Self-consistent-field approximation vibrational states

R.B. Gerber, V. Buch and M.A. Ratner, Time-dependent self-consistent field approximation for intramolecular energy transfer. I. Formulation and application to dissociation of van der Waals molecules, J. Chem. Phys., 77 (1982), 3022 M.A. Ratner and R.B. Gerber, Excited vibrational states of polyatomic molcecules the semiclassical self-consistent field approach, J. Phys. Chem., 90 (1986) 20 R.B. Gerber and M.A. Ratner, Mean-field models for molecular states and dynamics new developments, J. Phys. Chem., 92 (1988) 3252 ... 

For the case of intramolecular energy transfer from excited vibrational states, a mixed quantum-classical treatment was given by Gerber et al. already in 1982 [101]. These authors used a time-dependent self-consistent field (TDSCF) approximation. In the classical limit of TDSCF averages over wave functions are replaced by averages over bundles of trajectories, each obtained by SCF methods. 

Here, Xni l) denotes the harmonic oscillator wave-functions, (pa(r) and (pb(r) correspond to the states of electrons localized on a and b ions, the index v numbers the hybrid cluster states in the molecular field. It should be noted that, within the scope of the adopted approach, the quantum properties of the vibronic states in a self-consistent field are taken into account. Therefore, it is reasonable to call the proposed approximation quasidynamical. The vibronic states obtained within the scope of the quasidynamical approach are hybrid, i.e. retaining the quantum properties of both electronic and vibrational states. In the case of strong vibronic coupling, i.e. in the case of adiabatic potentials possessing deep minima both the... 

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