J . Phys. Chem. 1994,98, 5221-5226
5221
Vibrational Spectra of Mixtures of Isotopomers of Formamide. Anomalies in the Carbonyl Stretching Region A. Mortensen,t 0. Faurskov Nielsen,’??J. Yarwood,S and V. Shelley5 Department of Chemistry, University of Durham, South Road, Durham, DHl 3LE, England, Chemistry Department, University of Copenhagen, 5 Universitetsparken, DK-2100 Copenhagen, Denmark, and Materials Research Institute, Sheffield Hallam University, Pond Street, Sheffield SI I WB, England Received: February 8, 1994”
The infrared and Raman spectra of liquid mixtures of H C O N H 2 and HCOND2 are presented. Contrary to what is expected, the isotropic Raman spectra of the mixtures show only one carbonyl stretching band, whose position depends upon the composition of the mixture. It is shown that the apparent collapsing of bands is not due to fast exchange between different “sites” (i.e. the fast exchange limit). Similar phenomena have been observed previously in solids. Thus, the phenomenon might reflect “solid-like” behavior of liquid formamide close to its melting point. The depolarized component of the Raman spectrum and the I R spectrum of the carbonyl stretching band are observed a t approximately the same frequencies, whereas the isotropic components are observed a t a lower frequency (noncoincidence). The same is observed for the NH2 bending mode. The noncoincidence splitting of this mode is shown to follow a model for binary mixtures of isotopomers developed by Logan. The asymmetry of the I R and Raman bands can be explained in terms of two “sites”, one belonging to a hydrogen-bonded species and the other to a “free” species without hydrogen bonding to the carbonyl group, but maybe forming hydrogen bonds to the carbonyl group of other formamide molecules.
Introduction Being the simplest molecule containing the biologically important peptide group (-CONH-) and being a highly versatile solvent, formamide (HCONHz) has been studied extensively in the past. Studies of the vibrational spectra of formamide include work on the gaseous,lA liq~id,l,~-13 and crystalline5J4 states. The vibrational spectra of some isotopomers of formamide have been reported as well. These are mainly concerned with the various deuterated isotopomers (Le. DCONH2, HCOND2, and DCONDZ),~,~.~-IO,IZ-~~ but HCO15NHz has also received some attention.12J5 Ab initio calculations (including vibrational frequencies) on models of the liquid state have also been performed (ref 16 and references cited therein). A little work has been done on the vibrational properties of mixtures of various isotopomers. This includes infrared spectra of HCONHz and HCONDz, and DCONJ32 and DCONDz in chloroform,l7 Raman spectra of the same mixtures in the neat liquids,8and IR and Raman spectra of HCONHZand HCONDz in the N H and ND stretching regions of the neat liquids10 and of solutions in various s o l v e n t ~ . ~ ~However, J9 no detailed studies on the mixtures of isotopomers in the neat liquids across the entire concentration range (i.e. at concentrations ranging from the pure formamide to the pure isotopomer) have been previously reported. In this paper the IR and Raman spectra of liquid mixtures of HCONH2 and HCOND2 at various compositions are presented. In a mixture of the isotopomers HCONH2 and HCONDz, two new molecules are formed due to exchange of hydrogen and deuterium between the amide groups. The two new molecules, cis- and trans-HCONHD, exist in a dynamic equilibrium with HCONH2 and HCOND2. If the mole fraction of HCONDz in a mixture of HCONH2 and HCONDz before any exchange has taken place is denoted as x, the mole fraction of HCONHz is 1 - x. If a random distribution of hydrogen and deuterium is assumed, the concentrations, after equilibrium has been estabt University of Copenhagen.
t Sheffield Hallam University. i University of Durham. e Abstract published in Aduance ACS Abstracts, April 15, 1994.
