Nonadiabatic dynamics by mean-field and surface-hopping approaches: energy conservation considerations

The mean-field and surface-hopping approaches are mixed quantum-classical algorithms designed to efficiently incorporate nonadiabatic effects into molecular dynamics simulations. In this report, analytical relations underpinning the two methods are derived within the adiabatic basis to provide an implementation-level overview, with particular attention given to two avoidable sources of energy conservation deviation. It is not widely known that accuracy improvements can be obtained at negligible computational expense by allowing: (a) construction of the Schrodinger equation to account for analytic electronic phase propagation, and (b) inclusion of a Hellman-Feynman correctional term in the calculation of atomic forces. Particular emphasis on the algebraic formalism contrasts these inherent approximations, vis-a-vis the correctional approaches. The sensitivity of energy conservation with respect to phase propagation is exemplified by simulation of Xe-3(+) molecular photodissociation on the repulsive Pi(1/2)(u) excited surface. Simulations of a representative two-state avoided crossing system are presented to exemplify analytic quantities of the mean-field and surface-hopping approaches as well as to illustrate the inclusion of the Hellman-Feynman correctional term. Nonadiabatic propagation of the molecular wavefunction is observed by monitoring ground and excited state occupational probabilities, energy conservation, and nonadiabatic coupling as the system evolves along the model potential energy surfaces.