J. Phys. Chem. 1995, 99, 4435-4440
4435
Anomalies in the Isotropic Raman Spectra of Liquid Mixtures of Isotopomers of Formamide. Intermolecular Interactions in the Carbonyl Stretching Region A. Mortensen and 0. Faurskov Nielsen* Chemistry Department, University of Copenhagen, 5 Universitetsparken, DK-2100 Copenhagen, Denmark
J. Yarwood Materials Research Institute, Shefield Hallam University, Pond Street, Shefield, SI 1WB, England
V. Shelley Department of Chemistry, University of Durham, South Road, Durham, DHI 3LE, England Received: September 29, 1994; In Final Form: November 28, 1994@ Raman spectra of liquid mixtures of HCONH2 and H13CONH;!, and of HCOND;! and DCOND;?are presented. The isotropic Raman spectra of the former mixture show two bands in the carbonyl stretching region, whereas the latter only show one. The same phenomenon is observed in the solid mixture at -20 "C. At low concentrations of this mixture in DMSO solutions, the bands due to individual molecular species of HCOND;! and DCOND2 are observed. The phenomenon is due to an intermolecular coupling causing oscillators with not too different frequencies to oscillate with the same frequency, if the strength of the coupling exceeds a critical value, K,. In liquid mixtures of HCONH;! and DCONH2, the isotropic Raman carbonyl bands are to close in frequency to decide whether they show this phenomenon as well. In the case of mixtures of HCONH;! and H13CONH2, the intermolecular coupling strength is less than K,,and the two carbonyl bands due to individual molecular species are observed.
Introduction Recently, we reported the IR and Raman spectra in the carbonyl stretching region of mixtures of neat liquid HCONH2 and HCOND2 and in DMSO In a liquid mixture of HCONHz and HCOND2 only one carbonyl stretching band was observed in the isotropic Raman spectrum even though four species exist in the mixture (HCONH2, HCOND;!, and cis- and trans-HCONHD).' The carbonyl bands of HCONH:! and HCOND;?in the isotropic Raman spectrum were separated by 30 cm-', and the carbonyl bands of cis- and trans-HCONHD were believed to be situated in between these two bands; yet it was clear that the carbonyl band observed in the mixture of the isotopomers was not simply made up of the contributions from the individual species, since the widths of the isotropic Raman carbonyl stretching bands of HCONH2 and HCOND2 were less than 20 cm-'. It was shown that this apparent collapsing of the bands was not due to fast exchange of hydrogen with deuterium; Le., the rapid exchange limit, which could cause bands to collapse, did not apply.' The observation of just one carbonyl stretching band when four bands were expected was believed to be due to intermolecular coupling in liquid formamide. The phenomenon of just one band being present when two are expected has until recently only been observed in solids. (For a review on earlier works, see ref 3.) Besides mixed alkali halides3 like NaXK1.,, the phenomenon has also been observed in mixed crystals of K14N03 and Ki5N03,4 of chromium, molybdenum, and tungsten hexa~arbonyls,~ of [14N]-and [15N]urea,6 of [12C]-and ['3C]glycine,7and of ['HI- and [2H]alanine.8 The phenomenon is observed in crystals of mixtures of isotopes of germanium9J0and in diamond consisting of 12Cand 13C.11-'3 Here we present spectra of mixtures of isotopomers of formamide which are not complicated by the presence of four species as in the case of mixtures of HCONHz and HCOND2. @Abstractpublished in Advance ACS Abstracts, March 1, 1995.
These binary mixtures consist of HCONH2 and H13CONH2and of HCOND2 and DCOND;!. No exchange of hydrogen with deuterium takes place, and hence, only two species exist in each of these mixtures. The band profile of the carbonyl bands of these mixtures in DMSO as a function of mole fraction is examined. The Raman spectra of the solid mixtures of HCOND2 and DCOND2 and of HCONH2 and HCOND2 have been obtained as well. Due to lack of H13CONH2, the spectrum of a solid mixture of HCONH;! and H13CONH2 has not been obtained.
