Polyatomic systems vibrational excitations

Gerber, R. B., Ratner, M. A. Self-consistent field methods for vibrational excitations in polyatomic systems. Adv. Chem. Phys. 70 (1988) 97-132... 

An alternative approach widely used in polyatomic molecule studies is based on the Golden Rule and a perturbative treatment of the anharmonic coupling (57,62). This approach is not much used for diatomic molecules. In the liquid O2 example cited above, the Hamiltonian must be expanded to 30th order or so to calculate the multiphonon emission rate. But for vibrations of polyatomic molecules, which can always find relatively low-order VER pathways for each VER step, perturbation theory is very useful. In the perturbation approach, the molecule s entire ladder of vibrational excitations is the system and the phonons are the bath. Only lower-order processes are ordinarily needed (57) because polyatomic molecules have many vibrations ranging from higher to lower frequencies and only a small number of phonons, usually one or two, are excited in each VER step. The usual practice is to expand the interaction Hamiltonian (qn, Q) in Equation (2) in powers of normal coordinates (57,62) ... 

R.B. Gerber and M.A. Ratner, Self-consistent field methods for vibrational excitations in polyatomic molecules, Adv. Chem. Phys., 70 (1988) 97. P. Jungwirth and R.B. Gerber, Quantum dynamics of large polyatomic systems using a classically based separable potential method, J. Chem. Phys., 102 (1995) 6046 Quantum dynamics of many atom systems by classically based separable potential (CSP) method Calculations for T (Ar),2 in full dimensionality, J. Chem. Phys., 102 (1995) 8855. 

SELF-CONSISTENT-FIELD METHODS FOR VIBRATIONAL EXCITATIONS IN POLYATOMIC SYSTEMS... 

This chapter is devoted to recent developments in a class of approximation methods that aim at describing the energy-level structure and dynamics of energy transfer in vibrationally highly excited polyatomic systems. The meth ods that are the subject of the present study are the self-consistent-field (SCF) approximations, in which framework each vibrational mode is described as moving in an effective field obtained by averaging the full potential function... 

When vibrational excitation is supplied to a polyatomic molecule by a technique such as pulsed-laser pumping, the return of the system to equilibrium via collisions is an enormously complex process for a molecule with more than just a few energy levels as should be evident from the data presented for CH4, CD4, CD3H, CHjDj, and CH3F in the preceding section. For example, let = -)- ,(/) be the population density of... 

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