm-’)
0.088 M/CCI,
IW
0 W P IW
t Ln V
v (cm-’)
Figure 5: Raman (top) and IR absorption (bottom) spectra of u(CH) modes in Ph-C*HD-CH2D. neat lot
0
2200
2100 4cm-’)
Figure 3. Raman (top) and IR absorption (bottom) spectra of v(CD) modes in Ph-C*HD-CH3.
There is a band at 2970 cm-’ which is intense in the IR and weak and depolarized in the Raman, and hence it is assigned to the two antisymmetric CH stretching modes in the C H 3 group16
and designated uas(CH3). There are two intense polarized Raman bands at 2940 and 2860 cm-’which are weak in the IR. We assign these respectively to the symmetric C H stretching mode of the methyl group, designated u,(CH3),and to the overtone or combination band with which it has interacted by Fermi re~onance.’~J’ Using a standard treatment of the Fermi resonance interaction,” it is possible for one to derive the unperturbed energy of u,(CH,) from the observed frequencies and relative intensities of the two (16) Bellamy, L. J. The Infrared Spectra of Complex Molecules, 3rd ed.; Halsted: New York, 1975; p 270. (17) Fermi, E. 2.Phys. 1931, 71,250. Herzberg, G. Infrared and Raman Spectra of Polyatomic Molecules; Van Nostrand: New York, 1945; p 215. Califano, S. Vibrarional States; Wiley: New York, 1976; p 294. Dellepiane, G.; Abbate, S.; Bosi, P.; Zerbi, G. J . Chem. Phys. 1980, 73, 1040.
3304
The Journal of Physical Chemistry, Vol. 92, No. 11, 1988
Abbate et al.
neai
>
t
t z
b
z
vi
vi
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',
1
dcD2H
I 1I
z
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0.085 M/C~CLL
2100
@.u (cm-'I
30
0.088 MiCC IL 301
E
' O I L-4 10
2200 u(cm-l)
2100
Figure 8. Raman (top) and IR absorption (bottom) spectra of v(CD) modes in Ph-C*HD-CD,H.
'
n
t v) z
neat
!I
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3100
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I
A V ( c m-')
3000 2900 Adcm-') 0.077 M/CCI,
501
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,
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neat
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3000 2903 ~(cm-')
Figure 7. Raman (top) and IR absorption (bottom) spectra of v(CH) modes in Ph-C*HD-CD2H.
bands. The unperturbed frequency for vs(CH3) turns out to be at 2907 cm-', and the unperturbed overtone (or combination) is at 2892 cm-'. The assignment of the stretching modes of Ph-C*HD-CD2H and Ph-C*HD-CH,D is straightforward. Shown in Figure 5 are the IR and Raman spectra of Ph-C*HD-CH2D in the C H stretching region. Since the band at 2970 cm-' is strong in the IR and weak and depolarized in the Raman, it is assigned to the antisymmetric CHI stretching mode and designated u,(CH,). The band at 2930 cm-' is assigned to the corresponding symmetric stretching mode and designated as u,(CH,) because it is strong and polarized in the Raman. As before, the broad band centered at 2920 cm-I is ascribed to u(C*H). The two expected fundamental modes in the C D stretching region of Ph-C*HD-CH2D (Figure 6), v(C*D) and the methyl mode v,(CD), are assigned to the broad band a t 2160 cm-l and to the narrower band su-
Figure 9. Raman (top) and IR absorption (bottom) spectra of v(CD) modes in Ph-C*HD-CD,.
