J. Phys. Chem. 1990, 94, 4778-4783
4178
Isotropic Raman Line Broadening through Vibrational Depopulation. A Comparative Line Shape Study of the C-H and C-D Stretching Modes in Deuterated Species of Methanolt Frank Seifert, Karl-Ludwig Oehme,* Sektion Chemie, Friedrich-Schiller- Universitat Jena, Jena, 6900 DDRIGDR
and Wolfgang Holzer Sektion MathematiklPhysik, Padagogische Hochschule “Dr. Theodor Neubauer” Erfurt, Erfurt, 5010 DDRICDR (Received: May 11, 1989; In Final Form: October 5 , 1989)
The isotropic Raman line widths of C-H and C-D stretching modes in deuterated species of methanol have been measured throughout the whole range of the liquid state. The significant narrowing of the C-H Fermi doublet (peaked near 2835 and 2945 cm-I) in CH30D compared to CH30H is discussed in terms of a fast intramolecular transfer of the vibrational energy to the overtone of the C-0-H bending mode. This process occurs within 1 ps, and no significant temperature dependence has been found. The corresponding C-D bands in CD30H and CD30D are insensitive to the OH/OD exchange. The line shapes of the isolated C-H oscillators in CHD20Hand CHD,OD are indistinguishable. Just like the C-D oscillator in CDH20H, they are sensitive to the internal rotation of the -CHD, (-CDH,) group; Le., their line shapes exhibit a doublet structure near the triple point which collapses with increasing temperature. The C-D oscillator in CDH,OD, however, has a nearly symmetric and temperature-independent line shape.
I. Introduction Vibrational depopulation (i.e., T I )and dephasing (Le., T,) phenomena in the picosecond time scale of polyatomic liquids have been an object of interest since the early 1 9 7 0 ~ . ’ *The ~ main probes of these processes are the rotational invariant isotropic Raman line shape (IRLS) and the picosecond laser pulse and probe (LPP) techniques3 The instantaneous frequency fluctuations A w ( t ) which are responsible for dephasing are caused (a) by fluctuating intermolecular forces leading to the so-called environmental broadening (EB) or “pure” dephasing and (b) by resonance couplings (RC) between (two) identical oscillator^.'^^^,^ Within the second cumulant approximation, the line shape J ( w ) is determined if the correlation function (CF) of Aw(t), i.e., (Ao(0) A w ( t ) ) ,is Usually it is characterized by its zero-time value (Aw2) and its correlation time T,. Depending on whether ( A w , ) ’ / , T > / ~ 1,r the , fluctuations are either in their “fast” or in their “slow” modulation limit. In the former case a Lorentzian J ( w ) results; a Gaussian, however, results in the It is commonly believed that the (nearly) Lorentzian IRLS which are very often observed are caused by the T2processes only. This is justified for diatomics; 2 c ~ sin polyatomic systems, however, LPP experiment^^*^-^ indicate that TI processes may become “Raman-active” (Le., T I 5 10 ps) if the vibrational energy Evib may be transferred to “nearby” states j such that the excess energy can be given to or taken from the heat bath, Le., hlwi - w,l S kBT. Therefore, a given IRLS must be considered a priori as the convolution of all these mechanisms; e.g., for a Lorentzian the half-width at half-height (hwhh) becomes (in units of wavenumbers) 2achwhh = ( l / 2 ) x l / T , , r
+ 1 / T z E B +I/T2RC+ l/T,EB-RC
I
(1)
where r sums over the depopulation channels which may be of inter- and intramolecular nature, and T2EB-RC accounts for the cross CF between the Aw(t) caused by the purely environmental effect and the resonance coupling.2 The sign of 1/T2EB-RC is not defined a priori; it may possibly overcompensate l/T2RCso that the coupling may even result in line narrowing instead of broadening as commonly expected.2a ‘Dedicated to the 60th birthday of Professor Georg Rudakoff.
