Raman spectra anharmonicities

The resonance Raman spectrum of K4[Mo2C18] has been reinvestigated using 488.0 and 514.5 nm excitation. An enormous enhancement of the intensity of the Mo—Mo stretching mode relative to the intensity of other fundamentals was observed and an overtone progression in Vj to 5vj identified. From these data the harmonic frequency and anharmonicity constant X, were calculated as 347.1 + 0.5 cm -1... 

Figure 6 Simulations of the 2D Raman spectrum for the anharmonically (fully) coupled v and v4 modes [Equation (20)]. (a) The coupled response, (b) The g44 coupled response.

In the specific example of ACN (46) (point group C3V), there is one C-H stretch and one C-H bend of ai-symmetry and a pair of doubly degenerate stretches and bends of e-symmetry (84). In Fig. 5, the ACN Raman spectrum in the C-H bending region can be seen. The spectrum consists of a sharper ai-symmetry bend 1372 cm-1 and a broader e-symmetry bend at 1440 cm 1. The e-symmetry bend is broadened by Fermi resonance because the e-bend overtones (2 x 1440 cm 1) are degenerate with the e-stretches ( 3000 cm-1). The ai-bend and stretch have no Fermi resonance because the bend overtone (2 x 1372 cm 1) is not degenerate with the stretch (2943 cm-1). In the gas phase, the anharmonicity of the e-bend is 25 cm-1 [85], For an e-bend v = 1 0 transition at 1440 cm-1, the... 

We have compared the intensity of harmonic bands with one of G-bands, which has weak dependence on the wavelength of excitation. As can be seen from Fig. 7.11a, the intensity of 2vd harmonic band increases linearly under the excitation frequency Vl increase, and significantly exceeds the increase of the 2vq harmonic vibration. When A,l changes from 514.5 to 476.5 nm the intensity of the 2vd tone increases 1.69 times. This is significantly higher than the theoretical value for the Raman spectrum enhancement (1.36 in accordance to (6 law). These results cannot be explained only by the resonance Raman spectrum enhancement mechanism due to the fact that the multiplication factor is different for G- and D-band harmonics. We explain the anomalous enhancement of the 2vd and 2vq tones by an opposite frequency displacement of the main bands v, Vg and by a different variation of the anharmonicity of D and G modes under excitation frequency Vl increase. 

The principal progression-forming mode (vi) in the resonance Raman spectrum is harmonic within experimental error with the anharmonicity constant Xu = 0.0cm . For the stibine complex, vj shows a long overtone progression in the resonance Raman spectrum. This mode is also almost harmonic, the anharmonicity constant Xj2 being <0.1cm. Other modes show only one or two harmonics. Again harmonicity is a reasonable assumption in this calculation. 

Figure 19 The Raman spectrum and time cross correlation function when the motion on the excited electronic state potential is anharmonic, compare to Figs. 17 and 18, which are for a harmonic approximation. (Top, a) Computed time correlation function using a wide window function (b) The maximal entropy representation of this function, determined from the spectrum. Note the clear separation of time scales due to the anharmonicity (cf. Fig. 20). (Bottom) The Raman excitation spectrum obtained from the computed time correlation function (a). The arrows are the sequence of computations (a) is determined from the dynamics. The spectrum is determined from (a). The maximum entropy cross-correlation function (b) uses only the spectrum as input.

A typical resonance Raman spectrum of iodine consists of a long progression of the vibrational mode showing anharmonicity and rotational structure (Kiefer and Bernstein, 1973 Rousseau and Williams, 1976). This structure is readily understood on the basis of the calculations in Section III,A,B. The very simple Eq. (33) gives a qualitative picture of such a progression. The corresponding REPs are readily derived from the absorption spectrum (Berjot et ai, 1971). Thus the principal features of resonance Raman scattering by I2 are well understood. 

The Raman spectrum of acetylene was the subject of many investigations [18,49,173-177] concentrating on the rotational spectrum and the Raman active fundamentals Vi, V2, and V4. Through recording of the second-order rovibrational Raman spectrum of C2H2, the anharmonicity constant X22, which had been predicted by Strey and Mills [178], could be determined by analyzing the combination band which overlaps with 21 2 [49]. The... 

H Finsterholzl, HW Schrotter, G Strey. Determination of anharmonicity constants from the Raman spectrum of gaseous acetylene. J Raman Spectrosc 11 375-383, 1981. 

Since molecular vibrations in general are slightly anharmonic, both the infrared and Raman spectrum may contain weak overtone and combination bands. A combination energy level is one which involves two or more normal coordinates with different frequencies that have vibrational quantum numbers greater than zero. For example, a combination band which appears at the sum of the wavenumbers of two different fundamentals involves a transition from the ground vibrational level (belonging to the totally symmetric species) to an excited combination level where two different normal coordinates each have a quantum number of one and all the others have a quantum number zero. To obtain the spectral activity of the combination band transition it is necessary to determine the symmetry species of the excited wave-function. In quantum mechanics the total vibrational wavefunction is equal... 

In order to treat larger systems and/or high numbers of conformers or iso-topomers at the anharmonic level at a reasonable computational cost, it is possible to restrict the VPT2 treatment to a small part of the system on the basis of the spectroscopic observables of interest (for instance, the most intense bands of an IR of the Raman spectrum), by reducing the number of the normal modes treated at the anharmonic level. Such an approach, referred to as the reduced dimensionality VPT2 RD-VPT2) [55, 75] can be also combined with the hybrid model described in Section 10.3.2.5, allowing the treatment of complex macromolecular systems. 

Thus far we have discussed the direct mechanism of dissipation, when the reaction coordinate is coupled directly to the continuous spectrum of the bath degrees of freedom. For chemical reactions this situation is rather rare, since low-frequency acoustic phonon modes have much larger wavelengths than the size of the reaction complex, and so they cannot cause a considerable relative displacement of the reactants. The direct mechanism may play an essential role in long-distance electron transfer in dielectric media, when the reorganization energy is created by displacement of equilibrium positions of low-frequency polarization phonons. Another cause of friction may be anharmonicity of solids which leads to multiphonon processes. In particular, the Raman processes may provide small energy losses. 

Raman spectra of S2 in its triplet ground state have been recorded both in sulfur vapor and after matrix isolation using various noble gases. The stretching mode was observed at 715 cm in the gas phase [46], and at 716 cm in an argon matrix [71]. From UV absorption and fluorescence spectra of sulfur vapor the harmonic fundamental mode of the S2 ground state was derived as t e = 726 cm . The value corrected for anharmonicity is 720 cm [26, 27]. Earlier reports on the infrared absorption spectrum of 2 in matrix isolated sulfur vapor [72] are in error the observed bands at 660, 668 and 680 cm are due to S4 [17] and other species [73]. 

As 1 is a nonpolar symmetric top with symmetry, it should have no pure rotational spectrum, but it acquires a small dipole moment by partial isotopic substitution or through centrifugal distortion. In recent analyses of gas-phase data, rotational constants from earlier IR and Raman spectroscopic studies, and those for cyclopropane-1,1- /2 and for an excited state of the v, C—C stretching vibration were utilized Anharmonicity constants for the C—C and C—H bonds were determined in both works. It is the parameters, then from the equilibrium structure, that can be derived and compared from both the ED and the MW data by appropriate vibrational corrections. Variations due to different representations of molecular geometry are of the same magnitude as stated uncertainties. The parameters from experiment agree satisfactorily with the results of high-level theoretical calculations (Table 1). 

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