perposed on it a t 2170 cm-', respectively. For Ph-C*HD-CD2H, the observed IR and Raman spectra are shown in Figures 7 and 8. Again we ascribe v(C*H) to the broad feature at 2920 cm-' (Figure 7) and the superposed narrow band at 2950 cm-' to v,(CH). The band at 2220 cm-l in Figure 8 is assigned to v,,(CD2) since it is strong in the I R and is weak and depolarized in the Raman. The broad band at 2165 cm-' is assigned to u(C*D), and the strong, polarized Raman and medium IR band at 21 30 cm-' is assigned to the symmetric CD, stretching mode v,(CD2). The assignment in the C D stretching region of Ph-C*HD-CD3 (Figure 9) requires some elaboration. There are four CD stretching modes to be assigned. The band at 2230 cm-I is weak and depolarized in the Raman and strong in the IR. These are the characteristics of the doubly degenerate antisymmetric stretching modes in a -CD3 fragment. Hence, the band at 2230 cm-' is assigned to the antisymmetric stretching mode va,(CD3). The band at 2130 cm-' has high Raman intensity and is polarized,
Vibrational Optical Activity in Deuteriated Phenylethanes TABLE I: Calculated and Observed Aliphatic CH and CD Stretching Frequencies (cm-I) in Optically Active Phenylethanes
calcd using calcd from force constants present of_______ ref 2 work" obsd Ph-C*HD-CH3
Ph-C'HD-CHZD
Ph-C*HD-CD*H
Ph-C*HD-CD3
i;;;}
2967
2913 2907 2150
2915 2907b 2160
2966 2916 2881 2172 2127
2977 2933 2913 2181 2150
2967 2930 2922 2172 2160
2943 288 1 2215 2131 21 18
2956 2913 2224 2151 2135
2950 2916 2222 2165 2133
2881 2218 22131 2127 2079
2913
2910
igi;}
2227
2968 2967 2885 288 1 2127
1
2149 2095
The Journal of Physical Chemistry, Vol. 92, No. 11, 1988 3305 TABLE II: Calculated and Observed Phenyl CH Stretching Frequencies (cm-') in Phenylethanes force constants adjusted"
obsd
3075 3069 3066 3059 3058
3073 3065 3059 3023 3021
3086 3065
assignt
213gb 2111b
"See text for discussion. bunperturbed frequency for mode in Fermi resonance with overtone or combination mode. thus making it a good candidate for the corresponding symmetric stretch v,(CD3). The band a t 2160 cm-', being broad, exhibits v(C*D) character, and we assign it as such. However, there is still one more band in the region at 2075 cm-'. This band is likely to be an overtone or combination band enhanced by Fermi resonance with one of the fundamentals in the region. From the strong Raman intensity of both the 2075-cm-' band and v,(CD3), one is tempted to conclude that v,(CD3) is the only fundamental involved in the Fermi resonance. But a concomitant and equally strong interaction of the 2075-cm-' band with v(C*D) is recognized for two reasons. First, the band a t 2075 cm-I in the IR spectrum is stronger than the 2130-cm-' band, and borrowing intensity from only v,(CD3) would violate a well-established rule in a two-level Fermi resonance scheme, according to which the overtone never exhibits greater IR intensity than the fundamental with which it interacts." Second, from the VCD spectrum (Figure lo), one sees that the band at 2075 cm-I has the same sign as the band a t 2130 cm-'. In ref 12 it is shown, subject to certain assumptions, that both levels in a two-level Fermi resonance scheme have the same sign in the VCD spectrum. Our conclusion then is that the 2075-cm-l band is in Fermi resonance with both vs(CD3) and v(C*D). The dual Fermi resonance just noted is readily accommodated by a scheme in which the 2075-cm-' band itself is of dual origin. One can make the assumption that one component of the 2075cm-I band is in Fermi resonance with v,(CD3) to provide the observed Raman intensity, and the other component is in Fermi resonance with v(C*D) to provide the observed I R and VCD intensity. If one treats these as separate Fermi interactions, by standard methods one calculates the unperturbed u,(CD3) to be at 21 11 cm-' and the unperturbed v(C*D) to be at 2138 cm-I. The erstwhile forbidden overtone or combination bands are calculated to have unperturbed frequencies of 2105 and 2096 cm-l. The values just given for the unperturbed frequencies for us(CD3) and v(C*D) are consistent with the values found in the normal-coordinate calculations presented later on,and this agreement lends support to the Fermi resonance scheme just presented. Of course, one cannot exclude other schemes of Fermi interactions. The assignments just discussed are listed in Table I. IV. Normal-Coordinate Calculations
Since no force field is available for ethylbenzene, we have transferred force constants from chemically similar molecules. For the phenyl group, we use the in-plane force constants from
calcd with ortho CH
calcd using force constants of ref 3
3028
"See text for discussion. TABLE III: Observed Frequencies, Dipole Strengths D, and Rotational Strengths R for v(CH) end u(CD) Modes of Ph-C*HD-CHs v, cm-I 103990, esu2.cm2 io4% esu2-cm2 assignt"
~as(CH3) vS(CH3)+ w, v(C*H) w, + Vs(CH3) u(C*D)
2967
;E] 2876 2160
+15 51
2
-18
" w , = overtone or combination mode in Fermi resonance with the fundamental vibration us(CH3).
