Extended Lagrangian free energy molecular dynamics

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 matrixbased 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.

Extended Lagrangian Born–Oppenheimer molecular dynamics with dissipation

“…In this way the costly overhead of the iterative, self-consistent field (SCF) optimization of the electronic ground state, which is required in regular direct Born-Oppenheimer molecular dynamics simulation, can be avoided or reduced. Various versions and techniques of XL-BOMD have been used and implemented in a number of software packages, including applications for density functional theory, semi-empirical electronic structure theory, polarizable force fields, excited state dynamics, and superfluidity [3,4,7,8,10,14,[20][21][22][23][24][25][26][27][28][29][30][31][32][33][34].…”

“…where I ∈ R N ×N is the identity matrix. The density-matrix calculation in Eq (20). can be performed using a straightforward matrix diagonalization or by using a serial Chebyshev or recursive Fermi-operator expansion scheme[43,[46][47][48][49][50][51].…”

First principles molecular dynamics without self-consistent field optimization

“…where the dots denote time derivatives. The equations of motion can be integrated, for example, with the regular velocity Verlet algorithm using Hellmann-Feynamn and Pulay forces [1,30,39,40]. The extended Lagrangian equation of motion for the extended auxiliary electronic dynamical variable, P , is given by a harmonic oscillator centered around the self-consistent electronic ground state density matrix, D, wherë…”

Canonical density matrix perturbation theory

“…The recursive grand canonical Fermi operator expansion, derivations, convergence analysis, and tests with various basis sets have been published previously in Refs. [45][46][47][48].…”

“…The effective single-particle density matrix, P , at the electronic temperature T e , can be calculated from the Hamiltonian, H, using a recursive Fermi operator expansion [45][46][47][48],…”