Exact Factorization Adventures: A Promising Approach for Non-Bound States

Abstract

Modeling the dynamics of non-bound states in molecules requires an accurate description of how electronic motion affects nuclear motion and vice-versa. The exact factorization (XF) approach offers a unique perspective, in that it provides potentials that act on the nuclear subsystem or electronic subsystem, which contain the effects of the coupling to the other subsystem in an exact way. We briefly review the various applications of the XF idea in different realms, and how features of these potentials aid in the interpretation of two different laser-driven dissociation mechanisms. We present a detailed study of the different ways the coupling terms in recently-developed XF-based mixed quantum-classical approximations are evaluated, where either truly coupled trajectories, or auxiliary trajectories that mimic the coupling are used, and discuss their effect in both a surface-hopping framework as well as the rigorously-derived coupled-trajectory mixed quantum-classical approach.

Factorized Electron–Nuclear Dynamics with an Effective Complex Potential

“…Description of the light particles, such as electrons, as wavepackets evolving on the time-dependent potential energy surface, rather than as a superposition of a few stationary energy states, may be advantageous when numerous stationary electronic states are involved. Thus, there is a renewed interest in the wave function factorization methods, in large part thanks to active research in Exact Factorization with the vector potential reviewed in ref 41.…”

“…Finally, we show that it is possible to keep the average nuclear momentum of the electronic wave function, p Φ ̅ , equal to zero, and in case of a single nuclear DOF, a unique (up to a constant) purely real effective potential of eq , V i = 0 and V d = V r , can be constructed. In this limit, the wave function factorization in our approach becomes unique, which is similar to the exact factorization method, where (in the same limit of a single nuclear DOF) the vector potential is equal to zero and the dynamics is driven by a real scalar potential. ,, …”

“…In this limit, the wave function factorization in our approach becomes unique, which is similar to the exact factorization method, where (in the same limit of a single nuclear DOF) the vector potential is equal to zero and the dynamics is driven by a real scalar potential. 33,34,41 First, for electronic functions Φ = |Φ| exp(ı arg(Φ)), normalized to 1 at all times, the x-averaged nuclear momentum, p (eq 25), can be computed via a simple linear operator,…”

Surface hopping modeling of charge and energy transfer in complex environments

“…Furthermore, trajectory-based exact-factorization methods for dynamics have been proposed, including a few based on surface hopping, [199][200][201] as discussed in Ref. 205 .…”

“…Electronic excitation energy transfer is vital for many biological processes (such as photosynthesis 66,203 ) and technological applications (photovoltaics cells 204,205 and photochemical switches, 206,207 for instance). Electronic energy transfer involves the transfer of the energy absorbed by a chromophore (the donor) to a nearby acceptor, which is then promoted to the excited state.…”