TABLE IV: Observed Frequencies, Dipole Strengths D , and Rotational Strengths R for v ( C H ) and v(CD) Modes of Pb-C*HD-CHzD v. cm-I 103~90, esu2em2 i045R, esu2-cm2 assignt
Ej 2910 2170 21501
13 6
-28
v,(CD) v(C*D)
Net0 et al.,3 and the out-of-plane force constants we take from the work of Kakiuti and Shimanowhi: The ethyl force constants we take from the work of Schatchtschneider and Snyder2 (set 11), treating the ethyl group as in ethane. The geometry adopted for the phenyl ring is r(C-H) = 1.084 A, r(C-C) = 1.397 A, and all angles are assumed to be 120'. For the ethyl group we take r(C-H) = 1.093 A, r(C-C) = 1.54 A, and all angles are assumed to be tetrahedral. The length of the C-C bond connecting the phenyl ring and the ethyl group is assumed to be 1.54 A. We will not discuss here the full normal-coordinate calculations but concentrate only on the aliphatic C H and CD stretching fundamentals. For further details, the interested reader should consult ref 12. Some minor modifications of the CH stretching force constants are required in order to match the observed frequencies. To achieve the observed separation in the frequencies of the phenyl C H stretchings, we have changed the value of KcH(ortho) from the 5.101 mdyn/A of Net0 et al. to 4.96 mdyn/A. The final results for the phenyl group are reported in Table 11. In the ethyl portion of the molecule we use the values KcH(CH2) = 4.624 mdyn/A, K c ~ ( c H 3 )= 4.762 mdyn/A, and FcH,cH(CH~)= 0.052 mdyn/A, which are very close to the original values of Schachtschneider and Snyder.2 With these values we obtain the aliphatic C H stretching frequencies presented in Table I. These calculated frequencies are independent of the rotameric positions of the phenyl group to within a wavenumber. V. Vibrational Circular Dichroism Spectra
In Figures 10-17 we show the VCD spectra of the CH and CD stretching modes of the four optically active deuteriated phenylethanes, along with the transmittance spectra recorded on the same apparatus. In none of the four compounds do we observe any significant VCD signal in the phenyl CH stretching modes (3100-3000 cm-'), as can be seen from Figures 11, 13, 15, and 17. The dipole strengths D for the CH and CD stretching fundamentals are given in Tables 111-VI, as are the rotational strengths R. In these tables we sometimes report only sums of D or R values over neighboring modes. One reason for this is that the over-
3306 The Journal of Physical Chemistry, Vol. 92, No. 11, 1988
Abbate et ai.
0.090M/CCI,
5 U
51 x
o
W
a -5
% T
2200
2100 c m-'
Figure 10. VCD (top, 16 scans) and IR transmittance (bottom, 1 scan) spectra of u(CD) modes in Ph-C*HD-CD3. Concentration is 0.090 M in CC14.
2200
2100 c m-'
Figure 12. VCD (top, 8 scans) and IR transmittance (bottom, 1 scan) spectra of u(CD) modes in PhC*HD-CH3. Concentration is 0.177 M
0.046M/CCI
in C2C14.
'1. T
0
Figure 11. VCD (top, 6 scans) and IR transmittance (bottom, 1 scan) spectra of u(CH) modes in Ph-C*HD-CH3. Concentration is 0.046 M in CCL. TABLE V Observed Frequencies, Dipole Strengths D , and Rotational Strengths R for v(CH) and v(CD) Modes of Ph-C*HD-CD,H U, cm-I i039D, esu2.cm2 i045R,esu2.cm2 2950 2916 2222 2165 2133
1 1
8
3l
9
+S
-1 7
assignt V,(CH) u(C*H) UdCDZ) u(C*D) UdCDI)
TABLE VI: Observed Frequencies, Dipole Strengtbs D , and Rotational Strengths R for u(CH) and u(CD) Modes of Ph-C*HD-CD,
assignta 2910 5 u(C*H) 2221 dCD3) 2165 u(C*D) + w, -1 8 2130 1 "s(CD3) + O b 2078 1 w, + u(C*D) w b + Ys(CD3) O w , , wb = overtones or combination modes in Fermi resonance with fundamental vibrations. Y,
cm"
1 0 ~ ~ esu2.cm2 0,
7
1045R,esu2.cm2 +25
1
3100
1
3000
I
2900 9 (cm-')
2800
Figure 13. VCD (top, 4 scans) and IR transmittance (bottom, 1 scan) spectra of u(CH) modes in Ph-C*HD-CH2D. Concentration is 0.093 M in CC14.
lapping of the observed bands sometimes makes accurate assessment of individual D or R values tenuous a t best. Another reason concerns the couplings among the local CH and CD stretching motions. In the case of VCD spectra, these couplings play a significant role in determining how rotational strength is distributed among neighboring modes. Since we currently lack a precise determination of these couplings, we will frequently concern ourselves only with sums of R values. The experimental values of these sums of rotational strengths range between about f30 X esu2.cm2 in both C H and CD
Vibrational Optical Activity in Deuteriated Phenylethanes
The Journal of Physical Chemistry, Vol. 92, No. 11, 1988 3307 0.085M IC& I
0.088M I C C I,
'lo
T
%T
cm-'
Figure 16. VCD (top, 4 scans) and IR transmittance (bottom, 1 scan) spectra of v(CD) modes in Ph-C*HD-CD2H. Concentration is 0.085 M in C2CI4.