Experimental Section HCONH2 (puriss. p.a.) was obtained from Fluka, DCONH;! (99.1% D) from Campro Scientific B.V., H13CONH2(99% 13C) from IC Chemikalien GmbH, and DMSO (p.a.) from Merck. HCOND;! and DCOND2 were obtained by allowing an excess of D20 to react ovemight with HCONH2 and DCONH2, respectively, and subsequently distilling off the water in vacuo. The process was repeated once. The IR spectra were recorded on a Perkin-Elmer 1760 X FTIR spectrometer at a resolution of 4 cm-'. CaF2 plates were used since KBr is soluble in formamide. At low concentrations of formamide, it was necessary digitally to subtract the spectrum of DMSO, obtained at the same path length, since DMSO has a weak band in the carbonyl stretching region. The Raman spectra were obtained with a Dilor 224 spectrometer using the 488.0 nm excitation line of a Spectra Physics argon ion laser providing an output of 400 mW. Both the polarized and depolarized scattering were measured, and the isotropic spectra were constructed in the usual way (Ziso = Ivv
- 4/31vh). Raman spectra of formamide in the solid state were obtained in the 180" scattering configuration at a temperature of -20 "C. The melting point of formamide is 2.5 "C, but it was possible to supercool formamide below -10 "C. No crystal
0022-365419512099-4435$09.00/0 0 1995 American Chemical Society
Mortensen et al.
1. Phys. Chem., Vol. 99, No. 13, 1995
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Figure 1. Isotropic (thick line) and anisotropic (thin line) Raman spectra of HCONH2 (A), HL3CONHz(C), and an equimolar mixture of the two (B). The spectra have been normalized to the same height.
splitting was observed, and it is hence believed that the mixtures and the neat isotopomers formed a glass.
Results and Discussion Liquid Mixtures. In Figure 1 are shown the isotropic and anisotropic Raman spectra in the carbonyl stretching region of HCONH2, H13CONH:!, and an equimolar mixture of the two. Besides the carbonyl bands, the NH2 bending band is observed around 1590 cm-l. First of all, it is observed that the isotropic and anisotropic components of the carbonyl bands of both neat liquid HCONH2 and of neat liquid H13CONH:! have different frequencies. This is called the noncoincidence effect and is caused by intermolecular interactions (ref 1 and references cited therein). In the case of HCONH:! the noncoincidence splitting A Y , ~ is~22- and ~ ~ 15 ~ cm-’ for H13CONH2. Secondly, the intensity of the carbonyl band of neat liquid HCONH:! is approximately twice that of neat liquid H13CONH2. (The CH bending band at 1390 cm-l was used as an internal standard.) However, in the equimolar mixture (Figure 1B) the carbonyl band of H13CONH2 seems to be the most intense. The reason for this is not known to us. In the isotropic Raman spectra the carbonyl bands of neat liquid HCONH2 (1668 cm-’) and HI3CONH2 (1647 cm-’) are separated by 21 cm-’. In the equimolar mixture the carbonyl bands of HCONH2 and H13CONH2 are observed at 1684 and 1652 cm-’, respectively. This shift in frequency of the isotropic component upon dilution with an isotopomer is another consequence of the intermolecular coupling leading to the noncoincidence effect. According to a model developed by Logan,l4 the frequency of the isotropic component is predicted to shift linearly with mole fraction when the species in question is diluted with an isotopomer. Figure 2 shows the frequencies of the isotropic components of the carbonyl bands of neat liquid HCONH:! and H13CONH2and mixtures of the two as a function of mole fraction of H13CONH2, obtained by fitting two bands to the experimentally observed spectral profile. As Figure 1B shows, the carbonyl bands of HCONH2 and H13CONH2overlap
Figure 2. Peak position of the isotropic carbonyl bands of HCONHZ (A) and H13CONHz ( x ) as a function of mole fraction of HI3CONHz.
