J . Phys. Chem. 1986, 90, 1081-1085 near xA = 1 ( 2 cm-I) happened to be very close to AuAB for the isotope dilution. The behaviors of AuAA and AuABdescribed above imply that the present mixtures are distinct from the methanol/water solution. Therefore, the immediate environments around the methyl groups of methanol/water solution are inferred to be greatly different from those of the other two solutions. Although the hydrophilic group may have an inductive effect, yielding some polarization of the methyl group through intramolecular interaction, the fact that the A v A B values for isotope dilution for acetone, acetonitrile, and methanol are all alike suggests that states of the methyl groups in these three liquids are also alike. Therefore, it seems more likely that the hydrophilic group induces some specific network structure of water, which extends to the hydrophobic hydration region around the methyl group. As a result, the magnitude of the methyl-water interaction on one hand and the stability of the hydrophobic association on the other become variable, depending on the character of the hydrophilic group. In the analysis of the excess molar volume of the acetonitrile/water solution with a segmented composition model,5 the solution was tentatively divided into three segments: segment I for 0 < xA 50.25, segment I1 for 0.25 < xA 5 0 . 7 , and segment 111 for 0.7 < xA. In the concentration region of segment I, AvAA decreases linearly, while in the region of segment 111, AuAA = 0 and AuAB = constant. Accordingly, each segment might indeed be characterized by a solution structure, but further study along this line seems necessary. When the solution is not homogeneous from a thermodynamic view, the Kirkwood-Buff integral,24especially G22,can be used to represent the local fluctuation of the correlated number density. In our previous study, AvAA from the methanol/water and methanol/carbon tetrachloride solutions exhibited some correlation with G22. Recently G I 1(water-water), G22(solute-solute), and (24) J . G. Kirkwood and F. P. Buff, J..Chem. Phys., 19, 774 (1951).
1081
G12(solute-water) were determined for acetone/water and acetonitrile/water along with other substances by Matteoli and Lip01i.~~In their result, G22exhibited a large maxima at xA = 0.3 for acetonitrile and a vague one at xA = 0.1-0.3 for acetone. These behaviors are considerably different from the monotonous decrease of AvAA shown in Figure 3. Therefore, for the acetone/water and acetonitrile/water solutions, AvAA is not correlated with the thermodynamically deduced fluctuation. On the other hand, Singh and Krueger investigated the Raman spectra of these solutions,26pointing out that the C O stretching frequency of acetone increased but the CN stretching frequency of acetonitrile decreased upon mixing with water linearly with the concentration. However, the bandwidths of the vco and vCN modes showed some features near the concentrations where Gz2 gave their maxima. Similar correlation appeared between GI I and the bandwidth of the vOH mode of water. Therefore, the bandwidth of the polar groups seems to be correlated with the macroscopic inhomogeneity in these solutions. In conclusion, the homogeneous and heterogeneous interaction factors obtained from the Raman difference analysis seem to serve as a sensitive indicator of a structural change of molecular association. For some systems, the behavior of these shift factors suggests a correlation with a thermodynamic function. We stress that combination of thermodynamic and spectroscopic information should give a more complete picture of solution structures. Acknowledgment. The authors express their gratitude to Professor D. M. Hanson of the State University of New York for reading this paper and for his stimulating discussion. Registry No. (CH,),CO, 67-64-1; H,O, 7732-18-5; CH,CN, 75-05-8; CHSOH, 67-56-1; CD,CN:, 2206-26-0; (CD,),CO, 666-52-4; CD,OH, 1849-29-2; CD,OD, 81 1-98-3; C,H,, 71-43-2; C6D6, 1076-43-3; CC14, 56-23-5. (25) E. Matteoli and L. Lipori, J. Chem. Phys., 80, 2856 (1984). (26) S. Singh and P. J. Krueger, J. Raman Spectrosc., 13, 178 (1982).