10 cm-1
Figure 14. VCD (top, 5 scans) and IR transmittance (bottom, 1 scan) spectra of v(CD) modes in Ph-C*HD-CH2D. Concentration is 0.088 M in CCI4.
0.090M ICCI,
&
0.085 M /C,C l L
. ? 3
0 2 x
W
'
0
a -1
'1. T
( 1 1 1
3 0 3100
3000 cm-'
Figure IS. VCD (top, 4 scans) and IR transmittance (bottom, 1 scan) spectra of u(CH) modes in Ph-C*HD-CD2H. Concentration is 0.085 M in C2CI4.
stretching regions. In a given molecule, they tend to be of opposite sign in the CH versus the C D stretching region, reflecting the quasi-mirror-image relationship of the hydrogen and the deuterium atoms in the -C*HD-fragment.
VI. Charge Flow Model Calculations In applying the CF model, we distinguish between principal charge flows and nonprincipal charge flows. Principal charge flows are those which occur in the bonds involved directly in the deformation under consideration, e.g., a stretch or a bend. Nonprincipal charge flows are the concomitant flows induced in bonds neighboring to those involved directly in the deformation. IR intensity studies of n-paraffins5-8 have shown that for such systems the nonprincipal charge flows are negligible compared to the principal charge flows. W e decided therefore to derive values for charges and charge flows in the Hornig approximation.18 In this approximation the only nonzero charge flows are the principal charge flows associated with bond stretching. The values (18) Hornig,
D. F.;MacKean, D. C . J . Phys. Chem. 1955, 59,
3000
2900
cm-1
2900
1133.
Figure 17. VCD (top, 4 scans) and IR transmittance (bottom, 1 scan) spectra of v(CH) modes in Ph-C*HD-CD3. Concentration is 0.090 M in CCI4.
we obtained are 0.065e for the equilibrium atomic charge ZHoe on the aliphatic hydrogens, and a principal charge flow" e(a[c~rcH)o(ethyl)= -0).187e/Ain the ethyl group. The sign of this charge flow indicates that a stretching of the C-H bond causes a flow of negative charge toward the hydrogen. The values are close to those employed by Gussoni et al.8 The derivation of these values is presented in the Appendix. For the phenyl ring we obtained ZHo= -Zco = 0.1 18e using the infrared intensity data of Spedding and Whiffen9 for the out-of-plane modes of benzene. This value is close to that derived by other workers.l0 From the intensity data for the C H stretching region in benzene, we obtained a charge flow of e(a,$cH/ar,H)o(phenyl) = -0.022eIA. As before, the sign of this charge flow is such that negative charge flows toward the hydrogen as the C-H bond stretches. The derivation of the phenyl ring parameters is also given in the Appendix. Finally, we have taken Zco= -0.195e for the methyl carbon in order to produce a neutral methyl group. From the gas-phase equilibrium dipole moment measurements on ethylben~ene,'~ we (19) Baker,
J. W.; Groves, L. G. J . Chem. SOC.1939, 1144.
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The Journal of Physical Chemistry, Vol. 92, No. I I, 1988
TABLE VII: Charge Flow Model Cnlculntioas of Dipole nod Rotational Strengths in Optically Active Phenylethanes (Effectof Polarizability of Phenyl Ring Not Included) cis conformation" 10390,
1045~,
orthogonal conformation 10390,
1045~,
esu2.cm2 esu2+cm2esu2.cm2 esu2.cm2 assignt Ph-C*HD-CH,
2.9 3.1 3.1 0.9 2.0
6.0 -5.6 1.8 -0.2 -1.4
2.9 3.1 3.1 0.9 2.0
1.4 -6.8 -1.9 -0.6 1.6
Ph-C"HD-CH2D
3.1 1.4 3.4 0.8 2.3
0.2 0.3 1.5 -0.4 -1.0
3.1 1.4 3.4 0.9 2.4
0.3 0.6 -2.1 -0.6 2.2
2.3 3.1 1.8 1.8 1.2
0.2 1.9 -0.2 -1.2
0.0
2.3 3.2 1.8 1.8 1.2
-2.1 -0.3 1.4 +0.6
3.0 1.6 2.1 2.4 0.4
2.0 3.8 -4.1 -1.2 0.1
3.0 1.6 2.1 2.4 0.4
-1.8 3.1 -4.2 2.1 0.2
Ph-CIHD-CDZH
Ph-C*HD-CD,
0.3
"See text.