0022-3654/90/2094-4178$02.50/0
In addition, the situation is further complicated if the fluctuations are so slow that the resulting J ( o ) is a superposition of homogeneously (in the sense above) broadened lines. This inhomogeneous broadening may even lead to an irregular J ( w ) ,i.e., if w ( t ) is modulated by only a limited number of disturbers (“associates”). The central limit theorem therefore no longer remains appli~able.~ To elucidate the physics behind a given IRLS, the following aspects are useful. (i) Isotopic dilution (ID), Le., the dilution of a given oscillator into an environment of isotopic modified molecules, may be applied to suppress the RC effect (the last two terms in eq 1). However, the sign of the cross CF should be known beforehand. Even if this can be presupposed, the dilution must not change the T , term in eq 1. Thus, the results of such an experiment (usually a blue shift and line narrowing are observedlO)are well-defined in the simplest cases only, i.e., in diatomic liquid^.^ Any ordinary dilution is useless because it affects all terms of eq 1 in a way which is as yet ~npredictable.~,’~ (ii) Isotopic substitution, Le., the comparison of only massmodified oscillators i, j in one and the same environment, may be useful to clarify whether the EB process dominates the IRLS or not. As long as the ratio of the half-widths hwhh,/hwhh, (uo,i/voJ)2 does not depend on the thermodynamic state of the liquid
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( 1 ) Rotfischild, W. G. Dynamics of Molecular Liquids; Wiley: New York, 1984. (2) (a) Oxtoby, D. W. Ado. Chem. Phys. 1979, 40, 1. (b) Adu. Chem. Phys. 1981, 47, 487. (c) Chesnoy, J.; Gale, G. M. Ann. Phys. Fr. 1984, 9, 893. (3) Laubereau, A.; Kaiser, W. Reo. Mod. Phys. 1978, 50, 607. (4) (a) Bratos, S.; Tarjus, G. Can. J. Chem. 1985,63, 2047. (b) Pbys. Rev. A 1985, 32, 243 I . (5) (a) Oehme, K.-L.; Rudakoff, G.; Klostermann, K. J. Chem. Phys. 1985, 83, 1499. (b) Oehme. K.-L.; Klostermann, K. J. Chem. Phys. 1989, 91, 2124. (6) Fendt, A.; Fischer, S . F.; Kaiser, W. Chem. Phys. 1981, 57, 5 5 . (7) Zinth, W.; Kolmeder, C.; Benna, B.; Irgens-Defregger, A,; Fischer, S. F.; Kaiser, W. J. Chem. Phys. 1983, 78, 3916. (8) Kohlmeder, C.; Zinth, W.; Kaiser, W. Chem. Phys. Lett. 1982, 91, 323. (9) van Kampen, N. G. Stochastic Processes in.Physics and Chemistry; North-Holland: New York, 1981. (IO) Logan, D. E. Mol. Phys. 1986, 58, 97. ( I I ) Rodriguez, A. A.; Schwartz, M. Chem. Phys. Lett. 1986, 129, 458. (12) Lynden-Bell, R. M. Mol. Phps. 1977, 33, 907. Fischer, S. F.; Laubereau, A. Chem. Phys. Lerr. 1975, 33, 6. Metiu, H.; Oxtoby, D. W.; Freed, K . F. Phys. Rei>.A 1977, IS. 361.
0 1990 American Chemical Society
C-H and C-D Stretching Modes in Deuterated Methanol
The Journal of Physical Chemistry, Vol. 94, No. 12, 1990 4119
(see for example the discussion in sections IV.F, IV.G, and V.B of ref 2a), the condition necessary for approximating 2achwhh by 1 / TzEBis fulfilled. Although implicit in the popular dephasing models,I2J3only a few attempts have been made to verify this e ~ p e r i m e n t a l l y . ~ For , ~ ~example, ,~~ this condition has been found to hold true, if the (isotropic) width of HCI (infinitely) diluted in DCI was compared with the width of DCI diluted in HC1,Sb i.e., in a system where (a) according to point i all resonance couplings can be safely excluded and where (b) the T I process is in the nanosecond region2c and therefore not "Raman-active". (iii) Due to difficulties in the preparation of lower frequency infrared pulses, LPP techniques are mainly used to determine T I of C-H stretching modes.68 Furthermore, the present techniques are unsuited to determine the homogeneous width within an inhomogeneously broadened band (see the discussion in refs 15 and 16), though this has been assumed b e f ~ r e h a n d . ~ J ' JThus, ~ the only