to a significant extent, and curve fitting is hence difficult. However, the data show that the isotropic components do indeed depend linearly on mole fraction, except for the carbonyl band of HCONH:! at a mole fraction of 0.75 of H13CONH2, the discrepancy most likely being due to the difficulties with curve fitting. It is also observed that the carbonyl band of HCONH:! is more shifted upon dilution with H13CONH2 than is the carbonyl band of H13CONH2. According to the model,14 the shift of the isotropic component is proportional to the transition dipole moment squared, Le., the infrared intensity. It has not been possible to verify this, since the intensity of the carbonyl band is very high.’ In the Bom-Oppenheimer approximation the dipole moments of HCONH:! and H13CONH2 are equal, indicating that the normal coordinate for the carbonyl stretching mode is different for the two isotopomers, if the transition dipole moments are different. In contrast to mixtures of HCONHz and HCOND2,’ mixtures of HCONH2 and H13CONH2 show, as usually expected, two carbonyl bands from the individual isotopomers. A possible explanation for this different behavior, as compared to the system HCONH2EICOND2, will be given later. The isotropic and anisotropic Raman spectra of HCOND2, DCOND2, and an equimolar mixture of the two are shown in Figure 3. As expected, the NH2 bending band is not present in any of these spectra. In the spectrum of DCONDz a weak band around 1750 cm-’ is observed. This band was also observed in the gas phase IR spectral5 of DCONH:! and DCOND:! and is most likely the overtone of the CD out-of-plane bending mode involved in a Fermi resonance with the carbonyl stretching mode.15 The isotropic Raman carbonyl bands are asymmetric, showing as a wing on the high-frequency side of the carbonyl band (Figure 3). This asymmetry was shown to be caused by two different “sites”, the high-frequency wing being assigned to a non-hydrogen-bonded species and the main band to a hydrogen-bonded species, presumably a “linear chain” of formamide molecules.2 The carbonyl bands of these isotopomers also show the noncoincidence effect as evidenced by the different peak frequencies of the isotropic and anisotropic components (Figure 3A,C). The carbonyl band of HCOND2 in the isotropic Raman spectrum is found around 1640 cm-’ and around 1617 cm-’ in the case of DCOND2, and the widths (fwhh) are 16 and 13 cm-’,
J. Phys. Chem., Vol. 99, No. 13, 1995 4437
Raman Spectra of Isotopomers of Formamide
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1 0
(cm-') Figure 3. Isotropic (thick line) and anisotropic (thin line) Raman spectra of HCONDz (A), DCONDz (C), and an equimolar mixture of the two (B). The spectra have been normalized to the same height. WAVENUMBERS
respectively. It is clear that the isotropic Raman spectrum of the equimolar mixture (Figure 3B) is not simply a superposition of the carbonyl bands of the individual isotopomers. This band is somewhat broadened (21 cm-' fwhh), but it is clear from the carbonyl bands of the individual isotopomers (Figure 3A,C) that two distinct bands would be obtained from an addition of these two bands, and not just a slightly broadened contour. That is, mixtures of HCOND:, and DCOND2 show the same behavior as do mixtures of HCONH2 and HCOND:,. The anisotropic Raman and IR carbonyl bands are broad, and they can therefore be interpreted simply as a sum of the carbonyl bands of the individual isotopomers. This has been demonstrated previously for mixtures of HCONH2 and HCOND2.l Liquid mixtures of HCONH2 and DCONH:, also show only one carbonyl stretching band in the isotropic Raman spectra. However, the isotropic carbonyl bands of HCONH:, and DCONH2 are only separated by 12 cm-', and the single band observed in the isotopomeric mixture could be explained by a superposition of the carbonyl bands of the individual isotopomers. Solid Mixtures. The Raman spectra, obtained without use of a polarizer in the scattered beam, of HCOND2, DCOND:,, and an equimolar mixture of the two and of HCONH2, HCOND:,, and an equimolar mixture of these two, all in the solid state, are shown in Figure 4. These spectra show the same phenomenon as do the spectra of the liquid mixtures; Le., only one carbonyl stretching band is observed in these mixtures. This shows that this phenomenon is not associated with breaking and forming of hydrogen bonds or with exchange of hydrogen and deuterium (in the case of HCONH2/HCOND:,), in accordance with previous findings.' DMSO Solutions. In Figure 5 are shown the isotropic Raman spectra of an equimolar mixture of HCONH2 and H13CONH:, in DMSO at various mole fractions. It is observed that as the equimolar mixture is progressively diluted in DMSO, the two carbonyl bands become more distinct. This is not due to an increased separation between the two carbonyl bands (in
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Figure 4. Raman spectra of HCOND2 (a), DCONDz (c), and an equimolar mixture of the two (b) and of HCONHz (d), HCOND2 (0, and an equimolar mixture of these two (e), all in the solid state. The spectra have been normalized to the same height.
