Schrodinger equation, nonadiabatic quantum dynamics

Quantum mechanical effects—tunneling and interference, resonances, and electronic nonadiabaticity— play important roles in many chemical reactions. Rigorous quantum dynamics studies, that is, numerically accurate solutions of either the time-independent or time-dependent Schrodinger equations, provide the most correct and detailed description of a chemical reaction. While hmited to relatively small numbers of atoms by the standards of ordinary chemistry, numerically accurate quantum dynamics provides not only detailed insight into the nature of specific reactions, but benchmark results on which to base more approximate approaches, such as transition state theory and quasiclassical trajectories, which can be applied to larger systems. 

Presumably the most straightforward approach to chemical dynamics in intense laser fields is to use the time-independent or time-dependent adiabatic states [352], which are the eigenstates of field-free or field-dependent Hamiltonian at given time points respectively, and solve the Schrodinger equation in a stepwise manner. However, when the laser field is approximately periodic, one can also use a set of field-dressed periodic states as an expansion basis. The set of quasi-static states in a periodic Hamiltonian is derived by a Floquet type analysis and is often referred to as the Floquet states [370]. Provided that the laser field is approximately periodic, advantages of using the latter basis set include (1) analysis and interpretation of the electron dynamics is clearer since the Floquet state population often vary slowly with the timescale of the pulse envelope and each Floquet state is characterized as a field-dressed quasi-stationary state, (2) under some moderate conditions, the nuclear dynamics can be approximated by mixed quantum-classical (MQC) nonadiabatic dynamics on the field-dressed PES. The latter point not only provides a powerful clue for interpretation of nuclear dynamics but also implies possible MQC formulation of intense field molecular dynamics. 

The following theoretical part of the chapter (see section 8.2) presents our developed quantum theories, which are capable of computing reaction rate constants for electronically nonadiabatic reaction dynamics. These recently developed time-dependent quantum wave packet theories mainly focused on solving the Schrodinger equation for nuclei motion, leaving the more... 

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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