determined the values of the charges for the carbon atoms at the phenyl-ethyl junction to be Zcoe = +.le for the phenyl carbon and Zcoe = -0.030e for the methylene carbon. The calculations for the dipole strengths D and the rotational strengths R were performed a t various dihedral angles of the phenyl ring about the ethyl group. A full discussion of the relative energies of the conformers is reported in ref 12 and the references therein. Here we report only the results obtained for the so-called cis conformation, where the plane of the phenyl ring plane bisects the angle between the methylene C-H and C*-D bonds, and for the so-called orthogonal conformation, where the phenyl plane has been rotated about the C-C junction by 90° with respect to the cis conformation. The orthogonal conformation is thought to be the most favored conformation from a number of studies, both experimental and theoretical,'2s20but the barrier is probably less than 2.3 kcal/mol and perhaps closer to 1 kcal/mol. The three different staggered rotamers of the methyl group in Ph-C*HDCH2D and Ph-C*HD-CD2H were also taken into account in the calculation of the dipole and rotational strengths for these molecules. In Table VI1 we present the averages of the three calculations in each case. The calculated dipole strengths compare favorably with experiments for Ph-C*HD-CH3 and Ph-C*HD-CD3. In particular, we match the following important observed features among the intensities Zv of the modes v: Zv,,(CH3) > Zv(C*H) > Zv,(CH3) in Ph-CH*D-CH3, and Zv,,(CD3) > Zv(C*D) > Zv,(CD3) in Ph-C*HI)-CD3. In the case of Ph-C*HD-CH2D the calculated dipole strengths agree with experiments to within a factor of 2. The same statement holds for Ph-C*HD-CD2H except for v(C*D) plus v,(CD~). The calculated rotational strengths, which show a conformational dependence in both absolute value and sign, are l order of magnitude lower than the corresponding observed quantities. The mechanism by which the rotational strengths are generated in these model calculations localizes the electric dipole transition moment in the ethyl C-H and C-D bonds, and the magnetic dipole transition moment arises from very small dynamical couplings with out-of-plane motions in the phenyl ring. From extensive investigations of the dynamical problem and checking of calculated frequencies against observed ones,12we conclude that there is no (20) Schaefer, T.; Kruczynski, L.; Niemczura, W. Chem. Phys. Lett. 1976, 38, 498. Hehre, W. J.; Radom, L.; Pople, J. A. J . A m . Chem. SOC.1972, 94, 1496.
Abbate et al. way to alter the force field so as to increase these couplings, and hence the rotational strength, without going to unacceptable values of interaction force constants that destroy the reasonable frequency fit. Moreover, postulating reasonable nonprincipal charge flows in the C*-phenyl and C*-CH3 carbon-carbon bonds due to C H or C D stretchings would not generate a magnetic dipole transition moment large enough to change the order of magnitude of the calculated rotational strengths. What seems to be needed here are some charge rearrangements sufficiently removed from the asymmetric carbon so as to give rise to a large magnetic dipole transition moment along the direction of the electric dipole transition moment. In what follows, we propose a mechanism that provides for such a charge rearrangement in the phenyl ring. (Note: a referee points out that in a recent paper [ J . Phys. Chem. 1987,91,46] Escribano, Friedman, and Nafie show that the bond dipole theory of VCD, when developed within the bond charge formalism, generates the sum of the fixed partial charge and the charge flow contributions.)
VII. Effect of the Phenyl Ring Polarizability on the Dipole and Rotational Strengths of the Aliphatic CH and CD Stretching Modes A . General Expressions. Polarizable groups play an important part in a number of theoretical models for optical activity.21 Such groups have been invoked by Barnett et a1?2 in their interpretation of the VCD of the methylene stretching modes of (S)-(+)-9,10dihydrodibenzo[c,g]phenanthrene. We use an approach here conceptually similar to theirs and develop expressions for the effect of polarizable groups appropriate for the charge flow model. We then apply them to assess the effect of the highly polarizable phenyl group on the rotational strengths calculated for the aliphatic C H and C D stretching modes in the phenylthanes. An electric field E, at the point p in a polarizable body gives rise to an induced electric dipole moment p,: Pp = 3QpEp
where A, is the polarizability tensor at the point p. For a transition from the ground vibrational state 10) to the fundamental state b) in the normal coordinate Qi, the contribution to the electric dipole transition moment from the polarization at the point p is
where we have made the harmonic approximation. Here and in what follows a subscript or a superscript zero refers to quantities at equilibrium. The polarization will also make a contribution (jlmplO) to the magnetic dipole transition moment. If we treat (Olp,b) as a point dipole located a t point p, it follows from the definition of the magnetic dipole transition moment24that
Here w j is the harmonic frequency in cm-' for the fundamental transition in Q,, and rp is the position vector to the point p. We now examine the term ( a ~ , / a Q ~ )From ~ . eq 1 we see that (4) where we have assumed (21) Barron, L. D. Molecular Light Scattering and Optical Activity; Cambridge University Press: New York, 1982. (22) Barnett, C. J.; Drake, A. F.; Kurcda, R.; Mason, S . F. Mol. Phys.