indication that inhomogeneous broadening dominates a given IRLS seems to be a (near) Gaussian shape which, as predicted t h e ~ r e t i c a l l y , ' ~ .broadens ' ~ ~ ' ~ with increasing temperature ( T ) . In polyatomic systems, the only Raman experiments which are useful to identify the nonrotational line broadening mechanisms, at least partially, are isotopic dilution and isotopic substitution, where as many isotopic modifications of a given compound as possible should be studied. C-H modes are most suited for this purpose. Stimulated by a LPP T I study of the C-H stretching mode in symmetric benzene-d3,8we recently started this work with a comparison of the IRLS of the symmetric C-H and C-D stretching modes of the species C6H,D6-, with m = 0, 1, 2, ..., 6 in the whole range of the (isotopically pure) liquid state.20 Most significant are the opposite T dependencies observed if the (nearly Lorentzian) IRLS of the C-H modes are compared with those of the C-D modes.20 To carry on this search for "Raman-active" T I channels by H/D isotopic modification of a given compound, our present material of choice is liquid methanol. This is primarily due to the widespread interest3*6J8,21-23 in the analysis of a band located near 2835 cm-' in liquid C H 3 0 H (see Figure 1 for a first survey). Hence, we compare the half-widths of the two most intense bands appearing in the C-H stretching region of the isotopic species CH30H(D) and CHD,OH(D) with the corresponding C-D modes of the species CD,OH(D) and CDH,OH(D). The study covers the whole range of the orthobaric liquid, Le., around 330 K. Summing up previous work,3,6*18*2'-23 the following should be known beforehand: ( I ) The two most prominent bands in C H 3 0 H (A, B in Figure 1) were often thought to be caused by the symmetric (A) and the antisymmetric (B) C-H stretching v i b r a t i ~ n . ~ * ~ *However, '**~~$~~ the unusual low peak frequency of the A band (2835 cm-I) and the polarized nature of both the A and the B band support the original idea25that this behavior is very probably caused by Fermi resonance (FR) coupling between the symmetric C-H stretching mode Y , and the overtone of the (symmetric) C-H bending mode 26,. (2) The above-mentioned, so-called "selective k-matching" LPP ~~~~~~~~~~
~
~
~
(13) Schweizer, K. S.; Chandler, D. J . Chem. Phys. 1982, 76, 2296. (14) Baglin, F. G.; Wilkes, L. M. J . Phys. Chem. 1981, 85, 3643. (15) Zinth, W.; Polland, H. J.; Laubereau, A.; Kaiser, W. Appl. Phys. B 1981, 26, 77. (16) George, S. M.; Harris, C. B. Phys. Reu. A 1983, 28, 863. Loring, R. F.; Mukamel, S. J . Chem. Phys. 1985, 83, 2116. (17) George, S. M.: Auweter, H.; Harris, C. B. J . Chem. Phys. 1980, 73, 5573. (18) Harris, C . B.; Auweter, H.; George, S. M. Phys. Reu. Lett. 1980, 44, 731. (19) George, S. M.; Harris, C. B. J . Chem. Phys. 1982, 77, 4781. (20) Seifert, F.: Oehme, K.-L.; Rudakoff, R.; Carius, W.; Holzer, W.; Schroter, 0. Chem. Phys. Lett. 1984, 105, 635. (21) Zerda, T. W.; Thomas, H. D.: Bradley, M.; Jonas, J . J . Chem. Phys. 1987, 86, 3219. (22) Tanabe, K.; Tsuzuki, S. Specrrochim. Acta 1986, 42, 61 1. (23) Kamagowa, K.; Kitagawa, T . J . Phys. Chem. 1985, 89, 153 1. (24) Laubereau, A.; Wochner, G.: Kaiser, W. Chem. Phys. 1978, 28, 363. (25) Herzberg, G. Molecular Structure and Molecular Spectra; Van Nostrand: New York, 1954; Vol. 2.
I
ANIS0
I
I
2 800
I
2900
I
3000 v/cm-'
I
Figure 1. Main spectral features in the C-H stretching region of liquid methanol ( C H , O H ) ; anisotropic (top) and isotropic (bottom) Raman spectra near the triple point. (A, a, B, b) Polarized Fermi doublet. (C, c) Overtone of the antisymmetric C-H bending vibration. (D, d, E, e) Conformational components of the (antisymmetric) C-H stretching vibration. Note that the accuracy of the fitting procedure is severely restricted in the case of the low-intensity and strongly overlapped components.
