Density-matrix based Extended Lagrangian Born-Oppenheimer Molecular
Dynamics
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by
Anders M. N. Niklasson
2020
Abstract
Extended Lagrangian Born-Oppenheimer molecular dynamics [Phys. Rev. Lett.
vol. 100, 123004 (2008)] is presented for Hartree-Fock theory, where the
extended electronic degrees of freedom are represented by a density matrix that
accounts for fractional occupation numbers at elevated electronic temperatures.
A 4th-order metric tensor, T = K'K, is used in the generalized extended
harmonic oscillator of the Lagrangian that generates the dynamics of the
electronic degrees of freedom. The kernel, K, is given in terms of an inverse
Jacobian of a matrix residual function and appears in the equation of motion
for the extended harmonic oscillator. A tunable low-rank approximation of this
4th-order kernel is used for the integration of the electronic degrees of
freedom. In contrast to regular direct Born-Oppenheimer molecular dynamics
simulations, no iterative self-consistent field optimization is required prior
to the force evaluations. The formulation and algorithms provide a general
guide to implement extended Lagrangian Born-Oppenheimer molecular dynamics for
quantum chemistry, density functional theory, and semiempirical methods using a
density matrix formalism.
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