1980, 41, 455. (23) Brand, J. C. D.; Speakman, J. C. Molecular Structure: The Physical Approach, 2nd ed.; Halsted: New York, 1975; p 329. (24) Condon, E. U. Rev. Mod. Phys. 1937, 9, 432.
Vibrational Optical Activity in Deuteriated Phenylethanes
(2) 0
=O
In the charge flow model," the total electric dipole moment is written as a sum of individual bond moments. These bond moments are taken to arise from equal and opposite point charges associated with the relevant bonded atoms. As such, the electric field a t the point p from these point charges can be written as
Here a1and azdenote the atoms that specify the bond a,raZpis a vector directed from atom a2to the point p, and 5, is the bond charge in units of electronic charge e. The convention" is such that bond a contributes charge eta to the total charge a t atom
The Journal of Physical Chemistry, Vol. 92, No. 11, 1988 3309 TABLE VIII: Calculated Dipole Strengths D (esu2.cm2 X lo") Including the Effect of Phenyl Ring Polarizability" 120'
150'
assignt
2.9 2.7 3.0 3.0 4.5 4.7 0.9 0.9 3.2 2.9
2.6 2.8 4.4 0.9 2.7
2.6 2.7 3.9 0.9 2.9
2.7 2.7 3.8 0.9 3.2
2.9 2.8 4.1 0.8 3.4
v,,(CH,) u(C*H) u,(CH~) u(C*D)
Ph-C*HD-CHzD
3.0 1.7 4.3 1.0 3.5
2.9 1.7 4.5 1.0 3.1
2.8 1.7 4.2 1.0 3.0
2.7 1.6 3.7 1.0 3.1
2.7 1.7 3.6 1.0 3.4
2.9 1.7 3.8 1.0 3.6
v,,(CH~) u,(CH~) u(C*H) u,(CD) u(C*D)
Ph-C*HD-CDzH
2.4 2.4 4.2 4.4 1.7 1.6 3.1 2.8 1.2 1.2
2.2 4.1 1.6 2.7 1.1
2.2 3.6 1.5 2.8 1.1
2.3 3.4 1.6 3.1 1.2
2.4 3.7 1.6 3.2 1.2
u,(CH) u(C*H) u,,(CDZ) u(C*D) v,(CDJ
Ph-C*HD-CD3
4.0 1.2 2.3 3.7 0.4
3.9 1.1 2.2 3.2 0.5
3.5 1.0 2.2 3.3 0.5
3.3 1.1 2.3 3.7 0.5
3.5 1.1 2.3 3.9 0.5
v(C*H) V,,(CD~)
0'
Ph-C*HD-CH,
a2and charge -etu to the total charge at atom al. Differentiating
(6) we obtain
30° 60° 90'
4.2 1.2 2.2 3.4 0.5
u(C*D) u,(CDp)
'The different columns refer to different rotamers. See text. Since the effective equilibrium atomic charge ZAoat atom A is the sum of its equilibrium bond charges," the first term on the right in eq 7 can be rewritten in terms of a sum over atoms:
Performing the differentiation indicated in eq 8, we have, after some manipulation
Here the unit vectors el, e2, and ej specify the x, y , and z directions and tAj is the Cartesian displacement of atom A in the normal modej. By combining eq 8 and 9, one can obtain the equilibrium charge contribution to (dEp/dQj)o. The charge flow contribution to (dEp/dQj)ois given by the second term on the right in eq 7. Because the charge flow parameters are given in terms of internal deformation of the molecule, it is expedient to expand this term in a complete set of internal coordinates Rk. Since"
it follows that
where stA are the Wilson vectors.25 From eq 7-10 we obtain an expression for the combined charge and charge flow contributions to (dE,/dQj)O,namely
(25) Wilson, Jr., E.B.; Decius, J. C.; Cross, P.C.Molecular Vibrations; McGraw-Hill: New York, 1955.
