Extended Lagrangian free energy molecular dynamics

TL;DR

This paper introduces extended free energy Lagrangians for stable, efficient first principles molecular dynamics simulations at finite electronic temperatures, utilizing recursive Fermi operator expansion and improved force calculations.

Contribution

It proposes a novel extended Lagrangian framework enabling stable integration and efficient force computation in finite-temperature first principles molecular dynamics.

Findings

Stable geometric integration schemes conserve free energy.

Recursive Fermi operator expansion avoids eigenvalue calculations.

Efficient Pulay force expression for fractional occupations.

Abstract

Extended free energy Lagrangians are proposed for first principles molecular dynamics simulations at finite electronic temperatures for plane-wave pseudopotential and local orbital density matrix based calculations. Thanks to the extended Lagrangian description the electronic degrees of freedom can be integrated by stable geometric schemes that conserve the free energy. For the local orbital representations both the nuclear and electronic forces have simple and numerically efficient expressions that are well suited for reduced complexity calculations. A rapidly converging recursive Fermi operator expansion method that does not require the calculation of eigenvalues and eigenfunctions for the construction of the fractionally occupied density matrix is discussed. An efficient expression for the Pulay force that is valid also for density matrices with fractional occupation occurring at finite electronic temperatures is also demonstrated.