0
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WAVENUMBERS (cm-ll Figure 5. Isotropic Raman spectra of an equimolar mixture of HCONH2 and H13CONHz in DMSO. Total mole fraction of formamide: (A) l , (B) 0.64, and (C) 0.31.
the neat liquid mixture the separation is 32 cm-' and at a total mole fraction of formamide of 0.31 (Figure 5C) it is around 34 cm-') but must be ascribed to a narrowing of the bands. The isotropic Raman spectra of the DMSO solutions clearly show that the interpretation of the band contour observed in the neat liquid mixture (Figures 1B and 5A) is correct. The isotropic Raman spectra of an equimolar mixture of
J. Phys. Chem., Vol. 99, No. 13, 1995
Mortensen et al.
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Figure 7. IR spectra of HCONDZin DMSO (- - -), DCONDz in DMSO and an equimolar mixture of HCONDz and DCONDz in DMSO (-) at a mole fraction of formamide of 0.018.
e..),
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Figure 6. Isotropic Raman spectra of an equimolar mixture of HCONDz and DCOND2 in DMSO (thick line) compared with the spectra obtained by adding the spectra of HCONDl in DMSO and of DCOND2 in DMSO (thin line). Total mole fraction of fonnamide: (A) 1, (B) 0.64, and (C) 0.31.
HCOND2 and DCOND2 in DMSO at various mole fractions are shown in Figure 6. Also shown are the spectra obtained by adding together the isotropic Raman spectra of HCOND2 and DCOND2 in DMSO. As stated above, the carbonyl band of the neat liquid mixture cannot be regarded as a superposition of the carbonyl bands of HCONH2 and HCOND2, as is evident from Figure 6A. At a total mole fraction of formamide of 0.64 (Figure 6B), it is still obvious that there is some interaction leading to one band, when two are expected. The intensity of the high-frequency wing is seen to increase relative to the main band, leading to a broadening of the band, since the proportion of the non-hydrogen-bonded species increases upon dilution in At a mole fraction of 0.31, the band resulting from addition of the bands of HCOND2 and DCOND2 is almost identical to the band of the equimolar mixture (Figure 6C). This is because the intermolecular interaction leading to one carbonyl band decreases with distance between the molecules, and dilution increases the distance between interacting molecules. For HCONH2 and HCOND2 it was shown that the widths of the isotropic Raman carbonyl bands increased initially upon dilution in DMSO, and at a mole fraction of formamide around 0.3 they started to decrease again.2 However, the isotropic Raman carbonyl bands of all isotopomers of formamide are rather weak, thus making it difficult to obtain the spectra at a dilution where the bands have narrowed to a degree where the individual carbonyl bands from HCOND2 and DCOND2 can be observed more distinctly. However, since this band is very strong in absorption, it is possible to obtain the IR spectra at very low concentrations. Figure 7 shows the IR spectra of HCONDz, DCOND2, and an equimolar mixture of the two in DMSO at a mole fraction of 0.018, The spectrum of the equimolar mixture clearly shows the two peaks assignable to HCOND2 and DCOND2. It must be recalled that the IR carbonyl band of the equimolar mixture can be interpreted as made up of the contributions from the individual isotopomers2 at all mole fractions including the neat liquid because bands
are broad. Therefore, it is not possible in the IR spectra, as it is in the case of the isotropic Raman spectra, to observe a change from a state where the carbonyl band of the equimolar mixture cannot be explained as a superposition of the carbonyl bands of the individual isotopomers to a state where it can. Models. When two oscillators couple, the corresponding energy levels are perturbed. If a two-level system is considered, the solution of the resulting 2 x 2 secular determinant shows that coupling leads to an increased separation of the two energy levels.16 This is different from mixtures of HCOND2 and DCOND2 where the energy levels move closer together. Therefore, a different coupling scheme must be invoked. It is well-known from everyday life that oscillators like for instance the individual cells of a heart can oscillate in unison." That is, some kind of interaction couples the different oscillators, which may have different intrinsic frequencies, and causes them to oscillate with one and the same frequency. This phenomenon is called mutual entrainment or (self-)synchr~nization.