Theoretical calculation of vibrational

All nonlinear molecules have 3n — 6 vibrational modes, where n is the number of atoms. Some of these modes arc active in the infrared spectrum, some are active in the Raman spectrum, and others do not give directly observable transitions. Analyses of these spectra usually make use of isotopically substituted molecules to provide additional experimental data, and in recent years, theoretical calculations of vibrational spectra have aided both in making assignments of the observed bands, and in providing initial estimates of force constants.97 Standard methods are available for relating the experimental data to the force constants for the vibrational modes from which they are derived.98... 

The products of reactive ion-neutral collisions may be formed in a variety of excited states. Excited products from nonreactive collisions have already been discussed in a previous section. Theoretical calculations of vibrational excitation in the products of symmetric charge-transfer reactions have also been mentioned previously.312-314 The present section deals with excited products from reactive ion-neutral scattering, with special emphasis on luminescence measurements. 

PJ Stephens, FJ Devlin, CS Ashvar, CF Chabalowski, MJ Frisch. Theoretical Calculation of Vibrational Circular Dichroism Spectra. Faraday Discuss 99 103-119, 1994. 

Theoretical calculations of R2Ge give bond parameters and vibrational frequencies. For example, Me2Ge has calculated GeC = 202 pm and CGeC = 98° with the Ge-C stretches at 560 cm-1 (Ai) and 497 cm-1 (Bi). As the latter agree reasonably with experimental values from matrix-isolated species (527 and 541 cm-1), the structural values are probably good indications. 

Chapter 3 is devoted to dipole dispersion laws for collective excitations on various planar lattices. For several orientationally inequivalent molecules in the unit cell of a two-dimensional lattice, a corresponding number of colective excitation bands arise and hence Davydov-split spectral lines are observed. Constructing the theory for these phenomena, we exemplify it by simple chain-like orientational structures on planar lattices and by the system CO2/NaCl(100). The latter is characterized by Davydov-split asymmetric stretching vibrations and two bending modes. An analytical theoretical analysis of vibrational frequencies and integrated absorptions for six spectral lines observed in the spectrum of this system provides an excellent agreement between calculated and measured data. 

There exists an extensive literature on theoretical calculations of the vibrational damping of an excited molecule on a metal surface. The two fundamental excitations that can be made in the metal are creation of phonons and electron-hole pairs. The damping of a high frequency mode via the creation of phonons is a process with small probability, because from pure energy conservation, it requires about 6-8 phonons to be created almost simultaneously. 

Finally, the repulsive forces, that as you said play a large role in the definition of advantageous foldings, do also play a big role in the definition of crystalline structures of organic compounds and of inter-molecular vibration movements. It is very unfortunate that theoretical calculations of repulsive forces are much more difficult than those of attractive forces. 

It is very likely that the metal-insulator transition, the unusual catalytic properties, the unusual degree of chemical reactivity, and perhaps even some of the ultramagnetic properties of metal clusters are all linked intimately with the dynamic, vibronic processes inherent in these systems. Consequently, the combination of pump-probe spectroscopy on the femtosecond time scale with theoretical calculations of wavepacket propagation on just this scale offers a tantalizing way to address this class of problems [5]. Here we describe the application of these methods to several kinds of metal clusters with applications to some specific, typical systems first, to the simplest examples of unperturbed dimers then, to trimers, in which internal vibrational redistribution (IVR) starts to play a central role and finally, to larger clusters, where dissociative processes become dominant. 

The theoretical treatment of vibration-vibration transfer was outlined in Section 3. Sufficient data for a priori theoretical calculations are only available for the simpler molecules. It is interesting first to discuss the general pattern revealed by the collision numbers in Tables 5 and 6 in terms of equations (18) and (19). 

Fig. 5.10. The theoretical calculation of the time trace of transient absorption (TRABS) for a one-mode system. The energy gap is 20 cm-1 and the vibrational mode is 420 cm-1. The dark curve is the reactant TRABS and the light-gray curve is the product TRABS. The probing frequency is set at respective peak positions of the induced absorption spectra of both reactant state and product state. For discussion see text.

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