Semiclassical adiabatic ground-state dynamics

Pig. 6.6 (Left) Bunch of branching paths given by the PSANB method (solid cnrves) and those of the semiclassical Ehrenfest dynamics (dotted curves) for initial momentums k = 16.06, 19.3, 22.5, 25.7, 28.9 and 32.1, starting from the initial position R = 2.0 on the ground state potential. (Right) The branching of the quantum wavepackets by the non-adiabatic transition with the initial central momentum of 1 = 32.1. A simple super position of xi (R, t) (denoted as Low) and x2 (R,t) (denoted as High) are drawn. (Reprinted with permission from T. Yonehara et al., J. Chem. Phys. 129, 134109 (2008)). 

Ohrn and co-workers have developed a direct dynamics approach which incorporates both the electrons and nuclei dynamics (END).""" The complete electron-nuclear coupling terms are retained in the calculation and, as a result, the dynamics is not constrained to a single Born-Oppenheimer potential energy surface i.e., electronic non-adiabaticity is explicitly included. A complication in this approach is the computational demand in propagating an electronic wavefunction which is an accurate representation of the ground electronic state as well as multiple excited electronic states. This approach will become more widely used as computation becomes more powerful. In its initial development,""" Deumens et al. used END and treated the dynamics of the nuclei purely classical as in the above classical direct dynamics. More recently, a semiclassical description of the nuclear motion has been implemented by incorporating Heller s""" "" Gaussian wave packet dynamics."" ... 

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