technique24was applied to a number of CH3-containing compounds," including C H 3 0 H and CD3ODI8 (see also Figure 32 in ref 3). The results suggested that the IRLS is primarily determined by slowly varying attractive forces;I0 this is seemingly plausible for hydrogen-bonded liquids. These experiments are, however, seriously called into question with the cognition that the decay curve of the coherent Raman intensity is influenced by the properties of the laser pulse.ls (3) Zerda et al.*I recently arrived at completely different results, Le., that about 80% of hwhhA should be caused by repulsive forces and the residual broadening is caused to nearly equal extents by the attractive forces and the FR coupling. This result was obtained through comparison of the pressure @) and T dependencies of J(w) which are determined (a) experimentally in the range 273 K < T < 363 K and 0 < p < 4 kbar and (b) by means of the Schweizer-Chandler (SC) theory of the EB process.13 Not only the state dependence of the half-width but also the p-induced blue shift agrees with the predictions of the SC theory. However, some of the properties of liquid methanol are so poorly defined that the approximations used in their place actually have the characteristics of parameters. (4) Compared to the neat liquids, the following blue shifts A u A upon ID have been measured by Raman difference spectroscopy:23 LA 3.8 cm-l for C H 3 0 H in CD30D, A u A 2 cm-' for CH30H in CH,OD, and AuA 0.9 cm-' for CH30D in CD30D. The only value which was reported for the B band is AvB 1.7 cm-' for CH,OH in CD,OH. Because these shifts vary linearly with mole fraction x, they may be understood as caused by the "switch off' of the RC effect upon ID.4310It cannot be excluded, however, that the conditions for the Fermi resonance are sensitive to isotopic dilution. Recent results indicate that the liquid structure might be different for hydrogen- and deuterium-bonded networks .26,27 (5) Tanabe and Tsuzuki22compared the dilution behavior of the u A mode in C H 3 0 H with the corresponding C-D mode in in CD30D if both isotopic species are diluted down to x = either H 2 0 or D20. In contrast to the C-D mode, the C-H mode
-
-
-
-
(26) Montague, D. G.;Dore, J . C.; Cummings, S. Mol. Phys. 1984, 53, 1049. Montague, D.G.; Dore, J. C. Mol Phys. 1986, 57, 1035. (27) Engdahl, A.; Nelander, B. J . Chem. Phys. 1987, 86, 1819. For a similar discussion on HX dimers (X = F, CI) see: Latajka, Z.; Scheiner, S. Chem. Phys. 1988, 122, 413.
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The Journal of Physical Chemistry, Vol. 94, No. 12. 1990
- 2 800
2900
v/cm-’
I A
rt,
CH3OH
3000 I
,/
CH3OD
I
1 2900
C H D,OH
I
CHD2OD
I
I
J
I
1
2200 v/cm-’ 230 Figure 3. Isotropic scattering of the isolated C-H and C-D stretching modes in CHD20D, CDH20H,and CDHIOD near T,. Note that the spectra of CHDIOH and CHD20Dare entirely indistinguishable in the C-H stretching region 2100
200 Temperature/K 500 I CH@H \ m , ~ ) / c H ~ b( D LA)
Figure 2. Isotropic scattering of the C-H and C-D stretching region in CH30H, CH30D, CD30H, and CD30D near T,.
11. Experimental Section CH2DOH and CD2HOH were prepared by treating an aqueous solution of polymeric formaldehyde (either (CH,O), or (CD20),) with NaBD4 and NaBH4, respectively.28 (CD20), and NaBD4 (deuterium content >99.5%) and CD30D and D 2 0 (D 199.8%) were purchased from Isocommerz, Leipzig, whereas C H 3 0 H (Uvasol quality) was obtained from Merck, Darmstadt. MeOH has been converted into MeOD (and vice versa) through repeated distillation of methanol from its solution in D 2 0 and H 2 0 , respectively. MgO and metallic sodium are used as drying agents, and the desired amount was then distilled from the MeOH(D)/MeONa mixture into a thick-walled glass tube (0.d. = 8 mm, i.d. = 4 mm, 180 mm). Each vial was filled so that the critical density was met within 5%. The Raman scattering apparatus (argon ion lasers ILA 120 or ILA 190, double monochromator GDM 1000; all from Zeiss, Jena) is identical with that described previously,20 except for the partial use of the more intense ILA 190 so that the irradiation (up to 2.5 W at 488 nm) of the sample is now limited by its optical quality. The samples are thermostated within f l K,Mand frequencies are correct within one wavenumber. Overlapping bands are separated by using a curve-fitting procedure. For simplicity, the individual line shapes are assumed to be a product of a Lorentzian and a Gaussian, although their convolution, i.e., a Voigt profile, would be more physical.] However, if J ( w ) is near a Gaussian or a Lorentzian (the present case), the product function remains a good approximation. 111. Results and Discussion Figure 1 compares (mainly for band assignment) the isotropic and anisotropic spectra of ordinary MeOH in a supercooled state (Le., 8 K below T,) because some details become clearly visible only at this low temperature. Figures 2 and 3 allow a qualitative comparison of the isotropic spectra of the different isotopic species, whereas the T dependencies (170 K < T < 500 K) of the halfwidths of the two most prominent bands in the C-H and C-D stretching region are collected in Figure 4 for the FR bands in CH,OH(D) and CD30D(H) and in Figure 5 for the isolated C-H and the isolated C-D oscillators in CHD20D(H) and CDH,OD(H). In Figure 4 a comparison is made with hwhh@,n obtained previously on CH30H.21 Finally, Table I collects, for the purpose (28) Kabisch, G.; Mobius, G. Specrrochim. Acra 1982, 38, 1189.