A Local Mode Analysis of the CD Stretching Fundamental and Overtone Spectra of Deuterated Dihalomethanes M. Khalique Ahmed and Bryan R. Henry* Department of Chemistry, University of Manitoba, Winnipeg, Manitoba, Canada R3T 2N2 (Received: September 30, 1985)
The overtone spectra of CD,Z2 (Z = CI, Br, or I) molecules in the liquid phase are measured in the region of the C D stretching local mode overtones corresponding to A u ~ D= 2-5 (CD2CI2and CD2Br2)and A v ~ D= 2-4 (CD212). These spectra, and those of the previously reported fundamentals, are analyzed in terms of the local mode model. At a given quantum number ti = u, + u2, the vibrational states corresponding to CD stretching are taken as symmetry-adapted states of the type ~ u , , c ~ ) + = (1/2'/2)(lolu2) A ~ u z , u , ) )where , lu,,u,) = Ivl)lu2)is the Morse oscillator product function of the two bond wave functions. Intramanifold coupling between the symmetrized states is determined from a harmonic coupling model, and intermanifold coupling is neglected. The agreement between the calculated and observed spectra is found to be good. A comparison of the spectra of the CD2Z2and CH2Z2molecules reveals the manifestations of increased coupling between the CD bonds.
Introduction The local mode model has been very successful in the interpretation and understanding of XH stretching overtone spectra of polyatomic molecule^.^-^ In this model, X H bonds (X = C, 0, N, or S) are considered as weakly coupled anharmonic oscillators. For example, consider molecules like the dihalomethanes where the two X H bonds share a common X atom. For these two (1) (2) (3) (4)
B. R. Henry, Acc. Chem. Res., 10, 207 (1977). B. R. Henry, Vib. Spectra Struct., 10, 269 (1981). M. L. Sage and J. Jortner, Adu. Chem. Phys., 47, 293 (1981). M . S. Child and L. Halonen, Adu. Chem. Phys., 57, 1 (1984).
0022-3654/86/2090- 108 1$01.50/0
coupled C H bonds, local mode basis states are taken as Morse oscillator product states, Le., IuI.uz) = Icl)Iu2),where 10,) and Iu,) are Morse oscillator wave functions for the first and second C H bond, respectively, for a given vibrational quantum number u = u, + Symmetrized states for the two coupled bonds are written as5-' (5) I. A. Watson, B. R. Henry, and I. G. Ross, Spectrochim. Acta, Part A , 37, 857 (1981). ( 6 ) 0 . S . Mortensen, B. R. Henry, and M. A. Mohammadi, J . Chem. Phys., 75, 4800 (1981). (7) A . W. Tarr and B. R. Henry, Chem. Phys. Lett., 112, 295 (1984).
0 1986 American Chemical Society
1082
The Journal of Physical Chemistry, Vol. 90, No. 6, 1986 lUlJh)*
=
1 3
( l U l P 2 ) f IUZJI))
@I+
+
+
(u12 ~2~ - aJ(a2’ - a 2 h w + U ~ ) W-
+ CI + UJWX + @I+
+ ad(a*+ + a2)dJw ( 2 )
GI2
2 GI1
and
I
W
0
z a a C L 0
cn m
a
In eq 2, o (cm-’) and w x (cm-I) are the harmonic frequency and diagonal local mode anharmonicity, respectively, for an isolated C H bond. el and c2 are the quantum numbers of the two C H oscillators, and E, is the ground-state energy in wavenumber units. y and dJ determine the kinetic energy and potential energy coupling between the two C H bonds and are defined in terms of the Wilson G and F matrix elements 1 y=---
,
I
(1)
We have used an extremely simple model to calculate the energies of the C H stretching peaks in the overtone spectrum of the dihalomethanes.6 The model contains all of the anharmonicity that is diagonal in a single C H oscillator but evaluates the matrix elements that couple the two C H oscillators in the harmonic limit. The local mode Hamiltonian for the CH2 system is taken to be6
H - E, = ( V I
Ahmed and Henry
P (cm-’) Figure 1. Liquid-phase overtone spectra of CD2C12,CD2Br,, and CD2I2 in the region of Agc0 = 2. Spectra were measured at room temperature with a path length of 0.1 cm. Absorbances of CD2Br2and CD212have been offset by 0.3 and 0.6 absorbance units, respectively.
