Extended Lagrangian formulation of time-reversible Born-Oppenheimer molecular dynamics for higher-order symplectic integration

TL;DR

This paper introduces an extended Lagrangian approach for time-reversible Born-Oppenheimer molecular dynamics, allowing higher-order symplectic integration that enhances accuracy and stability without increasing computational cost.

Contribution

It presents a novel Lagrangian formulation with auxiliary electronic variables enabling advanced integration schemes in molecular dynamics.

Findings

Improves accuracy by over an order of magnitude.

Maintains stability and energy conservation with incomplete self-consistency.

Enables higher-order symplectic integration schemes.

Abstract

A Lagrangian generalization of time-reversible Born-Oppenheimer molecular dynamics [Niklasson et al., Phys. Rev. Lett. vol. 97, 123001 (2006)] is proposed. The Lagrangian includes extended electronic degrees of freedom as auxiliary dynamical variables in addition to the nuclear coordinates and momenta. While the nuclear degrees of freedom propagate on the Born-Oppenheimer potential energy surface, the extended auxiliary electronic degrees of freedom evolve as a harmonic oscillator centered around the adiabatic propagation of the self-consistent ground state. The formulation enables the application of higher-order symplectic or geometric integration schemes that are stable and energy conserving even under incomplete self-consistency convergence. It is demonstrated how the extended Born-Oppenheimer molecular dynamics improves the accuracy by over an order of magnitude compared to previous formulations at the same level of computational cost.