Second-Quantized Surface Hopping

Abstract

The trajectory surface hopping method for quantum dynamics is reformulated in the space of many-particle states to include entanglement and correlation of trajectories. Used to describe many-body correlation effects in electronic structure theories, second quantization is applied to semiclassical trajectories. The new method allows coupling between individual trajectories via energy flow and common phase evolution. It captures the properties of a wave packet, such as branching, Heisenberg uncertainty, and decoherence. Applied to a superexchange process, the method shows very accurate results, comparable to exact quantum data and improving greatly on the standard approach.

Libra: An open-Source “methodology discovery” library for quantum and classical dynamics simulations

“…This slight technical reformulation expresses a fundamental change of the philosophy: considering each trajectory a part of the propagated wavepacket, rather than simply a repetition of a single simulation started with different initial condition and taking different stochastic pathways. I emphasize that the latter view is only a specific case of a more general group of methods that entangle trajectories . Thus, the “ensemble” class is devised as a platform for further development and study of the entangled trajectories methods.…”

Surface Hopping Dynamics with DFT Excited States

“…Moreover, the statistical ensembles are often of too reduced size to comply with the computational capabilities, leading to high statistical uncertainties [14]. (For recent discussions on nonadiabatic dynamics beyond the independent-trajectories approach, see [15][16][17]. )…”

Communication: Global flux surface hopping in Liouville space

“…19 Entanglement in an ensemble of trajectories has been considered with second quantization to account for nuclear tunneling effects. 20 Most relevant for this work, FSSH transition probabilities have been generalized to cover the gross population flow between states, resulting in the global flux SH (GFSH) method. 21 FSSH has been successfully re-formulated in Liouville space, 22 providing an equal treatment of quantum populations and coherences, and generating novel insights into quantum dynamical pathways.…”

“…This is the best SH result so far for the adopted super-exchange model. [20][21][22] The diabatic studies lead to a strong and clear conclusion: GFSH and Liouville space are superior to FSSH and Hilbert space, respectively. Thus, the investigated series of SH methods can be categorized and ranked based on performance ( Fig.…”