On the exact factorization equations and quantum-classical approximations

A time-dependent molecular wavefunction may be written exactly as a single product of the nuclear and electronic wavefunctions, with a pair of corresponding equations of motion [1]. Although the nuclear equation is a time-dependent Schrödinger equation, the electronic equation is not and has a structure with as yet unknown stability and convergence properties. We present preliminary studies of this, with a view to investigating approximations to the non-adiabatic terms.

This exact factorization provides a starting point for rigorous and practical approximations. One approximate scheme is the coupled trajectory mixed quantum classical approach [2] which captures non-adiabatic effects such as wavepacket splitting and decoherence remarkably well, and recently successfully simulated ring-opening in oxirane [3]. We study the roles of the coupling terms in this algorithm and show that nuclear wavepacket splitting can occur even if the nuclear forces are Ehrenfest-like, provided the quantum momentum term remains in the electronic equation.

[1] A. Abedi, et al, J. Chem. Phys 137, (2012)
[2] F. Agostini, et al, J. Chem. Theory Comput.12 , 2127, (2016)
[3] S. K. Min et al, J. Phys. Chem. Lett 8, 3048, (2017)