(99+ atom ?& D) were obtained from Merck Sharpe and Dohme Canada, Ltd. All samples were used as received. Liquid-phase overtone spectra in the CD stretching regions of vCD = 2-5 were In the harmonic approximation, the operators a+ and a have the recorded on a Beckman 5270 spectrophotometer with the near-IR usual step-up and step-down properties:6 light source. All of the spectra, in a digital format, were transferred to a Nicolet 1280 computer and converted to a linear energy (v + Ila+lc) = ( e 1)li2, (L’ - Ila(c.) = c I / ~ , etc. (4) scale. The spectra were plotted in wavenumber units with a Nicolet Zeta 160 plotter. According to this “ladder” coupling scheme,6 effective coupling A 0.1 cm path length cell was used to record the hcD =2 only occurs between states which belong to the same manifold, spectra. The spectra at AccD = 3-5 were recorded with a 1 cm e, which have the same symmetry, and where the bond excitations path length cell. However, a single measurement of the AecD = differ by a single quantum; Le., Icl,e2)+effectively couples to lel 4 spectra for all three molecules and the .lecD = 5 spectra of f 1 ,c2 =F 1 )+, etc. The effective coupling decreases as the level CD2CIZand CD2Br2with a 1-cm cell gave a very poor signalof excitation increases. Thus, the pure local mode states, Ie,O)*, to-noise ratio. The signal-to-noise ratio was improved by signal which carry most of the intensity, are split at AuCH = 1 and AeCH = 2 but become effectively degenerate for higher overtones (hCH averaging four base line corrected scans for AcCD = 4 and nine base line corrected scans for AuCD = 5 , on the Nicolet 1280 L 3). The transition energies for these overtones can be simply computer. described by the vibrational energy expression for a single Morse The peak maxima in the spectra for AvCD = 2 and 3 were oscillator determined from the digital data with a Nicolet 1280 program which simply identified the wavelength setting at the highest AE = W [ C - X ( U * c)] (5) absorbance value in the vicinity of the peak. Since the peaks are This local mode analysis scheme has successfully accounted for relatively well resolved in these regions, such a procedure was fairly the observed CH stretching spectral peaks in the fundamental and = 4 and 5 were composed of accurate. The spectra at kCD overtone spectra of CH2Z2molecules.6 The extension of this overlapping peaks. These spectra were deconvoluted with a scheme to XH, and XH, molecules has also produced results in Fortran curve analysis program YIRCAP” which fitted Lorentzian very good agreement with observation^.^**^^ peaks to the experimental bands. In this paper, we report the C D stretching overtone spectra of Results and Discussion CD2Z2molecules ( Z = Cl, Br, or I), and assign these spectra and the reported fundamentalslO~ll in terms of the same local mode Spectral Analysis. The liquid-phase overtone spectra of CD2Z2 analysis. In our work on the dihalomethanes, we determined that molecules in the regions of ACCD = 2, 3, 4, and 5 are shown in kinetic energy was the principal source of coupling between the Figures 1-4. The peak positions for these spectra and for the two C H oscillators. In the deuterated molecules, the change in fundamentals are given in Table I. Two types of peaks are mass ratio will significantly increase this coupling. We will analyze observed. The first type is only associated with CD stretching the spectral manifestations of this increased coupling and discuss and is assigned within the local mode description to symmetrized its effect on the applicability of the simple local mode analysis combinations of Morse oscillator product states IcI,u2)*. The scheme. second type of peak is marked by a C in Figures 1-4. For a given vibrational manifold, u , these peaks involve two quanta of DCD Experimental Section bending combined with C D stretching states with e - 1 quanta. A high-purity sample (99.6+ atom 95 D) of CD2Cl2was obWe first discuss the CD stretching peaks. For CD212,the local tained from Fisher Scientific Co. Samples of CD2Br2and CD,I, mode assignments are indicated in Figures 1-3. The corresponding assignments for CD2Br2and CD2C12are obvious from the figures, and in the following discussion the arguments apply to all three (8) B. R. Henry, A. W. Tarr, 0. S . Mortensen, W. F. Murphy, and D. A. spectra. C. Compton, J . Chem. Phys., 79,2583 (1983).