’
’
2.
narrows considerably (i.e., by 40%) if H 2 0 is replaced by D20.
c
’1
A
0 T‘=[T-Tt]/
1 [T,-Tt]=
[T/K-175.3]/337.3
Figure 4. Temperature dependence of :he half-width at half-height (hwhh) of the components of the Fermi doublet in CH30H, CH30D, CD,OH, and CD,OD. The pointed line gives the data of ref 21 after extrapolating to the density of :he orthobaric liquid. The two open circles are the data for 15% CD30H in CH30H (A band only).
of easy interpolation, the Tdependencies of the data in Figures 4 and 5 in a parametric form. A . Band Assignment. At first glance, Figure 1 shows features that are characteristic of the C-H stretching region of CH,containing molecules of C3, symmetry (e.g., CH3CN), Le., a comparatively narrow (low frequency) band and a broader band at higher frequency. Accordingly, “A” and “B” are very often assigned to the symmetric (A) and the antisymmetric (B) vibration. A more detailed inspection of the anisotropic part of the spectrum, however, indicates that the B band is by no means depolarized, as it should be for a 2-fold degenerate E-type vibration. Furthermore, if we compare v A (2835 cm-l) with that
C-H and C-D Stretching Modes in Deuterated Methanol
The Journal of Physical Chemistry, Vol. 94, No. 12, 1990 4781
TABLE I: Temperature Dependence of the Isotropic Half-Width Parameters of the Curves in Figures 4 and Sd
The frequency difference A u A B = vB - vA and the intensity ratio R = I A / I B are not sensitive to temperature changes and OH/OD exchange, Le., AvAB(-OH) = 110 (1) cm-I, AvAB(-OD) = 109 (1) cm-I, R(-OH) = 1.40 ( 9 , and R(-OD) = 1.42 (5). The value R 1 reported in ref 33 is seemingly in disagreement with our findings. However, it should be taken into account that the neglect of the “D” band (see Figure I), as in refs 21 and 33, must effect any line-fitting procedure and results in a considerable overestimation of le. It is obvious from Figure 2 that the coupling in the -CD3 groups is less significant that in the -CH3 groups. Because of LCOH < 180°, methanol should be strictly of C, symmetry. Thus, the degeneration of vas is lifted and two bands, one of A’ type and the other of A” type, should be observed. According to the 13C isotopic shifts of matrix-isolated isotopic species observed in the infrared region,34these two modes must be assigned to peaks “d” and “e” of the anisotropic spectrum. They are only clearly separable in the supercooled liquid state and may hardly be identified in the isotropic spectrum. B. The Fermi Doublet in CH30H(D)and CD,OD(H). (i) The following results are clearly evident from Figure 4: (1) As far as C H 3 0 H is concerned, our experimental data are in complete agreement with previous workz1(see the pointed line in Figure 4). To make this comparison, we slightly extrapolated the (four) isothermic density dependencies of hwhh, given in Table I1 of ref 21 to the densities of the orthobaric liquid. (2) The half-widths of both bands tend to become more similiar if T increases; Le., the initial broader B band narrows and the A band broadens. This holds not only for the CH, group but also for the CD3 group, although the narrowin of J;(w) with increasing T is less sigI ! nificant than that of JB(w). (3) C-D modes and C-H modes behave differently if MeOH is substituted by MeOD. Both the C-H bands “A” and “B” narrow considerably if C H 3 0 H is replaced by CH,OD; &-o, however, is clearly insensitive to OH/OD exchange. (4) No significant change of the width (and the position) of the Ji(w) is observed if neat C D 3 0 H is compared with its solution (15%) in C H 3 0 H . Unfortunately, it was not possible to determine the width of the Ji(w) because of its low intensity (see Figure 2). (ii) In principle, FR causes not only a line shift but also an additional broadening. Therefore, it might be argued that even a slight change of the unperturbed frequencies us