Correlated Electron-Nuclear Dynamics with Conditional Wave Functions

TL;DR

This paper introduces an exact, trajectory-based approach to simulate correlated electron-nuclear dynamics without relying on traditional potential-energy surfaces, enabling more efficient non-adiabatic quantum calculations.

Contribution

It develops a novel formalism linking exact wave function factorization with trajectory-dependent equations of motion for electrons and nuclei.

Findings

Circumvents calculation of potential-energy surfaces

Provides a new framework for non-adiabatic dynamics

Offers insights through simplified propagation schemes

Abstract

The molecular Schr\"odinger equation is rewritten in terms of non-unitary equations of motion for the nuclei (or electrons) that depend parametrically on the configuration of an ensemble of generally defined electronic (or nuclear) trajectories. This scheme is exact and does not rely on the tracing-out of degrees of freedom. Hence, the use of trajectory-based statistical techniques can be exploited to circumvent the calculation of the computationally demanding Born-Oppenheimer potential-energy surfaces and non-adiabatic coupling elements. The concept of potential-energy surface is restored by establishing a formal connection with the exact factorization of the full wave function. This connection is used to gain insight from a simplified form of the exact propagation scheme.