0022-3654/94/2098-5221$04.50/0
lished, of HCONDZ,HCONHz, and HCONHD (both species) are x2, (1 - x ) ~ and , 2x(1 - x ) , respectively. In the following, the above definition of x will be used; i.e. x would denote the mole fraction of HCONDz in the mixture if no exchange took place. The structure of crystalline formamide consists of centrosymmetricdimers linked together by hydrogen bonds to formsheets.20 In an alternative description, the structure can be regarded as hydrogen-bonded chains of formamide molecules cross-linked with other chains by hydrogen bonds. The hydrogen bonds within the cyclic dimers are 2.93 A long and within the chains 2.88 A long. As formamide is a strongly associating molecule (its melting point is 2.5 OC and its boiling point 210 “C), it is not unreasonable to expect that the “structure” of liquid formamide close to its melting point might resemble that of the solid. The hydrogen bonds within the chains are the shortest, and hence the strongest, and the prediction of chains being the most predominant form in the liquid seemsviable. However, some uncertainty (and maybe some controversy) still exists. X-ray diffraction data21 are consistent with a model of the liquid mainly consisting of hydrogen-bonded chains. However, the presence of a centrosymmetric dimer could not be completely ruled out. A comparison of low-frequency Raman scattering and far-IR datal2 was also in support of the “chain structure”. The intermolecular proton-proton distances were estimated from the NMR spectra of liquid formamide.2z The findings support a linear chain or a more open configuration. However, results from neutron diffraction experiment^^^ indicate that a cyclic dimer can best explain the data. Some calculations on the structure of liquid formamide have been performed. Monte Carlo simulationsz4favored the occurrence of branched chains. No preference for a centrosymmetric dimer was found. Ab initio calculations21*25showedthat thecyclic dimer is more stable than the open-chain dimer, since the latter has only one hydrogen bond whereas the former has two. However, as thechains become longer, the hydrogen bonds become strongerand, hence, it wasconcluded that thechain is thedominant species in liquid formamide. A molecular dynamics simulation using the so-called 9est particle” mode126 leads to the same conclusion. To summarize, the available evidence is in favor of cross-linked 0 1994 American Chemical Society
5222 The Journal of Physical Chemistry, Vol. 98, No. 20, 1994 or, in an alternative description, branched chains. This is very similar to thecrystallinestructure.. In thecrystal thecross-linking leads to centrosymmetric dimers. However, the liquid is not a rigid structure like the crystal, and therefore, cross-linking or branching does not favor centrosymmetric dimers. Experimental Section The IR spectra were recorded between 4000 and 1000 cm-l on a Perkin Elmer 580B double-beam infraredspectrometer. CaF2 plates were used since KBr is soluble in formamide. Due to the very high extinction coefficient of the carbonyl band, the spectra were obtained on capillary films except for dilute solutions (mole fraction less than 0.02) of formamide in DMSO where spacers could be used. The very high extinction coefficient will to some extent result in distortion of the observed infrared band shapes due to the so-called internal field effect.27 As far as we are aware, there are no refractive index data with which to make such corrections. However, the asymmetry of the observed bands cannot solely be due to this effect since the Raman bands, where this complication does not arise, are asymmetric too. We do not believe that the conclusions derived from the IR spectra are invalidated by the internal field effect. The Raman spectra were obtained in the region of 1500-1800 cm-l with a Cary 82 Raman spectrometer using the 514.5-nm excitation line of a Cambridge Lasers argon-ion laser. The power at the sample was about 350 mW. Both the polarized and depolarized scattering were measured, and the isotropic spectra were constructed in the usual way (Ziso= ,Z - 4/3Zvh). These spectra were in accordance with full-region spectra obtained on a Dilor 224 spectrometer. All the IR and Raman spectra are shown from 1500-1800 cm-1 (the carbonyl stretching ( v ( C 4 ) ) and NH2 bending (6(NHz)) region). All spectra wereobtained at room temperature. DMSO and HCONH2 (both spectrophotometric grade) were obtained from Aldrich and used without further purification. HCOND2was made from HCONH2 by adding an excess of D2O (99.9 atom 7% D). The DtO and HCONH2 were allowed to exchange overnight, and the water was subsequently distilled off in vacuo. The process was repeated once. The vapor pressure of formamide at room temperature is much lower than the vapor pressure of water, and therefore a single distillation in vacuo was sufficient to achieve almost complete separation of formamide and water. It was, therefore, assumed that it was not necessary to dry the formamide. A sample of formamide was treated with molecular sieves (4A) in order to test this assumption. As expected, the spectra of dried and undried formamide were identical, and the samples were therefore used without special drying. Theory Resonant Energy Transfer. One of the manifestations of resonant intermolecular coupling28 (known as resonant energy transfer (RET)) is the so-called Raman noncoincidence effect (NCE), that is, the observation that for some bands the anisotropic and isotropic Raman components have different band positions, the former normally at the highest frequency. The effect has been observed in many carbonyl group containing molecular liquids (ref 29 and references cited therein). It is often associated with vibrations having a large transition dipole moment (for instance the v(C=O) stretching band), i.e. modes that have high infrared transition moments. In the case of formamide it should, in principle, be possible to follow this effect for the individual isotopomers in a mixture of HCONHz and HCOND2. One of the ways in which RET can occur is via interactioninduced transition dipole-transition dipole coupling.28-30 When two identical molecules interact strongly in the liquid (for example via dipole-dipole interactions), for a given normal mode, transfer
Mortensen et al. of vibrational excitation (RET) from one molecule to the other is possible. This coupling gives rise to two new vibrations of the pair: an in-phase and an out-of-phase vibration. Only the inphase vibration is active in the isotropic Raman spectrum, whereas both components are active in the IR and anisotropic Raman spectra. The separation in frequency between the isotropic and anisotropic Raman bands is predicted to be proportional to the squared transition dipole moment of the vibration in question (Le. proportional to the intensity of the IR band). However, the NCE has been observed in the v6vibration of 1,2,5-thiadiazole,31J2 which is very weak in the infrared, and in vibrations which are forbidden by symmetry in absorption in mixtures33of CsH6 and C6D6. Transition dipole-transition dipole coupling is, hence, not the only mechanism which can give rise to the NCE. A model for the noncoincidence effect in isotopic binary mixtures has been developed by Logan.30 This model predicts that through dipoleaipole interactions the anisotropic and isotropic Raman bands are blue-shifted upon dilution with an isotopomer whereas the IR band is not shifted. However, the anisotropic Raman band is only slightly blue-shifted whereas the isotropic Raman band is blue-shifted to a considerable extent (according to the theory, the shifting of the isotropic Raman band is a factor of 25 larger than the shifting of the anisotropic Raman band). Eventually, at infinite dilution the IR and both Raman bands coincide, that is, when one isotopomer is at so low a concentration that it can no longer couple with an identical molecule in its first solvation shell. The noncoincidence splitting is also predicted to depend linearly on the mole fraction of the compound showing this splitting. The assumptions of the model are that the isotopomers have the same size (a), the same permanent dipole moment (M), and the same dielectric constant ( E ) . These assumptions are valid in the Born-Oppenheimer approximation. One- and Two-Mode Behavior. It may seem inappropriate to discuss some of the vibrational properties of mixed crystals (e.g. germanium and diamond) in a study of liquid formamide. However, as it will become evident in the next section, these systems have some features in common with the liquid mixtures of formamide isotopomers. The phonon spectrum of mixed crystals (for example mixed alkali halides like Na,KI-,C1 or NaCl,Brl,) can exhibit two different characteristics called “one-” and “two-mode” behavior, respectively (for a review see ref 34). In the former case only one optical phonon band, which is situated in between the optical phonon bands of the pure crystals, is observed-hence the socalled “one-mode” behavior. The peak frequency varies smoothy and monotonically with composition of the mixed crystal. A model called the virtual crystal approximation (VCA), in which the mixed crystal is treated as a real crystal with translational symmetry and the masses of the positive (in for example the case of NaXK1,C1) or negative (in for example thecaseof NaCl,Br,-,) ions are replaced by an average mass m, predicts the same frequency dependence upon mass as in the case of a real crystal, Le. v 0: The model accounts fairly well for the observed spectra, i.e. the frequency as a function of composition. The “two-mode“ behavior is characterized by the appearance of two optical phonon bands close to the positions of the optical phonon bands in the pure crystals. The relative intensity of the two bands follows the composition of the crystal. Natural germanium consists of five isotopes. A sample of natural germanium shows only one optical phonon band, as do crystals of the pure i s o t o p e ~ . ~ ~ItJ 6has been shown that this band is not made up of the contributions of the individual isotopes. The frequency of the band depends upon the average mass of the isotopes weighted by their relative abundance. The dependence is the same as in the case of the VCA model, Le. v m-lP. The occurrence of a single optical phonon band in natural germanium is believed to be due to the small difference in mass between the
Mixtures of Isotopomers of Formamide Ibl
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Figure 1. (a) Isotropic Raman spectra of HCOND2 (A), HCONHz (E), and mixtures of the two. Mole fraction of HCOND2: (B) 0.75, (C) 0.5, and (D) 0.25. (b) Same as part a but anisotropic Raman spectra.