+
+
(9) L. Halonen and M. S . Child, Mol. Phys., 46, 239 (1982). (10) T. Shirnanouchi and I. Suzuki, J . Mol. Spectrosc., 8, 222 (1962). (1 1) M. Avanessof, H. D. Thang, and R. Gaumann, Helu. Chim.Acta, 54, 1013 (1971).
(12) The Fortran 77 program modified by A. W. Tarr.
VIRCAP
was written by R. K . Marat and
The Journal of Physical Chemistry, Vol. 90, No. 6, 1986 1083
Overtone Spectra of Deuterated Dihalomethanes
0 0012
w
0
z a
t
/ i
i
m
E 0
cn 0 0008 m
a
0.0004
0 00
pv 1
6900
1
1
I
10950
10550
0 0000
I
6600
6300
i7 (cm-'1
10150
i 7
Figure 2. Liquid-phaseovertone spectra of CD2CI2,CD2Brz,and CD212 in the region of A u ~ D= 3. Spectra were measured at room temperature with a path length of 1 .O cm. Absorbances of CD2Br2and CD212have been offset by 0.1 and 0.2 absorbance units, respectively.
(cm-') Figure 4. Liquid-phase overtone spectra of CD2CI2and CD2Br2in the region of AucD = 5. These spectra are the sum of nine base line corrected scans. Individual scans were measured at room temperature with a 1.0 cm path length cell. The absorbance of CD2Br2has been offset by 3.6 X absorbance units. TABLE I: Observed Peak Positions (cm-') for CDzZz Molecules AUCD CD2C12 CD2Br2 CDJ2 assignt 2198" 2195' 2182' Il.O)& 2304" 2312' 2291'
0 000
9000
8800
8600
8400
V (cm-I) Figure 3. Liquid-phase overtone spectra of CD2CI2,CD2Br2,and CD212 in the region of Aoc0 = 4. These spectra are the sum of four base line
corrected scans. Individual scans were measured at room temperature with a path length of 1 .O cm. The right-hand ordinate scale represents the absorbance of CD2I2. The absorbance of CD2Br2has been offset by 3.4 X lo-' absorbance units with respect to the absorbance of CD2C12. The principal peaks in the AuCD = 2 spectra (Figure 1 ) are 12,0)+,12,0)-, and 11.1). The splitting between the 12,0)+and 12,O)peaks is appreciable, more than twice as large as the corresponding splitting in the spectra of the CH,Z2 molecule^.^ In the absence of coupling, the 12,0)+ and 12,O)- states would be degenerate. However, harmonic coupling of 12,0)+ and 11,l) via the y and d, parts of the Hamiltonian (eq 2) lowers the energy of 12,0)+ and provides the splitting between it and 12,0)-. At A U C D = 3 (Figure 2), splitting occurs between 13,0)+and 13,0)-. The corresponding peaks are totally unresolved in the spectra of the CH2Z, molecule^.^ However, this splitting is much smaller than the corresponding splitting at A u C D = 2. Well-resolved local mode combination peaks, 12,1)+ and 12,1)-, occur on the high-energy side of the )3,0)- peak. The splitting for the 12,1)* peaks is greater than for the 13,0)+ peaks because the former
4286 4367 4442 4573
4250 4333 4351 4445 4589
6447 6502 6548 6616 6612 6807
6381 -6463 6483 6541 6584 6679 6829
841 l C -8555C -8555C -861SC 8702c -884OC
8498' -8559' -8594' -8675' 8727' 8869'
-
10476' -10601' -10832'
'
4265 4326 4414 4551 -6380 6429 6487 6626 6719 8392< -8483' -8516' -8563' 8660' 8804'
-10391' -10539' 10609' 10797'
--
Reference 10. Reference 11. From deconvolution; see text.
