RARE in the original weekly printed wrappers! Feynman, Richard P.: Forces in Molecules; Lancaster PA: American Physical Society, 1939. 1st edition. Physical Review 56, August 15, 1939 Royal 8vo. Original printed wrappers. Very good condition. The Hellman-Feynman equation. Early Feynman occupies pp 340-343 in this issue of pp 291-385. Scarce in the original green wrappers. Other contributors include Kusch, Shockley, Swann, ALvarez, Van Allen and others. 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 [21] 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.

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