Graph-based Quantum Response Theory and Shadow Born-Oppenheimer Molecular Dynamics

TL;DR

This paper introduces a graph-based quantum response theory integrated with shadow Born-Oppenheimer molecular dynamics, enabling stable, large-scale simulations of complex chemical systems with fractional occupations.

Contribution

It develops a graph-based canonical quantum perturbation theory compatible with extended Lagrangian Born-Oppenheimer molecular dynamics for fractional occupations.

Findings

Enables stable simulations of large chemical systems with tens of thousands of atoms.

Accelerates self-consistent field calculations using graph-based methods.

Demonstrates applicability with SCC-DFTB for complex molecular dynamics.

Abstract

Graph-based linear scaling electronic structure theory for quantum-mechanical molecular dynamics simulations is adapted to the most recent shadow potential formulations of extended Lagrangian Born-Oppenheimer molecular dynamics, including fractional molecular-orbital occupation numbers, which enables stable simulations of sensitive complex chemical systems with unsteady charge solutions. The proposed formulation includes a preconditioned Krylov subspace approximation for the integration of the extended electronic degrees of freedom, which requires quantum response calculations for electronic states with fractional occupation numbers. For the response calculations we introduce a graph-based canonical quantum perturbation theory that can be performed with the same natural parallelism and linear scaling complexity as the graph-based electronic structure calculations for the unperturbed ground state. The proposed techniques are particularly well-suited for semi-empirical electronic structure theory and the methods are demonstrated using self-consistent charge density-functional tight-binding (SCC-DFTB) theory, both for the acceleration of self-consistent field calculations and for quantum molecular dynamics simulations. The graph-based techniques combined with the semi-empirical theory enable stable simulations of large, complex chemical systems, including tens-of-thousands of atoms.