Propagation Methods for Quantum Molecular Dynamics

R Kosloff
1994 Annual review of physical chemistry (Print)  
INTROIDUCTION Our current understanding of molecular dynamics uses quantum mechanics as the basic underlying theory to elucidate thc processes involved. Establishing numerical schemes to solve the quantum equations of motion is crucial for understanding realistic molecular encounters. The introduction of pseudo-spectral methods has been an important step in this direction. These methods allow an extremely accurate representation of the action of an operator, usually the Hamiltonian, on a
more » ... ction: q~ = fI~p. A solution for the quantum molecular dynamics can be obtained by recursively applying the elementary mapping step. This recursive application of the elementary step, termed the propagator, is the subject of this review. The na~:ural application of a propagator is in a time-dependent description of quantum molecular dynamics, where the propagator U(z) maps the waw~function at time t, ~p(t) to the wavefunction at time t + ~: 0(t+ ~) = ~(z)0(t). The decomposition into a recursive application of the elementary step is performed by a polynomial expansion of the propagator.
doi:10.1146/annurev.physchem.45.1.145 fatcat:itb7otvv4vhbjpmzd2a5746qny