With the aid of eq 4 and 11 we are now in a position to compute the polarization contributions to the electric and magnetic dipole transition moments given in eq 2 and 3 . B. Calculations for Phenylethanes. In the calculations for the phenylethanes, we put one-sixth the polarizability of a benzene ring at each phenyl carbon atom. (The polarizability of benzene is 12 A3in the plane and 6 A3perpendicular to the plane of the ring.z3) Each phenyl carbon atom corresponds then to a point p i n eq 11. The values achieved for D and R with the inclusion of the phenyl polarizability are given in Tables VI11 and IX, respectively, for six different conformers. The column labeled 0' refers to the cis conformer. The columns labeled 30°,60°,etc., refer to rotamers generated from the cis conformation by rotating counterclockwise 30°, 60°,etc., about the phenyl-ethyl C-C bond as viewed from the phenyl toward the ethyl portion of the molecule. The changes effected by including the polarization terms can be seen from a comparison of Tables VII, VIII, and IX. As regards IR intensities, the agreement between calculated and experimental D values is improved for v(C*H) and v(C*D), but in general there are no drastic changes. As before, the D values depend little on the conformation. Much more dramatic changes, however, occur for the calculated R values. To begin with, there is generally an order of magnitude increase of the calculated R values in the significant conformers (vide infra) we have called cis (OO), orthogonal (go'), and the forms (60' and 120') in which the phenyl ring and the C*-H bond or C*-D bond are coplanar. These latter forms we shall refer to as "eclipsed". Also, a strong conformational dependence is now exhibited in the R values for all C H and C D stretching modes. The correct signs for the total sum of R values over the CH stretching region C R ( C H ) and the corresponding total sum over the C D stretching region Z R ( C D ) are shown by both the eclipsed and the orthogonal conformations. The orthogonal conformation is the form predicted to be of lowest energy by both a molecular orbital and an NMR study.20 Although there is not complete unanimity as to what the lowest energy form is, the conformers we have called cis (O'), orthogonal (go'), and eclipsed (60' and 120') are all sufficiently close in energy that all have significant populations at room temperature.20 An assumed population distribution consisting of 40% orthogonal and 20% of each of the other conformers provides an agreement with experiment in both sign and order of magnitude in all cases. (See column labeled "average" in Table X.) We note too that other population distributions can be accommodated equally well. Our motivation here is not to perform a conformational analysis, but
3310 The Journal of Physical Chemistry, Vol. 92, No. 11, 1988
Abbate et al.
TABLE IX: Calculated R o t n t i o ~ Strengths l R (esu2.cmzX 1v)Including the Effect of Phenyl Ring Polarizabilitya 0" -25.9 21.6 -45.9 5.2 18.3
30" 1.6 6.2 14.0 5.2 19.9
60" 40.2 -45.5 57.5 13.5 -3.6
90"
1200
150"
assiant
57.9 -71.9 42.3 20.9 -27.7
42.1 -60.2 -17.9 20.7 -28.2
-2.2 -19.4 -62.8 13.4 -5.4
uaS(CHd
Ph-C*HD-CHzD
-2.3 -4.7 -38.8 6.4 13.5
3.6 7.0 23.9 9.0 15.4
-2.8 -12.6 76.9 12.1 -12.5
-6.9 -13.7 68.6 14.4 -40.5
-8.9 -10.7 5.8 13.2 -41.4
-10.7 -7.2 -48.6 8.2 -15.1
vACHZ) US(CH2) u(C*H) Um(CD) u(C*D)
Ph-C*HD-CDZH
-2.9 -43.9 5.0 21.2 -4.5
-0.8 14.2 10.2 23.7 -4.4
-6.4 63.2 10.3 5.4 -12.5
-8.8 55.1 10.0 -14.8 -19.3
-8.4 -3.4 7.3 -16.2 -19.3
-8.2 -53.4 2.6 1.5 -12.8
Vm(CH) u(C*H) Uas(CD2) u(C*D) us(CD2)
Ph-CZHD-CD3
-47.8 23.2 -12.8 13.3 -0.6
5.8 28.2 -7.6 17.3 -2.7
51.8
44.8 -1.1 22.3 -40.3 -2.8
-9.7 -6.5 22.3 -43.5 -0.8
-56.2 1.8 4.2 -17.3 -0.5
u(C*H) Vas(CD3)
Ph-C*HD-CH3
13.1
8.6 -10.4 -3.7
u(C*H) VS(CH3) u(C*D)
u(C*D) VS(CD3)
"The different columns refer to different rotamers. See text.
TABLE X Observed and Calculated Values for CR(CH) (esu2.cm2 X lv)and CR(CD) (wu2-cm2X 10'5))0 obsd
cis
15 -18
-45.0 18.3
49.2 -27.7
25.2 -15.9
20.8 -13.8
21 -28
-45.8 19.9
48.0 -26.1
23.9 -14.3
19.6 -12.2
5 -17
-46.8 21.7
46.3 -24.1
22.5 -12.4
18.2 -10.3
25 -18
-47.8 23.1
44.8 -21.9
21.1 -10.0
16.8 -8.3
TABLE XI: Values of (aMU/8Sa),, for Methane calcd from exptl intensities"
" Reference 8.
