Abstract
By utilizing the time-independent semiclassical phase integral, we obtained modified coupled time-dependent Schrödinger equations that restore coherences and induce decoherences within original simple trajectory-based nonadiabatic molecular dynamic algorithms. Nonadiabatic transition probabilities simulated from both Tully’s fewest switches and semiclassical Ehrenfest algorithms follow exact quantum electronic oscillations and amplitudes for three out of the four well-known model systems. Within the present theory, nonadiabatic transitions estimated from statistical ensemble of trajectories accurately follow those of the modified electronic wave functions. The present theory can be immediately applied to the molecular dynamic simulations of photochemical and photophysical processes involving electronic excited states.
Highlights
A mixed quantum-classical dynamics starts from solving electronic adiabatic potential energy surfaces Uj(R) and nonadiabatic coupling vectors dij(R) by applying various ab initio quantum chemistry methods
In order to preserve simplicity of trajectory-based algorithms for large-scale nonadiabatic molecular dynamic simulations, we propose both simple and accurate scheme to restore electronic coherence/decoherence
We show in Supplementary Note 2 that if we shrink E0 = 0.015 in eq (8) by well satisfying (E − U) ≫ U2(R) − U1 (R) = E0, the overall nonadiabatic transition probabilities calculated from both original eq (1) and the present eq (6) all agree with exact quantum results in the high-energy regime
Summary
A mixed quantum-classical dynamics starts from solving electronic adiabatic potential energy surfaces Uj(R) and nonadiabatic coupling vectors dij(R) by applying various ab initio quantum chemistry methods. The results simulated from the original semiclassical eq (1) cannot reproduce exact quantum results, and besides Tully’s fewest switches and semiclassical Ehrenfest methods do not agree each other for oscillations and amplitudes of the overall nonadiabatic transition probabilities.
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