47 research outputs found
Canonical density matrix perturbation theory
Density matrix perturbation theory [Niklasson and Challacombe, Phys. Rev.
Lett. 92, 193001 (2004)] is generalized to canonical (NVT) free energy
ensembles in tight-binding, Hartree-Fock or Kohn-Sham density functional
theory. The canonical density matrix perturbation theory can be used to
calculate temperature dependent response properties from the coupled perturbed
self-consistent field equations as in density functional perturbation theory.
The method is well suited to take advantage of sparse matrix algebra to achieve
linear scaling complexity in the computational cost as a function of system
size for sufficiently large non-metallic materials and metals at high
temperatures.Comment: 21 pages, 3 figure
Shadow Energy Functionals and Potentials in Born-Oppenheimer Molecular Dynamics
In Born-Oppenheimer molecular dynamics (BOMD) simulations based on density
functional theory (DFT), the potential energy and the interatomic forces are
calculated from an electronic ground state density that is determined by an
iterative self-consistent field optimization procedure, which in practice never
is fully converged. The calculated energies and the forces are therefore only
approximate, which may lead to an unphysical energy drift and instabilities.
Here we discuss an alternative shadow BOMD approach that is based on a backward
error analysis. Instead of calculating approximate solutions for an underlying
exact regular BO potential, we do the opposite. Instead, we calculate the exact
electron density, energies, and forces, but for an underlying approximate
shadow BO potential. In this way the calculated forces are conservative with
respect to the shadow potential and generate accurate molecular trajectories
with long-term energy stability. We show how such shadow BO potentials can be
constructed at different levels of accuracy as a function of the integration
time step, dt, from the minimization of a sequence of systematically
improvable, but approximate, shadow energy density functionals. For each
functional there is a corresponding ground state BO potential. These pairs of
shadow energy functionals and potentials are higher-level generalizations of
the original "0th-level" shadow energy functionals and potentials used in
extended Lagrangian BOMD [Eur. Phys. J. B vol. 94, 164 (2021)]. The proposed
shadow energy functionals and potentials are useful only within this dynamical
framework, where also the electronic degrees of freedom are propagated together
with the atomic positions and velocities. The theory is general and can be
applied to MD simulations using approximate DFT, Hartree-Fock or semi-empirical
methods, as well as to coarse-grained flexible charge models.Comment: 16 pages, 3 figure
Time-reversible Born-Oppenheimer molecular dynamics
We present a time-reversible Born-Oppenheimer molecular dynamics scheme,
based on self-consistent Hartree-Fock or density functional theory, where both
the nuclear and the electronic degrees of freedom are propagated in time. We
show how a time-reversible adiabatic propagation of the electronic degrees of
freedom is possible despite the non-linearity and incompleteness of the
self-consistent field procedure. Time-reversal symmetry excludes a systematic
long-term energy drift for a microcanonical ensemble and the number of
self-consistency cycles can be kept low (often only 2-4 cycles per nuclear time
step) thanks to a good initial guess given by the adiabatic propagation of the
electronic degrees of freedom. The time-reversible Born-Oppenheimer molecular
dynamics scheme therefore combines a low computational cost with a physically
correct time-reversible representation of the dynamics, which preserves a
detailed balance between propagation forwards and backwards in time.Comment: 4 pages, 4 figure