dug
is the CD2 rocking mode. TABLE 11: Local Mode Parameters (cm-') for CDIZ2 Molecules
molecule
w
iL'X
y'w
CD2C12 CD2Br2 CD212
2306.5 2306.5 2289.5
28.5 28.0 27.5
48.4 55.4 54.9
splitting originates from a first-order coupling whereas the latter splitting originates from a third-order coupling. In terms of the unsymmetrized Morse product states, 12,l) is directly coupled to )1,2) but 13,O) couples to 10,3) via the coupling route 13,O) z 12,l) z 11,2) + 10,3). At AuCD = 4 (Figure 3) prominent peaks arise due to transitions to the symmetrized states 14,0)+, 14,0)-, 13,1)+, and 13,1)-.
1084
The Journal of Physical Chemistry, Vol. 90, No. 6, 1986
Ahmed and Henry
TABLE 111: Observed and Calculated Peak Positions (cm-') for CDIZz Molecules CD2Cli obsd 2198 2304 4367 4442 4573 6502 6548 6672 6807 -8555 -8555 8702 -8840 10601
-
10832
CD2Br, calcd 2201 2298 4370 4442 457 1 6502 6548 6670 6818 8590 8612 8741 8871 10622(+) 10629(-) 1 1046 10892 10789 11227
CD2Iz
obsd 2195 2312 4357 4445 4589 6483 6541 6679 6829 -8559 -8594 8727 8869 10609
-
10797
calcd
obsd
calcd
2195 2306 4359 4445 4587 6488 6548 6680 6842 8577 861 1 8742 8889 10616(+) 10630(-) 11073 10904 10782 11270
2182 2297 4326 4414 4551 6429 6487 6626 6179 -8483 -8516 8660 8804
2180 2290 4328 4414 4555 6444 6503 6634 6794 8520 8553 8683 8828 10546(+) 10560(-) 10998 10830 10709 11192
However, there are a number of combination peaks in this region, and several of the peaks overlap. This overlap is particularly severe for the peaks 14,0)+, 13,0)-12v2), and (4,0)-. Even given our deconvolution procedure, the positions of these peaks, as listed in Table I, should be considered only as estimates. At AvCD = 5, the prominent peaks in the spectra of CD2CI2 and CD2Br2(Figure 4) are the pure local mode peaks 15,0), and the local mode-normal mode combination peaks 14,0)&!v2). Symmetry splitting between the 15,0), states is not observed at A u C D = 5 due to a smaller effective coupling. The combination peak 14,0),12v2) lies on the low-energy side of the )5,0), peak and has considerable intensity due to near-resonant interaction with the pure local mode peaks. Most of the combination peaks with two quanta of the DCD bending mode (peaks denoted C in Figures 1-4) can be assigned to states of the form Iu - 1,0),12v2) (see Table I). Such peaks have been observed in the C H stretching overtone spectra of a number of polyatomic m o l e ~ u l e s ~ J and ~ - ~gain ' intensity principally through resonant or near-resonant interactions with lu,O), states. Combination states corresponding to 11,1)12v2)and 12,l )+12v2) can be assigned in the regions of h u c D = 3 and hucD= 4, respectively. The assignments can be made straightforwardly on the basis of the local mode peak positions and the fundamental DCD bending frequencies ( v 2 = 995, 1026, and 1002 cm-l for CD2CI2," CD2Br2,11and CD212,11respectively). Local Mode Parameters and Calculated Spectra. In C H stretching overtone spectra, the states lv,O)+ and lo,O)- are effectively degenerate for vCH I3. Because of this, local mode parameters (harmonic frequency, w , and diagonal anharmonicity, w x ) can be obtained by fitting the energies of the pure local mode peaks, Ic,O),, to eq 5 . In our previous work on the dihalomethanes,6 we obtained the effective coupling parameter y' = y - 4 from the observed spectral splitting between the harmonically coupled ll,O)+ and 11,O)- states (2y'w = E(ll,O)..) - E(ll,O)+)). However, there are two difficulties in the application of this procedure to the calculation of the spectra of CD2Z2. In the first place, the peaks (u,O)+ and (u,O)- are spectrally resolved, even at A u C D = 4. Secondly, extensive interactions between the C D stretching states and the combination states involving DCD bending strongly perturb the peak positions in the regions of AuCD = 4 and 5. In fact, the assignments given in Table I for strongly interacting peaks are approximate in the sense that the states must be strongly mixed. ( 1 3 ) H. L. Fang and R. L. Swofford, J . Chem. Phys., 72, 6382 (1980). (14) B. R. Henry and M. A. Mohammadi, Cbem. Phys., 55, 385 (1981). (15) H. L. Fang and R. L. Swofford, J . Chem. Phys., 73, 2607 (1980). (16) B. R. Henry, M. A. Moharnrnadi, I. Hanazaki, and R. Nakagaki, J . Phys. Chem., 87, 4827 (1983). (17) H. R. Dubal and M. Quack, J . Cbem. Phys., 81, 3779 (1984).
