Density-Matrix Propagation Driven by Semiclassical Correlation

TL;DR

This paper explores a semiclassical approximation for electron correlation in density-matrix propagation, improving accuracy over traditional methods but facing challenges with physical constraints like positivity and N-representability.

Contribution

It introduces a semiclassical correlation approach coupled with time-dependent Hartree-Fock that captures dynamic occupation numbers and excitations, advancing density-matrix simulation methods.

Findings

Captures changing occupation numbers and double excitations

Improves over TDHF and adiabatic approximations

Sometimes violates positivity conditions

Abstract

Methods based on propagation of the one-body reduced density-matrix hold much promise for the simulation of correlated many-electron dynamics far from equilibrium, but difficulties with finding good approximations for the interaction term in its equation of motion have so far impeded their application. These difficulties include the violation of fundamental physical principles such as energy conservation, positivity conditions on the density, or unchanging natural orbital occupation numbers. We review some of the recent efforts to confront these problems, and explore a semiclassical approximation for electron correlation coupled to time-dependent Hartree-Fock propagation. We find that this approach captures changing occupation numbers, and excitations to doubly-excited states, improving over TDHF and adiabatic approximations in density-matrix propagation. However, it does not guarantee $N$-representability of the density-matrix, consequently resulting sometimes in violation of positivity conditions, even though a purely semiclassical treatment preserves these conditions.