~~J~ The phenomenon has been observed in many different systems (see ref 17 for references to earlier work in the field), for instance in oscillating chemical systems like the Belousov-Zhabotinskii rea~ti0n.l~ The time evolution of the phase of an unperturbed oscillator can be described by bi = wi, where bi is the time derivative of the phase of the ith oscillator and wI is its angular frequency. In the case of coupling between the individual oscillators, this equation is modified to20%21 N
where r(O, - Oi) is a 2n periodic function describing the coupling between the oscillators and Kij is the strength of the coupling. Usually a sinusoidal coupling is assumed, and the oscillators are assumed to couple with equal ~ t r e n g t h , ' ~i.e., -~~ KJ(Oj - Oi) = K sin(Oj - Oi). In this case it is possible to solve (1) analytically. A system described by (1) shows mutual entrainment if the coupling strength exceeds a certain critical value Kc.18-26The exact value of K, depends upon the separation in intrinsic frequency between the oscillators: the larger the separation (or spread, if a continuous distribution of intrinsic frequencies is assumed), the larger the K,. If the coupling strength K is only a little smaller than Kc, clusters of oscillators are formed, the
J. Phys. Chem., Vol. 99, No. 13, 1995 4439
Raman Spectra of Isotopomers of Formamide
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oscillators in each cluster showing mutual entrainment but each cluster oscillating at its own f r e q ~ e n c y . ' ~ . ~ ~ This model can qualitatively explain the observations made in the isotropic Raman spectra of mixtures of HCONH2 and HCOND2 and of HCONDz and DCONDp. The broadening of the carbonyl band in the mixtures (Figures 3B and 8 and ref 1) as compared to the carbonyl bands of the neat liquid isotopomers (Figure 3A,C and ref 1) could be due to the presence of clusters of different compositions. As a simple example, consider mixtures of HCOND2 and DCOND2 and small clusters containing only three molecules. Four different compositions of the clusters are now possible: (HCONDZ)~, (HCONDz)zDCONDz, HCOND2(DCOND&, and (DCOND2)3. Each one of these clusters will oscillate with its own frequency, different from the frequencies of the clusters with different compositions. That is, the carbonyl band observed in the mixtures is inhomogeneously broadened. In the neat liquid isotopomers, clusters are formed as well, but in this case, the clusters have the same composition and hence the same frequency. The smooth shift of the frequency of the carbonyl band of mixtures of HCONH2 and HCONDz observed in the isotropic Raman spectra as a function of composition (Figure 5 of ref 1) and in mixtures of HCONDp and DCOND2 (Figure 8) is in this model due to a change of the composition of the clusters. The average composition of the clusters follows the composition of the mixture. At low concentrations of one isotopomer the clusters will mainly consist of one type of molecule (the most abundant isotopomer), and the frequency will be close to the frequency of this isotopomer. In mixtures which are approximately equimolar, the frequency will be situated in between the frequencies of the neat isotopomers. As Figures 8 and 5 of ref 1 show, the frequency does not shift linearly with mole fraction. This is probably because the isotropic Raman carbonyl band of HCONDz is more intense than the carbonyl band of HCONH2, and the carbonyl band of DCOND2 is more intense than the carbonyl band of HCONDp. Since the carbonyl bands of the mixtures is made up of the contribution from clusters
