Towards a variational formulation of mixed quantum-classical molecular dynamics

Abstract

A variational formulation of mixed quantum-classical dynamics is proposed, based upon a wave function form of Gaussianbased multiconfiguration time-dependent Hartree (G-MCTDH) type. Using semiclassically scaled Gaussian wave packets that lead to a classical evolution in an appropriate limit, a multiconfigurational Ehrenfest dynamics is obtained. Due to the variational framework, the resulting quantum-classical dynamics is consistent and accounts for correlations between the quantum and classical subspaces.

Multi-configurational Ehrenfest simulations of ultrafast nonadiabatic dynamics in a charge-transfer complex

“…In Ref. 29, the G-MCTDH method, 30,42,43 i.e., a Gaussianbased variant of MCTDH, 27,28 is taken as a starting point to construct the quantum-classical limit of a GWP based multiconfigurational expansion. In the following, we briefly review the formulation of Ref.…”

“…26 Furthermore, we have shown in Ref. 29 that MCE can be understood as the quantum-classical limit of the Gaussian-based Multi-Configuration Time-Dependent Hartree (G-MCTDH) method. 30 The latter MCE variant represents a rigorous quantum-classical limit, whereas MCEv1 and MCEv2 refer to finite-width wavepackets and therefore represent quantum-semiclassical rather than quantum-classical approaches.…”

“…First, we aim to connect the development of Ref. 29 with the MCEv1 and MCEv2 methods of Refs. 25 and 26.…”

“…In practice, the rigorous quantum-classical limit representation of Ref. 29 is replaced by a Gaussian wavepacket (GWP) based representation, which at least, in principle, permits a full description of phase interference between Ehrenfest configurations. We will show that this leads to a formulation which is close to the MCEv2 approach.…”

“…Section II reviews the MCE approach from the viewpoint of our earlier development of Ref. 29 and shows how the latter formulation is augmented so as to correspond to finite-width GWPs. Section III describes the Hamiltonian of the charge transfer donor-acceptor complex which is employed as a case study in the present work, and Sec.…”