and 26, may detune the resonance conditions and consequently should be sufficient to explain the narrowing of the FR doublet in C H 3 0 D compared to those in CH30H. However, neither the frequency difference AvABnor the intensity ratio R differs significantly (see above). (iii) It is also not possible to explain the 30-40% narrowing of the Fermi doublet upon O H / O D exchange based on the assumption that only the dephasing contributes to line broadening. One might argue, however, that the liquid structure is imaginable to be slightly different in MeOH and MeOD.26 (The 0-D-0 interaction is stronger than the 0-H-0 interacti~n.~’)Therefore, it might be possible, at least in principle, that the distribution of Aw(t) and subsequently J(o) may narrow because of a possibly more static deuterium-bonded network. However, any change of the intermolecular potential upon OH/OD exchange must be similar for CH, and CD, species. Thus, the C-D modes of the CD30H/CD30D pair should behave as the C-H modes of the CH30H/CH30D pair. Figure 4 clearly indicates that this is not the case. (iv) Because neither the FR coupling nor the dephasing process is responsible for the narrowing of the FR doublet in CH30D, only t h e T , process remains as an explanation. According t o (2achwhh) = 1/2T1, the observed change of the half-width
hwhh/cm-I = A[1 species
curve
CH3OH
A Ab
CH3OD
A
B A
CD3OD
A
B
A/cm-’
C
rsa/cm-’
Figure 4 7.99 0.725 -0.661 8.51 [7.72] 0.284 [0.728] 16.34 -0.610 -0.378 5.05 0.851 -0.367 11.99 -0.404 -0.289 3.49 1.037 -0.318 11.41 -0.517 -0.864 3.89 0.48 1 0.561 -1.354 14.27 -0.459
B CD3OH
+ SP(l + CP)]
B B
0.30 0.37 0.15 0.37 0.35 0.93 0.14 1.03
Figure 5 CHD20Hc CHD20D
IOW high
CDH20H
IOW high
CDH20D
0.237 0.480 0.491 1.253 -0.065
17.86 17.78 12.33 15.32 15.92
-1.069 -0.084 0.415 -0.818 0.798
0.57 1.16 0.91 0.87 0.41
Ors = residual scatter; Le., rs = [ X i ( y i-&)2/iVll/2. bDeduced from Table I1 in ref 21; the values in square brackets are for isochoric conditions (p = 0.842 g/cm3). eParameters were not determined; see text. d f= ( T - T , ) / ( T ,- T,) = (T/[K] - 175.3)/337.3.
200
500
Temperature /K I
I
’
- .2
YI
-
n
.3
> I
h
*“
“I
-
r c
3
f
i4
N
- .3
-
0
T*
u
.4
1
Figure 5. T h e function hwhh(T) for the high- and low-frequency com-
ponents of the isolated C-H and C-D modes in C H D 2 0 H ( D ) and C D H 2 0 D ( H ) . Note that one single band only has been observed for CDH2OD.
of lines of a truly symmetric character in, for example, CH31(2948 cm-’),19 CH3CN (2945 CH3CHz0H(2929 cm-I),l9 and CH,Si(CD3)3 (2893 c n ~ - ~ ) it , * ~becomes evident that vA is “unusually low”. It is not possible to explain this behavior with an intrinsic property of the C-H bond (see ref 30). Thus, it is justified to assume the A, B structure is caused by Fermi resonance.Z1J3 (29) Biedermann, S.; Burger, H.; Hassler, K.; Hofler, F. Monatsh. Chem. 1980, I l l , 703. (30) McKean, D. C:; Boggs, J. E.; Schafer, L. J . Mol. Struct. 1984,116, 3 13. The frequency of isolated C-H stretching vibrations correlates with the spectroscopically determined C-H bond length according to rC+ A = 1.3982 - 0 . 0 0 0 ~ 0 2 3 ~ C(cm). ~ H If the gas-phase value of rC+ = 1.0936 A is used,” then Y ~ =- 2978 ~ cm-’ results, which is in full agreement with the gas-phase
value observed for the isolated C-H vibration in the trans position to the - O H proton.32
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(31) Lees, R. M.; Baker, J. G . J . Chem. Phys. 1968, 48, 5299. (32) Mallinson, P. D.; McKean, D. C. Spectrochim. Acta 1974.30, 1133. (33) Schwartz, M.; Wang, C. H. J . Chem. Phys. 1973, 59, 5258. Schwartz, M.; Moradi-Araghi A.; Koehler, W . H. J . Mol. Struct. 1980, 63, 279; 1982, 81, 245. For a discussion of the coupled oscillator model see also: Monecke, J. J . Raman Specfrosc. 1987, 18, 417. (34) Barnes, A . J . ; Hallam, H. E. Trans. Faraday Soc. 1970, 66, 1920.