isotopes which prohibits the formation of local modes. Exactly the same is observed in the case of synthetic diamonds37-39 with varying concentrations of 13C. The phenomenon of one band being observed when two are expected is not restricted to atomic or ionic crystals. Mixed crystals of chromium, molybdenum, and tungsten hexacarbonyls show “one-mode” behavior in the carbonyl region.& One-mode behavior has been observed in the case of crystals of mixtures of isotopomers as well. Mixed crystals of 14Nand lSNurea:’ of 12C and glycine,42and of H and 2H alanine43all show “one-mode” behavior. In the case of molecular mixed crystals, some bands may show “one-mode” behavior whereas others show ”two-mode” behavior. Whether one or the other is encountered depends upon the separation of the bands and the strength of coupling between them. That is, the bands need to be close together in frequency and couple strongly in order to show “one-mode” behavior. So far “one-mode” behavior of vibrational modes has only been observed in crystals. It is well-known from N M R spectroscopy that in some instances one band is observed and in other instances two bands are observed (for example the N M R spectrum of formamide a t room temperature show two N M R signals from the NH2 protons due to hindered rotation around the C-N bond, whereas only one signal is observed at elevated t e m p e r a t ~ r edue s ~ ~to “free” rotation around the C-N bond). In this case, it is not due to coupling (as in the case of “one-” and “two-mode” behavior) but due to exchange between sites, in the so-called “rapid exchange” limit, which makes the bands coalesce. Coalescence of bands is also possible in vibrational spectra if the exchange is fast enough. However, due to the time scale involved only very fast exchange processes can lead to vibrational band coalescence.
Results and Discussion In Figure l a the isotropic Raman spectra of mixtures of HCOND2 and HCONH2 at various concentrations are shown. In the spectrum of pure HCONH2 (Figure Ia,E), two distinct bands are observed. One at 1668 cm-I is the C=O stretching mode, and the other broader band around 1590 cm-I is the NH2 bending mode. A slight asymmetry of the v(C=O) band to the high-frequency side is discernible. This is more clearly seen in the spectrum of HCOND2 (Figure la,A) where there is no interference from the 6(NHz) band. As expected, the NH2 bending band is not observed in the spectrum of HCOND2. In the Raman spectra, the ND2 bending band was found around 1120 cm-I, in agreement with previous findings.6-8 This band is barely visible in the IR spectrum because of the cutoff of the CaF2 plates. In the isotropic Raman spectrum of HCOND2, the
Figure 2. Position ofthe isotropicRaman NH2 bending mode of HCONHz as a function of mole fraction (y) of HCONH2 in mixtures of HCONHz and HCONDz.