(-+I
-0.775 0.393
calcd from exptl intensities"
orthogonal eclipsed averageb
Calculated values include the effect of phenyl ring polarizability. See text.
sign choice" (aMa/asas,rctch)O, D/A (aM'/asabnd)O,D/rad
TABLE XII: Charges and Charge Flows for Methane
(++I
0.679 0.349
calcd via ab initio methodsb -0.907 0.371
Reference 7
to stress the potential importance of polarization terms for signs and magnitudes of rotational strengths. VIII. Summary and Conclusions In this work we have recorded the VCD spectra of (S)-(+)1-phenylethane-1 -d,, (S)-(+)-1-phenylethane-I ,2-d2,(S)-(+)-1phenylethane-1 ,2,2-d3,and ( S ) - ( + ) -1-phenylethane-1,2,2,2-d4 in the CH and CD stretching regions, as well as their IR and Raman spectra. On the basis of these data, we have made a detailed assignment of the aliphatic CH and CD stretching vibrations. A full normal-coordinate analysis calculation was performed that gave a good fit to the CH and CD fundamental stretching frequencies. With charges and charge flows derived from this study and previous IR studies, we have calculated the dipole and rotational strengths for the aliphatic CH and CD stretching modes. These calculations failed to provide the correct order of magnitude for the rotational strengths in a number of instances. Hence, we have sought to improve the model through the introduction of polarization terms. Analytical expressions for these terms have been
sign choice" ZHO (a[cH/arcH)o,A-' Reference 8.
(-+I
0.065 -0.187
(++) 0.058 0.059
calcd from ab initio resultsb 0.059 -0.204
Reference 7.
derived, and we have applied them to the optically active phenylethanes where they lead to the observed orders of magnitude for the rotational strengths. It is our opinion that such terms will turn out to be of importance in other molecules, especially those that contain significantly polarizable entities.
Acknowledgment. This study could not have been done without the deuteriated phenylethanes synthesized by Dr. Harry S.Mosher and his co-workers a t Stanford University. We gratefully acknowledge our debt to them in this regard. We also express our gratitude for financial support for this research from grants provided by the National Science Foundation (CHE-8305808) and The Upjohn Co. Appendix
A . Aliphatic Charges and Charge Flows. Gussoni et a1.* have provided a method for obtaining electrooptical (valence-optical) parameters from IR intensity data and have applied their method to methane and ethane. We use some of their results here, and so to avoid confusion, we have carried over their notation without change in this Appendix. We call this fact to the reader's attention, since some of their symbols (e.g., a) have been used with a different meaning in the body of our text. The reader is referred to the paper of Gussoni et al. for detailed definitions of a number of their symbols. For methane, Gussoni et al. give the following relations between the valence-optical parameters and the derivatives of the a component (CY = x,y,z) of the molecular dipole moment with respect to the internal symmetry coordinate Sa that transforms as a:
Vibrational Optical Activity in Deuteriated Phenylethanes Here pCHois the component of the C-H bond dipole moment in the C to H direction a t equilibrium. The quantities (apk/ark), and (apk/arj), represent derivatives of the C-H bond dipole moment with respect to stretching of the same bond and with respect to stretching of a neighboring bond, respectively. The quantities (apk/aakj), and (apk/aaj,,,), represent derivatives of the C-H bond dipole moment with respect to the bending of adjacent and opposite HCH angles, respectively. Using the Homig approximation,’* we assume that
and employ eq 9 and 10 of ref 11 in conjunction with eq A1 and and (aM‘/aSuk,d)o in terms of A2 to express (aMu/aSustretCh)O charges and charge flow to the charge flow model
where rcHois the equilibrium C-H bond distance. In Table XI we report the values for (aM‘/aSa)o from ref 7 and 8. Two possible sets of values are obtainable from the experimental IR intensities, since two assumptions can be made as
The Journal of Physical Chemistry, Vol. 92, No. 11, 1988 3311 to relative signs for the derivatives of the molecular dipole moment with respect to normal coordinates. As is discussed in ref 8, the (-+) solution is the preferred one. This solution satisfies the isotopic invariance criterion and compares favorably with the values achieved from an ab initio calculation by Meyer and Pulay.7 (See Table XI.) The associated values for the charges and charge flows calculated via eq A3 and A4 are given in Table XII. B. Phenyl Charges and Charge Flows. The charge and charge flows for the phenyl portion of the molecule are derived from IR ~ the work of Spedding and intensity studies on b e n ~ e n e .Applying Whiffen9 to the charge flow model, we have
and
where, of course, all quantities labeled with subscripts H or C H in cA5) and (A6) refer to quantities appropriate for the phenyl ring. Also, (aM/dy), is the derivative of the total dipole moment of benzene with respect to an out-of-plane HCCC bending coordinate. From eq A5 and A6 we obtain the charge and charge flow parameters given in section VI of this paper. Registry No. (S)-(+)-1 -phenylethane-1 - d l , 68566-80-3;(S)-(+)-1 phenylethane-1,2-d2, 68525-08-6; (S)(+)-1-phenylethane-1,2,2-d3, 68525-09-7;(S)-(+)- 1-phenylethane-1,2,2,2-d4,68525-10-0.