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The Journal of Physical Chemistry, Vol. 94, No. 12, 199t3
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AhwhhA = hwhh,(MeOH) - hwhh,(MeOD) 2.8 ( 1 ) Cm-' corresponds to T,(A) = 0.95 (4) ps. Notably, this value is nearly independent of T. For the B component, Tl(B) seems to be even smaller, i.e., 0.62 (9) ps near Tt and 0.75 (9) ps near Tc,though the small T dependence indicated by these values might be somewhat accidental because of the larger scattering of the hwhh, data. However, for any depopulation to become effective in the picosecond region, "nearby" states which may accept the main portion of Evlbare necessary. At best, (nearly) resonant conditions should be met. Furthermore, Ti of the delivering state and T2 of the final state are correlated; Le., the Ti decreases if the accepting state has a large width.' Because the spectra of C H 3 0 H and C H 3 0 D do not differ in the C-H stretching region (except the width of the bands),3s the faster TI process in C H 3 0 H must have to do with the different frequencies of the OH(D) modes. Obviously, the stretching modes cannot be made responsible for this behavior; Le., no reason exists that the energy flow to the O H mode near 3400 cm-' should be more effective than the flow to the OD mode at 2490 cm-l. Next we consider the overtone of the bending mode 2bo-H. The fundamental of the C U H in-plane vibration has been found near 1335 cm-l for CH,OH and near 1293 cm-l for CD,OH; the corresponding C-0-D mode, however, is located near 865 cm-' (CH30D) and 777 cm-l (CD30D).32 Compared to these values of the isolated molecule, methanol aggregates in argon matrices34 show up to nine lines with frequencies between 1328 and 1420 cm-' in (CH30H),/Ar and between 861 and 931 cm-l in (CH,OD),/Ar. It is reasonable to assume that a similar spread of frequencies also exists in the liquid. If this is taken into account. it becomes clear that the overtone of the C-0-H mode must be a very broad (say, 200 cm-I) band just below the C-H stretching region and therefore very suitable to accept Ewbfrom both Fermi components. In CH30D, however, such an effective transfer is not possible because the overtone region of the C-0-D mode must be located below 1850 cm-l, Le., definitely "far from resonance" with the Fermi doublet. Going on in this context, we compare C D 3 0 H and CD,OD. It is obvious that neither the C-0-H vibrations ( u > 2600 cm-I) nor the C-0-D vibrations (v < 1700 cm-I) are able to act as accepting states in a similar manner as the C-0-H vibrations in CH30H. However, this only seems to be true for the A component of the Fermi doublet. To all appearance, the B component in CD,OD (see Figure 4) is broader than those of CD30H. This might suggest some kind of transfer of E v l b to the OD stretching mode (near 2490 cm-I) although we cannot exclude that this additional broadening is to some extent artificial because of systematic errors in the line fitting. (v) In light of these results it is worth reconsidering (a) the LPP T , experiment of Fendt et a1.6 on neat C H 3 0 H and 2% CH,OH in CC14 and (b) the above-mentioned dilution study of the A component of C H 3 0 H and C D 3 0 H in H 2 0 / D 2 0 :22 In case a the decay time TI (2835 cm-l) = 1.5 (6) ps was found to be the same in the pure and the diluted state, whereas in case b a nearly constant line width of the A component was observed down to about xMeOH= 0.1, followed by a sharp decrease of hwhh, for even larger dilution, again except for CH30H-H20, where hwhh, remains insensitive to dilution down to x = Consequently, both experimental results are consistent with the idea of a picosecond-active energy transfer from the C-H stretching region to the overtone of the C-0-H bending mode. This process is presumably of an intramolecular nature, because any kind of intermolecular transfer is suppressed in the very diluted state studied in ref 22. (vi) I t is not possible to finally decide to which extent other Ti channels are active; surely the FR broadening will give some further contribution, The application of the model developed by (35) LPP TI studies of C 2 H 5 0 Hand CH,CC13 (see ref 3) indicate that after initial rapid distribution of .Evib between all the C-H stretching states, they may relax via (intermolecular) transfer to the C-H bending modes. If this is really active, it should affect the shapes of both CHIOH and C H 3 0 D in one and the same way; thus, this mechanism is not suited to explain the very significant difference in line width between OH and OD species.