with different frequencies and intensities, the peak frequency as a function of composition is expected to be nonlinear. One question still needs to be addressed: Why do mixtures of HCONH2 and H13CONH2 show two carbonyl bands whereas mixtures of HCONHp and HCONDp and of HCOND2 and DCOND2 only show one? For real molecules the intermolecular potential depends upon their mutual orientation and separation. That is, the magnitude of coupling depends on local order. In the case of formamide, local ordering is mainly imposed by hydrogen bonding. The orientation of molecules in mixtures of HCONH2 and HI3CONHp and in mixtures of HCONDp and DCOND2 should therefore be the same, and an angular dependent potential alone cannot account for the different behavior of these two mixtures. The separation in frequency between the carbonyl bands of HCONH2 and H13CONH2 is the same as it is for HCONDz and DCONDz (-22 cm-'). That is, K,, the mutual entrainment coupling constant, is the same for these two systems (K, depends upon the separation in frequency between the oscillators), and for some reason K (the actual coupling constant) is smaller for mixtures of HCONH2 and H13CONH2 than it is for mixtures of HCONDz and DCOND2. One obvious difference between these two systems is that in the latter case the hydrogen bonds contain deuterium. There is some e v i d e n ~ e ~ ' -that ~ ~ the strengths of hydrogen and deuterium bonds are somewhat different, which could lead to different K ' s for these two systems if the coupling is via the hydrogen bonds. However, this difference is small, and we do not believe that it can account for the different behavior of these two systems. Another possibility is that the coupling is via transition dipole moments. In order to see whether this is feasible, we have to resort to force constant calculations in order to obtain a more quantitative description of the vibrational modes. Calculations. In going from the gaseous to the liquid state, the carbonyl stretching frequency of formamide experiences a large shift. (For HCONH2 the gas phase value15 is 1753 cm-', and in the liquid' (IR) it is 1682 cm-l.) This shift is mainly due to hydrogen bonding. Hydrogen bonding leads to a weakening of the CO bond and thereby a lower frequency for the carbonyl stretching band. We performed some simple calculations of the frequencies and potential energy distributions (PED's) of the various normal modes of formamide. The calculations were done by use of the computer program VIBROT30 using the experimentally found geometry3' and the harmonic force field of Fogarasi and B a l i i ~ s .The ~ ~ program VIBROT calculates both the frequencies and the PED, the input parameters being the geometry and the force field. The same definition of the internal and symmetry coordinate^^^ was used in the calculations. The in-plane symmetry coordinates relevant for this work (i.e., contributing to the CO stretching mode) are as follows: SI, CH stretching; S2, CO stretching; S3, CN stretching; s6, OCN bending; S7, CH bending; s8, NH2 bending; S9, NHz rocking. It is believed that it is mainly a change of the CO stretching diagonal force constant which causes the large shift in frequency in going from the gaseous to the liquid state. Of course, the off-diagonal force constants may contribute, but (we expect) to a much lesser extent. We have therefore changed the CO stretching (diagonal) force constant, keeping the other force constants fixed.32 A value of 11 mdyn/A for this force constant (reduced from 12.2 mdyn/A for the isolated molecule)32 was found to exactly reproduce the v(C=O) band frequency of HCONH2 while at the same time the calculated v(C=O) band positions for HCOND2, DCOND2, and H13CONH2were within 12 cm-' of their observed ~ a 1 u e s . l However, ~ what is most interesting is the PED's (Table 1). It is clear that there are only
4440 J. Phys. Chem., Vol. 99, No. 13, 1995
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TABLE 1: Potential Energy Distribution for the Carbonyl Band of the Various Isotopomers of Formamide“ HCONHz
HCOND;!
