80 research outputs found
Application of self-consistent method to improve the performance of model exchange potentials
Self interaction error remains an impotrant problem in density functional
theory. A number of approximations to exact exchange aimed to correct for this
error while retainining computational efficiency had been suggested recently.
We present a critical comparison between model exchange potentials generated
through the application of the asymptotically-adjusted self-consistent
, AASC, method and BJ effective exchange potential advanced in
[A.D. Becke and E.R. Johnson, J. Chem. Phys. 124, 221101 (2006)] and [V.N.
Staroverov, J. Chem. Phys. 129, 134103 (2008)]. In particular we discuss their
compliance with coordinate-scaling, virial and functional derivative
conditions. We discuss the application of the AASC method to generate
the AA-BJ potential. A numerical comparison is carried out through the
implementation of a fully-numerical diatomic molecule code yielding molecular
virial energies and ionization potentials approximated by the energies of the
HOMO orbitals. It is shown that some of the shortcomings of these model
potentials, such as the non-compliance with the Levy-Perdew virial relation,
may be eliminated by multiplying the response term by an orbital-dependent
functional , which can be simplified to a constant determined during
the self-consistent procedure (self-consistent )
Finite-temperature orbital-free DFT molecular dynamics: coupling Profess and Quantum Espresso
Implementation of orbital-free free-energy functionals in the Profess code
and the coupling of Profess with the Quantum Espresso code are described. The
combination enables orbital-free DFT to drive ab initio molecular dynamics
simulations on the same footing (algorithms, thermostats, convergence
parameters, etc.) as for Kohn-Sham (KS) DFT. All the non-interacting
free-energy functionals implemented are single-point: the local density
approximation (LDA; also known as finite-T Thomas-Fermi, ftTF), the
second-order gradient approximation (SGA or finite-T gradient-corrected TF),
and our recently introduced finite-T generalized gradient approximations
(ftGGA). Elimination of the KS orbital bottleneck via orbital-free methodology
enables high-T simulations on ordinary computers, whereas those simulations
would be costly or even prohibitively time-consuming for KS molecular dynamics
(MD) on very high-performance computer systems. Example MD simulations on H
over a temperature range 2,000 K <= T <=4,000,000 K are reported, with timings
on small clusters (16-128 cores) and even laptops. With respect to KS-driven
calculations, the orbital-free calculations are between a few times through a
few hundreds of times faster
The importance of finite-temperature exchange-correlation for warm dense matter calculations
Effects of explicit temperature dependence in the exchange-correlation (XC)
free-energy functional upon calculated properties of matter in the warm dense
regime are investigated. The comparison is between the KSDT finite-temperature
local density approximation (TLDA) XC functional [Phys.\ Rev.\ Lett.\
\textbf{112}, 076403 (2014)] parametrized from restricted path integral Monte
Carlo data on the homogeneous electron gas (HEG) and the conventional Monte
Carlo parametrization ground-state LDA XC functional (Perdew-Zunger, "PZ")
evaluated with -dependent densities. Both Kohn-Sham (KS) and orbital-free
density functional theory (OFDFT) are used, depending upon computational
resource demands. Compared to the PZ functional, the KSDT functional generally
lowers the direct-current (DC) electrical conductivity of low density Al,
yielding improved agreement with experiment. The greatest lowering is about
15\% for T= 15 kK. Correspondingly, the KS band structure of low-density fcc Al
from KSDT exhibits a clear increase in inter-band separation above the Fermi
level compared to the PZ bands. In some density-temperature regimes, the
Deuterium equations of state obtained from the two XC functionals exhibit
pressure differences as large as 4\% and a 6\% range of differences. However,
the Hydrogen principal Hugoniot is insensitive to explicit XC -dependence
because of cancellation between the energy and pressure-volume work difference
terms in the Rankine-Hugoniot equation. Finally, the temperature at which the
HEG becomes unstable is 7200 K for -dependent XC, a result that the
ground-state XC underestimates by about 1000 K
Comparison of Density Functional Approximations and the Finite-temperature Hartree-Fock Approximation in Warm Dense Lithium
We compare the behavior of the finite-temperature Hartree-Fock model with
that of thermal density functional theory using both ground-state and
temperature-dependent approximate exchange functionals. The test system is bcc
Li in the temperature-density regime of warm dense matter (WDM). In this
exchange-only case, there are significant qualitative differences in results
from the three approaches. Those differences may be important for
Born-Oppenheimer molecular dynamics studies of WDM with ground-state
approximate density functionals and thermal occupancies. Such calculations
require reliable regularized potentials over a demanding range of temperatures
and densities. By comparison of pseudopotential and all-electron results at
K for small Li clusters of local bcc symmetry and bond-lengths
equivalent to high density bulk Li, we determine the density ranges for which
standard projector augmented wave (PAW) and norm-conserving pseudopotentials
are reliable. Then we construct and use all-electron PAW data sets with a small
cutoff radius which are valid for lithium densities up to at least 80 g/cm
