Born-Oppenheimer Direct Dynamics Classical Trajectory Simulations

Lipeng Sun and William L. Hase, Born-Oppenheimer Direct Dynamics Classical Trajectory Simulations. 

Two approaches have been advanced for performing direct dynamics simulations on a potential energy surface for a single electronic state. The Born-Oppenheimer (BO) direct dynamics approach is considered here. It bears a close resemblance to traditional classical trajectory simulations and electronic structure calculations. At each step of the trajectory integration the potential energy V(q) and gradient dV q)/dqi are obtained by optimizing the electronic wavefunction. 

Two methods, identified as Car-Parinello [113] and Born-Oppenheimer [114], have been advanced for performing direct dynamics simulations. For the former, the motions of the electrons are determined simultaneously as the nuclear classical equations of motion are integrated, to determine the change in the electronic wave function as the nuclei move. For the second method the electronic wave function is optimized during the numerical integration of the classical trajectory. 

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