DCONDz
H13CONHz
s1
0
0
1
0
s3
68 12
71 11
74 14
65 12
s6
1
Sl
15 1 3
1 14 0 2
sz
SS s9
1
I 0 1
1 15 3
3
SI = CH stretching, SZ = CO stretching, S3 = CN stretching, S g = OCN bending, ST = CH bending, SS = NHz bending, and S9 = NHz rocking.
very minor differences between the PED’S of the various isotopomers. The only notable changes are that the carbonyl “stretching” mode of H13CONH2 contains some small NHz bending motion (SS) (whereas this motion is not involved in the carbonyl stretching mode for the other isotopomers) and that the corresponding C-0 stretching motion for this motion makes a lower contribution to the normal coordinate. This difference in normal coordinates, which, in principle, might affect the aa/aQ, value, could be the reason for the change in relative intensities between the carbonyl stretching and NHz bending bands between HCONHp and H13CONH2 (Figure 1A,C). The shape of these bands depends upon the details of the vibrational relaxation processes and could be different for the two molecules if the laa/3Ql2 values are different. However, the Q values for this mode for the two molecules are so little different that any differences in intensity are more likely due to changes in the electronic polarizability from one molecule to another in the liquid state. If the intermolecular coupling is through the transition dipoles14 [Le., K = (ap~laQ2).(ap~laQz), A and B being two molecules (identical or different)], then a difference in either (or both) of the transition moments can lead to a coupling difference. This is under the assumption that local ordering is the same for mixtures of HCOND2 and DCOND2 and for mixtures of HCONHz and H13CONH2. Otherwise, the molecules could orientate to give different K s even if the transition dipole moments were all the same. The transition dipole of the carbonyl stretching band is smaller for H13CONH2 than it is for HCONH2 (since the noncoincidence splitting A Y i s o - h s o is proportional to this quantity).14 Furthermore, the shift of the isotropic band profile (on isotopic dilution) for Hl3CONH2 is only -10 cm-’ as compared with 32 cm-’ for HCONHz. On the other hand, the noncoincidence splitting is the same for HCONDz and DCONDz (about 30 cm-l). Since the coupling is proportional to (a~i/aQ2)~, these differences reflect considerably different degrees of coupling. Thus, for mixtures of HCONHZand HCOND;?(ref 1) or for HCONDz and DCOND2 (this paper), the coupling is strong enough to achieve mutual entrainment whereas in mixtures of HCONH2 and H13CONH2 it is not. The difference in behavior between these three pairs of molecules serves to confirm the mechanism which leads to apparently anomalous behavior in liquid mixtures. Mutual entrainment is a collective vibration in a cluster of molecules. Cooperative modes have been observed before in amorphous solid^,^^^^^ and low-frequency vibrational spectra.36 These cooperative modes, however, do not show mutual entrainment. As far as we are aware, this is the first time that mutual entrainment has been unambiguously observed in the fluid phase. Conclusions. The single carbonyl stretching band observed in the isotropic Raman spectra of liquid and solid mixtures of HCONH2 and HCONDz and of HCONDz and DCONDz is due to intermolecular coupling. This coupling causes the different
oscillators to vibrate with the same frequency (mutual entrainment), if the coupling strength exceeds a certain critical value, K,. At coupling strengths just below K,,clusters of oscillators showing mutual entrainment are formed. The coupling could be due to transition dipole moments, which are very large for the carbonyl stretching mode of formamide. The coupling is related to the molecules and not to the way of observing it and is therefore also “present” in the IR and anisotropic carbonyl spectra, even though it cannot be observed in the IR and anisotropic Raman spectra because bands are too broad, and thus can be regarded as a simple superposition of the individual components. The phenomenon is not observed in mixtures of HCONH2 and H13CONHz because in this system the coupling strength is too low to induce mutual entrainment.
