Schrodinger equation nonadiabatic methods

The surface-hopping trajectories obtained in the adiabatic representation of the QCLE contain nonadiabatic transitions between potential surfaces including both single adiabatic potential surfaces and the mean of two adiabatic surfaces. This picture is qualitatively different from surface-hopping schemes [2,56] which make the ansatz that classical coordinates follow some trajectory, R(t), while the quantum subsystem wave function, expanded in the adiabatic basis, is evolved according to the time dependent Schrodinger equation. The potential surfaces that the classical trajectories evolve along correspond to one of the adiabatic surfaces used in the expansion of the subsystem wavefunction, while the subsystem evolution is carried out coherently and may develop into linear combinations of these states. In such schemes, the environment does not experience the force associated with the true quantum state of the subsystem and decoherence by the environment is not automatically taken into account. Nonetheless, these methods have provided com-... 

The basic idea of the PSS method is to start from the molecular wave-function and to take the nonadiabaticity as a perturbation. However, in the case of symmetrical resonance the energy splitting of a and corresponding u state gives the transition probability even when the nonadiabatic interaction is negligibly small. The Schrodinger equation describing the whole system composed of two atoms is... 

One of the most powerful methods to study the nonadiabatic transition starts from a time-dependent electronic Schrodinger equation... 

The following part of this section describes our recent advances in applying accurate quantum wave packet methods to compute rate constants and to understand nonadiabatic effects in tri-atomic and tetra-atomic molecular reactions. The quantum nonadiabatic approaches that we present here are based on solving the time-dependent Schrodinger equation formulated within an electronically diabatic representation. 

In this chapter we present the time-dependent quantum wave packet approaches that can be used to compute rate constants for both nonadiabatic and adiabatic chemical reactions. The emphasis is placed on our recently developed time-dependent quantum wave packet methods for dealing with nonadiabatic processes in tri-atomic and tetra-atomic reaction systems. Quantum wave packet studies and rate constants computations of nonadiabatic reaction processes have been dynamically achieved by implementing nuclear wave packet propagation on multiple electronic states, in combination with the coupled diabatic PESs constructed from ab initio calculations. To this end, newly developed propagators are incorporated into the solution of the time-dependent Schrodinger equation in matrix formulism. Applications of the nonadiabatic time-dependent wave packet approaches and the adiabatic ones to the rate constant computations of the nonadiabatic tri-atomic F (P3/2, P1/2) + D2 (v = 0,... 

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