the Munich group to approximate the intramolecular transition rates' yields an additional broadening of about 1 cm-I hwhh which only slightly depends on the thermodynamic state.21 If we transfer this value to CH,OD, as is justified because the FR parameters are not sensitive to O H / O D exchange, a line width (hwhh) of about 4 cm-I remains, i.e., close to the width of C-H stretching bands in nonassociated or weakly associated liquids. The similar T dependencies of C-H line shapes on the one hand and the corresponding C-D line shapes on the other (Figure 4, compare hwhh(T) of C H 3 0 D with those of CD,OD(H)) and the ratio hwhhA(CH3)/hwhhA(CD3) < 2 do not contradict the assumption of T , < T , . (vii) Although the idea of dominant inhomogeneous broadening suggests itself for a hydrogen-bonded liquid, it is negated by the non-Gaussian shape of the A band of CH,OD. Furthermore, it is not possible to achieve agreement between the small T dependencies observed and those predicted theoretically using either the SC modell, or the GAH model; Le., according to hwhhsc
0:
h , t [ p k T T ] ' / 2 or
hWhhGAH
0:
p[k,flii2
a much more marked broadening should be observed if T raises. This is due to the decreases in density ( p ) and the attractive force induced gas-to-liquid shift (Aunt)which are overcompensated to a large extent by the increase in the isothermic compressibility ( k T ) , especially just below T,. It has been shown2] that the alternative assumption of repulsive force induced broadening is in closer agreement with the experimental observations on the A band of C H 3 0 H even though the nearly quantitative agreement between the "repulsive version" of the SC theory and the experiment can no longer be maintained if the one-third contribution of the T,.process discussed above is taken into account. However, the qualitative conclusions drawn by these authors should not change. (viii) Although the blue shift of AuA 0.9 cm-', which has been observed2, if C H 3 0 D was diluted in CD,OD, and the blue shift of be 1.7 cm-I, observed if C H 3 0 H has been diluted in CD,OH, may be due to resonance couplings, we did not observe any change in hwhh,(-CD3) (see Figure 4) upon ID. To explain these contradictory findings, it should be taken into account that these couplings, if present, influence the C-D and the C-H stretching region in a similar ~ n a n n e r . ~ However, ~.'~ the C-D bands are more suited for studying the width phenomena caused by the couplings, whereas the C-H bands are more sensitive to the shift phenomena.s Overall, it is not possible to finally decide whether the RC effect is present or not, especially if it is taken into account that (a) its cross correlation with the EB process and (b) three-particle correlation^,"^^^^^^ which both may lead to narrowing, may compensate the broadening caused by the "flip-flop" transition between two moIecuIes.10 C. The Isolated C-H and C-D Stretching Vibrations. Figure 3 compares (near T I )the C-H stretching region of CHD20H(D) with the corresponding C-D region of CDH20H and CDH20D. The following features of the IRLS are most prominent. (1) The C-H bands of CHD20H and CHD20D are indistinguishable on the scale of Figure 3. We therefore only give the spectrum of CHD,OD. (2) In contrast to the C-D region of CDH20H and the C-H region of CHD20H(D),where two bands become clearly visible; CDHzOD shows only one band, which apparently peaks between the two bands of CDH20H. (3) The width of the isolated band in CDH,OD is independent of temperature (Figure 5 ) . For the doublets, however, at least the slightly less intense component broadens significantly with temperature increase. Furthermore, the two components, which are separated by 36 (7) cm-' (C-H) and 27 (3) cm-I (C-D) near TI, become closer with increasing T so that near T, only one band (hwhh 25 cm-', not shown) appears. This unusual behavior may be discussed as follows. (i) If the rotation of a -CH, or a -CD, group around the C-0 bond is considered, three positions of minimum energy ( 1 20' apart) are possible. For -CHD2 or -CDH, the isolated C-H or C-D oscillator therein is sensitive to its position relative to the
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C-H and C-D Stretching Modes in Deuterated Methanol 0-H(D) bond. Thus, three C-H (or C-D) bands should be observed, as in the solid phases of CHD2C6D?& and CHD2NOFMb However, no evidence for a third band in the C-H or C-D stretching region has been found. This means that two of the three positions are of identical frequency, and therefore one of the C-H bonds is in-plane with the 0-H(D) bond. The appearance of different bands is not bounded to a significant barrier height V between the minimum positions. Even in cases where V
