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Название: Forces in molecules
Автор: Feynman R.P.
The explicit incorporation of the non-local expression for the Pechukas force in a standard molecular dynamics code leads to considerable computational difficulties. For example, Webster et al. have derived a scheme in which quantum forces on the bath particles are calculated using the expression given in Eq. 13); however, the quantum coherence is only retained during typical time intervals comparable to the timestep used to evolve the dynamics of the bath, i.e. a few femtoseconds. After this period, the quantum subsystem is projected onto one instantaneous eigenstate which is chosen according to the result of a stochastic process. A somewhat more simplified procedure has been proposed by Tully. The quantum forces are considered local in time and computed according to the Hellman-Feynman expression. Recently, Coker and Xiao  have shown that Tully's scheme can be derived from the expression of Pechukas using first order perturbation theory. We will now briefly present the simulation algorithm that we have used to generate the time evolution of the electronic degrees of freedom coupled to a bath of classical particles with coordinates using a surface hopping algorithm. In our presentation, we will follow closely previous results of Tully [and Coker and Xiao.