assignt
In the present case we adopt a different procedure and determine the local mode parameters by fitting the observed frequencies for AuCD = 2 to the following equations:
+ (2~7')~]'/* E(I1,l)) = 2w - 5 w x + [(Oxy + (20y')2]'/2
E(12,0)+) = 2w - ~
W X [(OX)*
E(12,0)_)= 2~ - ~
W X
(6) (7)
(8)
Equations 6 and 7 are obtained by diagonalization of the 2 X 2 matrix6 of the Hamiltonian of eq 2 over the harmonically coupled 12,0)+and 11,l) states. Equation 8 for the energy of the uncoupled 12,O)- state is simply derived from eq 2 by setting both y and 4 equal to zero, v 1 = 2 , and u2 = 0. The local mode parameters are tabulated in Table 11. From the parameters of Table 11, it is straightforward to calculate the peak positions for all of the CD stretching states of the CD2Z2molecules. The procedure involves substitution of the local mode parameters into the intramanifold coupling matrices6 of eq 2. Matrix diagonalization yields the energies of the symmetrized states. The calculated and observed frequencies are compared in Table 111. The calculated and observed frequencies are in excellent agreement in the regions of A u c D = 1, 2, and 3. However, the agreement in the regions of AUCD = 4 and 5 is not as good. As we have noted, in these regions there are strong interactions between the CD stretching states and combinations which involve the bending mode. The calculation does not take account of these interactions, and this approximation is undoubtedly a major contribution to the discrepancies. Moreover, many of the experimental peak positions are only known approximately. Comparison of the CH2Z2and CD2Z2Spectra. The two principal differences between the spectra of CH2Z2and CD2Z2 molecules are that in the latter molecules there are greater splittings between the symmetrized states Iul,u2), and greater intensities for local mode combinations Iu - n,n), relative to pure local mode states lu,O),. Both of these effects arise because of the higher value of the effective coupling parameter, y'. Since y' is determined primarily by kinetic energy coupling, its marked increase for the CD2Z2molecules is expected. The CD2Z2values for wy' (Table 11) are approximately twice the corresponding values for the CH,Z2 molecules.6 For example, as we have already noted, 13,0)+and (3,O)- are well resolved in CD2Z2(Figure 2). 14,0)+and 14,0)-, though not completely resolved, are clearly at different energies (Figure 3). According to our local mode analysis scheme, the splitting between Ic,O)+ and lo,O)- is due to coupling to the Iu - l , l ) , states, which is determined by the off-diagonal terms in the matrices of eq 2. These matrix elements are given by - - - L ' ~ / ~ ~ lu,O)+ ' O . ~ and Iu,O)approach degeneracy, even for the CD2Z2molecules, but at sig-
Overtone Spectra of Deuterated Dihalomethanes nificantly higher values of u than for the CH2Z2molecules. Another effect of the increased coupling, y,’ on the peak positions is the relative ordering of the states. In CH2Z2,wy‘ is approximately half the value of w x . However, for CD2Z2,wy’ is approximately double the value of wx. Because of weak coupling between the C H bands, the ordering of states in CH2Zzis always E(lu,O)) < E(lu - 1 , l ) ) C E(lu - 2,2)) ... for both symmetric and antisymmetric states. A change in this ordering for CDzZz is observed first at A u c D = 5 where the stronger interbond coupling lowers the energy of 13,2)+ below that of 14,1)+. Thus, in summary, although a local mode analysis can be used effectively to analyze the CD stretching peak positions in CD2Z2,the patterns are not