asymmetry is clearly seen as a wing to the high-frequency side of the u(C=O) band. The peak frequency is at 1638 cm-I, that is, an isotope shift of 30 cm-l as compared to the spectrum of HCONH2. Since the u(C=O) bands of HCONHz and HCONDz in the liquid state are separated by 30 cm-1 and the widths (FWHH) are about 20 cm-’, and because the frequency of HCONHD is expected to be in between the frequencies of HCONH2 and HCONDz, it would be possible to distinguish four peaks (three if the frequencies of cis- and trans-HCONHD are almost identical) from the four different molecules and thereby follow the N C E for the four different molecules as a function of mole fraction. However, only one u(C=O) band is observed in the isotropic Raman spectra (Figure 1a), regardless of the composition of the mixtures. This has been observed before,* and the single band was assigned to HCONHD. However, no mention of the “missing” bands due to HCONHz and HCOND2 was made.8 A detailed discussion of this band will be deferred until a presentation of the IR spectra has taken place. As HCOND2 is gradually added to HCONH2, the intensity of the 6(NHz) band decreases relative to that of the u(C=O) band (Figure 1). At the same time, a new band around 1500 cm-I appears. This is due to the N H bending mode of HCONHD. This band is found (Figure lC), as expected, at its maximum intensity relative to that of the u(C=O) band when the mixture is made up of equimolar amounts of HCONHz and HCOND2. In addition to becoming less intense, the ~ ( N H z band ) shifts upward in frequency as HCOND2 is gradually added to HCONHI. In Figure 2 the peak frequency of the 6(NHz) band is plotted as a function of mole fraction of HCONHz. The mole fraction plotted is not the amount of HCONH2 present initially but the actual mole fraction in the mixture, Le. y = (1 - x)*. This band is rather broad, and the peak position is, hence, difficult to establish precisely. Therefore, the peak position was taken from the curve fitted to this band and only at mole fractions y > 0.25, where the band is distinct enough to obtain a reliable curve fit. The linear shift as a function of mole fraction is what theory30 predicts. The model’O only deals with binary isotopic mixtures, but it is not surprising that its predictions can be extended to mixtures of several isotopomers, considering the assumptions in the model. The anisotropic Raman bands (Figure 1b) have a very different behavior from that of the isotropic Raman bands. For a given mode (u(C=O)and6(NH2)), the former a r e a t a higher frequency than the latter (noncoincidence) and they are broader. They too are asymmetric in shape. However, the asymmetry is not in the form of a wing but is more like a poorly defined shoulder on the high-frequency side of the v(C=O) band. The I R spectra of the u(C=O) band (Figure 3) are very similar to the ansiotropic Raman spectra. Thelatter aresomewhat broader than the former and are at a slightly higher frequency. However, the trends in
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The Journal of Physical Chemistry, Vol. 98, No. 20, 1994 A
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Figure 3. IR spectra of HCONDl (A), HCONH2 (E), and mixtures of the two. Mole fraction of HCOND2: (B) 0.75, (C) 0.5, and (D) 0.25.
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Figure 5. Peak frequencies and widths of the isotropic Raman and IR carbonylbands as a function of isotopiccomposition: (-) Raman bands, (--) IR bands, (m) FWHH, (A) peak frequency.
Figure 4. IR spectrum of the carbonyl stretching mode of HCOND2 fitted by two bands: (-) experimental, fitted bands, (- - -) resultant band. (-a)
band shapes and position of the band are the same for the I R and anisotropic Raman bands a t all compositions of the mixtures. Therefore, in the following, what pertains to the IR bands also pertains to the anisotropic Raman bands. As HCONDz is added to HCONH2, the same intensity alteration of the 6(NH2) band and the N H bending mode in HCONHD is observed in the I R spectra (Figure 3) as it was in the isotropic Raman spectra (Figure la). However, the 6(NH2) band is not as distinct in the IR spectra as it is in the isotropic Raman spectra. Therefore, it is difficult to establish whether the band shifts upon dilution or not. It does not, however, seem to shift significantly. Theory’O predicts that it will not shift upon dilution. The u(C=O) band has the same shape regardless of isotopic composition. The peak frequency of the mixtures is observed in between the peak frequencies of the pure isotopomers. The u(C=O) band as observed in the IR spectra is certainly asymmetric to the high-frequency side. The IR and Raman bands of all the mixtures could be satisfactorily fitted by two bands; no more were needed. An example is shown in Figure 4. Since the IR and anisotropic Raman carbonyl bands are broad and the two fitted curves are close together, many different curve fits, which differed widely from one another, could be obtained. In the case of the isotropic Raman spectra where the asymmetry of the u(C=O) band has the form of a wing, curve fitting is difficult. Therefore, only the peak frequencies and widths for the full u(C=O) bands, and not for the fitted curves, are shown in Figure 5.