Acknowledgment. The Danish Natural Science Research Council is acknowledged for general financial support. A.M. thanks the Danish Natural Science Research Council for a Ph.D. grant. Dr. G. 0. Sorensen, University of Copenhagen, is thanked for the use of the program VIBROT. References and Notes (1) Mortensen, A.; Nielsen, 0. F.; Yarwood, Y.; Shelley, V. J . Phys. Chem. 1994, 98, 5521. (2) Mortensen, A.; Nielsen, 0. F.; Yarwood, Y.; Shelley, V. Vib. Spectrosc. 1994, 8, 37. (3) Chang, I. F.; Mitra, S . S. Adv. Phys. 1971, 20, 259. (4) Devlin, J. P.; Frech, R. J. Chem. Phys. 1975, 63, 1663. (5) Kariuki, D. A,; Kettle, S. F. A. Inorg. Chem. 1978, 17, 141. (6) Liapis, K.; Jayasooriya, U. A.; Kettle, S. F. A.; Eckert, J.; Goldstone, J. A,; Taylor, A. D. J . Phys. Chem. 1985, 89, 4560. (7) Kettle, S. F. A.; Lugwisha, E.; Eckert, J.; McGuire, N. K. Spectrochim. Acta 1989, 45A, 533. (8) Kettle, S. F. A.; Lugwisha, E.; Vorderwisch, P.; Eckert, J. Spectrochim. Acta 1990, 46A, 921. (9) Fuchs, H.D.; Grein, C. H.; Devlen, R. I.; Kuhl,J.; Cardona, M. Phys. Rev. B 1991, 44, 8633. (10) Fuchs, H. D.; Grein, C. H.;Cardona, M. Solid State Commun. 1992, 82, 225. (11) Chrenko, R. M. J. Appl. Phys. 1988, 63, 5873. (12) Hass, K. C.; Tamor, M. A.; Anthony, T. R.; Banholzer, W. F. Phys. Rev. B 1991, 44, 12046. (13) Hass,K. C.; Tamor, M. A.; Anthony, T. R.; Banholzer, W. F. Phys. Rev. B 1992,45, 7171. 114) Logan. D. E. Chem. Phvs. 1986. 103. 215. (15) Mcrtensen, A,; Nielsen,‘ 0. F. Spectrochim. Acta, in press. (16) Atkins, P. W. Molecular Quantum Mechanics, 2nd ed.; Oxford University Press: London, 1983; p 172. (17) Winfree, A. T. The Geometly of Biological Time; Springer: New York, 1980. (18) Strogatz, S. H.;Mirollo, R. E. J. Phys. A: Math. Gen. 1988, 21, L699. (19) Fujii, H.;Sawada, Y. J. Chem. Phys. 1978, 69, 3830. (20) Sakaguchi, H.;Kuramoto, Y. Prog. Theor. Phys. 1986, 76, 576. (21) Sakaguchi, H.;Shinomoto, S . ; Kuramoto, Y. Prog. Theor. Phys. 1987, 77, 1005. (22) Ermentrout, G. B. J . Math. B i d . 1985, 22, 1. (23) Kuramoto, Y.; Nishikawa, I. J . Stat. Phys. 1987, 49, 569. (24) Strogatz, S. H.;Mirollo, R. E. Physica D 1988, 31, 143. (25) Daido, H. Phys. Rev. Lett. 1988, 61, 231. (26) Okuda, K.; Kuramoto, Y. Prog. Theor. Phys. 1991, 86, 1159. (27) Brooker, M. H. In Proceedings of the Xlllth International Conference on Raman Spectroscopy; Kiefer, W., Cardona, M., Schaack, G., Schneider, F. W., Schrotter, H. W., Eds.; Wiley: Chichester, 1992; p 292. (28) Brooker, M. H.; Tremaine, P. R. Geochim. Cosmochim. Acta 1992, 56, 2573. (29) Buckingham, D.; Fan-Chen, L. Int. Rev. Phys. Chem. 1981,1,253. (30) Sgrensen, G. 0. Department of Chemistry, University of Copenhagen. The programs M O M and VIBROT for a VAX computer are available on reauest (1993). (31) Hirota,’E.; Sugisak, R.; Nielsen, C. J.; Scensen, G. 0. J . Mol. Spectrosc. 1974, 49, 251. (32) Fogarasi, G.; Balhs, A. J. Mol. Struct. (THEOCHEM) 1985, 105, 133. (33) Yvinec, M.; Pick, R. M. J . Chem. Phys. 1979, 71, 3440. (34) Devlin, J. P. J. Chem. Phys. 1989, 90, 1322. (35) Galeener, F. L.; Sen, P. N. Phys. Rev. B 1978, 17, 1928. (36) Nielsen, 0. F. Annu. Rep. Prog. Chem., Sec. C 1993, 90, 3.
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