as simple as for the corresponding CH2Z2 molecules. The combination peaks 1u - l , l ) * have significantly higher intensities relative to the pure local mode peaks lu,O)* in CD2Z2 than in CH2Z2 molecules. In a very recent paper,ls we have developed a general theory for intensities in local mode overtone spectra. In that paper we have specifically discussed the band intensities of CD2CI2and CH2C12. The dipole moment of the two coupled oscillators of these molecules was expanded as a Taylor series in the two local coordinates R, and RZ.The transition dipole moment between the vibrational ground state and symmetrized local mode states involved products of dipole moment derivatives, taken with respect to the local coordinates, and single Morse oscillator matrix elements over powers of the coordinate. Dipole moment derivative values were determined numerically from distorted geometry dipole moments which were calculated with a CNDO/2 molecular orbital program. Morse oscillator matrix elements were evaluated numerically. The oscillator strengths of the overtone spectra of CDzC12and CHzClzwere calculated with, and without, vibrational state mixing. The results clearly indicated that the dominant source of intensity for the Iu - 1,1)* states is the vibrational mixing of these states with the pure local mode states Iu,O),. In particular, the antisymmetric states, Iu (18) 0. S. Mortensen, M. K. Ahmed, B. R. Henry, and A. W. Tarr, J . Chem. Phys., 82, 3903 (1985).
The Journal of Physical Chemistry, Vol. 90, No. 6, 1986 1085 1,1)-, have no intrinsic intensity contributions.I8 Since the extent of vibrational mixing is proportional to Y’~,the higher coupling in CD2Zzprovides greater intensity for these Iu - l , l ) * states than in CH2Z2. In the spectra of CD2Br2and CD212,the peaks 12,1)+and 13,1)+ correspond to the most intense peaks at A u C D = 3 and 4, respectively. We have stated in the previous paragraph that vibrational mixing is the principal source of intensity for such peaks. However, vibrational mixing alone clearly cannot account for a higher intensity for Iu - l , l ) + than for Ju,O)+. There are two possible additional sources of intensity for peaks Iu - 1,l )+. One is an intrinsic contribution through the term (dZ,ii/dR, dR,),. This term was found to be small in our previous work,’* but our more recent calculation^'^ have indicated that C N D 0 / 2 is not adequate to accurately map out the dipole moment function as a function of CH/CD bond displacement. Although the C N D 0 / 2 method provides dipole moments in agreement with experiment for the equilibrium geometry, it would appear to have difficulty in accurately determining the derivatives. Thus, the question of a significant intrinsic contribution to the intensity of Iu - 1,1)+ is still open and requires further study. A second possible source of intensity for Iu - l , l ) + peaks is through intrinsic intensity contributions associated with states of the types Iu - 1,0)12v2)and Iu - 2,l )12v2). Such intensity could be transferred to the states Iu - 1,1)+through vibrational mixing. Such a mechanism could presumably contribute to the intensity of 13,1)+ where such mixing is evident in the region of A u C D = 4. However, it is unlikely to make a significant contribution to 12,1)+ in the well-resolved spectral region around A u c D = 3.
Acknowledgment. We are grateful to the Natural Sciences and Engineering Research Council of Canada for financial support. Registry No.
CD2C12, 1665-00-5; CD2Br2, 221 17-86-8; CDJ,,
15729-58-5.
(19) A. W. Tarr and B. R. Henry, unpublished results.