Asymmetric bands can have various origins: for instance, hot bands and combination bands. Another possibility is that there are two different “sites”. In Figure 6 the IR and isotropic Raman
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Figure6. IsotropicRaman (a) and IR (b) spectra of formamidein DMSO. Mole fraction of formamide: (thick line) 1, (normal line) 0.64, and (thin line) 0.17. The spectra have been scaled to the same height. spectra of HCONHz in DMSO a t various concentrations are shown. The I R and Raman spectra clearly show that as formamide is diluted in DMSO, the high-frequency component of the u(C=O) band increases in intensity relative to the lowfrequency component. The low-frequency component shifts upward in frequency whereas the high-frequency component seems to shift only a little, if at all. We therefore assign the high-frequency component to formamide molecules which have no hydrogen bonds to their carbonyl groups. These molecules may be monomers or, if they themselves hydrogen bond to other formamide molecules, molecules at the end of a chain. The low-frequency component could then be due to hydrogen-bonded molecules. Dilution causes the hydrogen bonds to break and the band to shift upward in frequency. Another possibility is that dilution destroys microscopic order induced by dipolar interactions and/or hydrogen bonds, which will also lead to an upward shift. It is not possible to distinguish between these
Mixtures of Isotopomers of Formamide
The Journal of Physical Chemistry, Vol. 98, No. 20, 1994 5225
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Figure 8. Positions of the IR and isotropic Raman carbonyl bands of
HCONHz (top) and HCONDz (bottom) and predicted30(- - -) positions
of the isotropic Raman bands of the two in a 1:l mixture. 1700
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Figure7. (-) IR spectrum of a 1: 1 mixture of HCONHz and HCOND2. (- - -) Curve resulting from the addition of the IR spectra of HCONHz and HCONDz. The curves have been normalized to the same height.
two effects because both cause “ordering” in the neat liquid which is destroyed by dilution. A comparison of the isotropic Raman spectra (Figure l a ) with the IR (Figure 3) and anisotropic Raman spectra (Figure lb) reveals that the relative intensity of the carbonyl band of the formamide “monomer” is lower in the isotropic Raman spectra than it is in the IR and the anisotropic Raman spectra. This is not necessarily surprising since the intensities are determined by different physical (i.e. molecular) quantities. It can be shown that the IR bands of the mixtures can be reproduced fairly well by adding the spectra of the pure isotopomers with varying weight (Figure 7). Applying this procedure allows the contribution from HCONHD to be ignored. However, the procedure can establish whether or not it is viable to regard the u(C=O) band observed in the isotopic mixtures as a composite band made up of the contribution from four different molecules. As Figure 7 shows, this interpretation is indeed possible. However, one is unable to do this for the isotropic Raman spectra. The reason why the IR bands can be constructed from the pure isotopomers is not because the I R bands reflect a different aspect of the behavior of liquid formamide from that of the isotropic Raman bands, but because the IR bands are broader than the corresponding isotropic Raman bands and the separation between the IR bands is less (Figure 5 ) . That is, the IR bands can apparently be regarded as a simple superposition of the individual components, but this is not likely to be the case since the isotropic Raman bands cannot be explained by a simple superposition. Three possible mechanisms can account for the observation of just one band in the isotropic Raman spectra when four are expected. These are (1) differential shifting, (2) coalescence, and (3) “one-mode” behavior. Each one of them will be considered in turn. Differential Shifting. Because the noncoincidence splitting is larger in the case of (pure liquid) HCONDz (23 cm-I) than in the case of HCONH2 (14 cm-I), the isotropic Raman band of HCONDz is predicted30 to be more blue-shifted upon dilution than the isotropic Raman band of HCONH2. In Logan’s model,30 the difference in noncoincidence splitting between two isotopomers is determined by the strength of the oscillating dipole moment. However, because capillary films were used, it was not possible to determine the difference in intensity of the carbonyl bands of the isotopomers and hence verify this prediction. In Figure 8 the positions of the IR and isotropic Raman u(C=O) bands of HCONH2 and HCOND2 are depicted together with the predicted30 positions of the isotropic Raman bands of HCONHz and HCONDz in an equimolar mixture. The difference in frequency between the predicted bands is 23 cm-I compared to 30 cm-1 between the bands of the pure isotopomers. That is, the bands have moved closer together because of differential shifting. However, a single composite band made up of the contributions of HCONH2, HCOND2, and HCONHD would be expected to
be considerably broadened as a consequence of this diminished but yet significant separation of the bands. As can be seen from Figures 1 and 5 , this is not the case. Therefore, the isotropic Raman band of the isotropic mixtures cannot be regarded as a composite band under the assumption that Logan’s model is valid. If the carbonyl band were a composite band, it would not be possible to use Logan’s model. Coalescence. The “coalescence” of vibrational bands45.46occurs in the fast modulation limit (i.e. A m
