“…1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19 Recent advances on these topics have enabled quantitative accurate simulations for medium-size molecules and qualitatively accurate simulations for nano-sized molecules or clusters. 20,21,22,23,24,25,26,27,28,29,30,31 The electronic structure must be treated quantum mechanically, and for simulating all but the smallest systems, one uses a semiclassical treatment of nuclear motion. The present article is concerned with direct dynamics, where, instead of requiring parametrized analytic functions for the energies and couplings, all required energies, forces, and couplings for each geometry that is important for evaluating dynamical properties are obtained directly from electronic structure calculations when they are needed in the dynamics calculation.…”