Recently it was shown how 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. This exact factorization provides a starting point for developing rigorous and physical approximations of the exact system. One such approximate scheme is the coupled trajectory mixed quantum classical approach (CT-MQC). This has been shown to capture non-adiabatic effects remarkably well, such as decoherence and the splitting of the nuclear wavepacket, and recently was successfully applied to simulate ring-opening in oxirane. Here we study the role of the different non-adiabatic coupling terms in the CT-MQC algorithm. For example, we show that the term in the electronic equation depending on the quantum momentum is essential for branching and decoherence, and can lead to nuclear wavepacket splitting even when the nuclear forces involve only Ehrenfest terms.<br/><br/>Beyond this, a direct, full solution to the EF questions has important applications, such as the investigation of arbitrary approximation schemes. Additionally, a density-functionalization of the exactly-factorized electronic equation was recently developed. Ideally, any implementation of this would work with the full electronic equation and only approximate the functional. However, although the equation for the nuclear wavefunction is a time-dependent Schrödinger equation, the equation for the electronic wavefunction is not and has a structure with as yet unknown stability and convergence properties. We present preliminary studies of these properties and difficulties in solving the full EF equations.

On the exact factorization equations and quantum-classical approximations

256th National Meeting (2018)

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