A Simple Generalized Gradient Approximation for the Non-interacting Kinetic Energy Density Functional
A simple, novel, non-empirical, constraint-based orbital-free generalized
gradient approximation (GGA) non-interacting kinetic energy density functional
is presented along with illustrative applications. The innovation is adaptation
of constraint-based construction to the essential properties of
pseudo-densities from the pseudo-potentials that are essential in
plane-wave-basis {\it ab initio} molecular dynamics. This contrasts with
constraining to the qualitatively different Kato-cusp-condition densities. The
single parameter in the new functional is calibrated by satisfying Pauli
potential positivity constraints for pseudo-atom densities. In static lattice
tests on simple metals and semiconductors, the new LKT functional outperforms
the previous best constraint-based GGA functional, VT84F (Phys.\ Rev.\ B
\textbf{88}, 161108(R) (2013)), is generally superior to a recently proposed
meta-GGA, is reasonably competitive with parametrized two-point functionals,
and is substantially faster.Comment: 3 figure
Local Spin-density Approximation Exchange-correlation Free-energy Functional
An accurate analytical parametrization for the exchange-correlation free
energy of the homogeneous electron gas, including interpolation for partial
spin-polarization, is derived via thermodynamic analysis of recent restricted
path integral Monte-Carlo (RPIMC) data. This parametrization constitutes the
local spin density approximation (LSDA) for the exchange-correlation functional
in density functional theory. The new finite-temperature LSDA reproduces the
RPIMC data well, satisfies the correct high-density and low- and high-
asymptotic limits, and is well-behaved beyond the range of the RPIMC data,
suggestive of broad utility
Study of Some Simple Approximations to the Non-Interacting Kinetic Energy Functional
Within the framework of density functional theory, we present a study of
approximations to the enhancement factor of the non-interacting kinetic energy
functional . For this purpose, we employ the model of Liu and Parr
[S. Liu and R.G. Parr, Phys. Rev. A {\bf 55}, 1792 (1997)] based on a series
expansion of involving powers of the density. Applications to 34
atoms, at the Hartree-Fock level showed that the enhancement factors present
peaks that are in excellent agreement with those of the exact ones and give an
accurate description of the shell structure of these atoms. The application of
Z-dependent expansions to represent some of the terms of these approximation
for neutral atoms and for positive and negative ions, which allows
to be cast in a very simple form, is also explored. Indications are given as to
how these functionals may be applied to molecules and cluster
Non-empirical Generalized Gradient Approximation Free Energy Functional for Orbital-free Simulations
We report the first wholly non-empirical generalized gradient approximation,
non-interacting free energy functional for orbital-free density functional
theory and use that new functional to provide forces for finite-temperature
molecular dynamics simulations in the warm dense matter (WDM) regime The new
functional provides good-to-excellent agreement with reference Kohn-Sham
calculations under WDM conditions at a minuscule fraction of the computational
cost of corresponding orbital-based simulations
Numerical local "hybrid" functional treatment of selected diatomic molecules: comparison of energies and multipole moments to conventional hybrid functionals
New local "hybrid" functionals proposed by V. V. Karasiev in [J. Chem. Phys.
{\bf 118}, 8567 (2003)] are benchmarked against nonlocal hybrid functionals.
Their performance is tested on the total and high occupied orbital energies, as
well as the electric moments of selected diatomic molecules. The new
functionals, along with the Hartree-Fock and non-hybrid functionals, are
employed for finite-difference calculations, which are basis-independent. Basis
set errors in the total energy and electric moments are calculated for the
6-311G, 6-311G++G(3df,3pd) and AUG-cc-pVnZ (n=3,4,6) basis sets used in
conjunction with the Hartree-Fock and conventional density functional methods.
A comparison between the results of the finite-difference local "hybrid" and
basis set nonlocal hybrid functional shows that total energies of local and
nonlocal hybrid functionals agree to within the basis set error. Discrepancies
for multipole moments are larger in magnitude when compared to the basis set
errors, but still reasonably small (smaller than errors produced by the 6-311G
basis set). Thus, we recommend using the new local "hybrid" functionals
whenever the accuracy is expected to be sufficient, because they require a
solution of just differential Kohn-Sham equations, instead of
integro-differential ones in the case of hybrid functionals
Improved analytical representation of combinations of Fermi-Dirac integrals for finite-temperature density functional calculations
Smooth, highly accurate analytical representations of Fermi-Dirac (FD)
integral combinations important in free-energy density functional calculations
are presented. Specific forms include those that occur in the local density
approximation (LDA), generalized gradient approximation (GGA), and fourth-order
gradient expansion of the non-interacting free energy as well as in the LDA and
second-order gradient expansion for exchange. By construction, all the
representations and their derivatives of any order are continuous on the full
domains of their independent variables. The same type of technique provides an
analytical representation of the function inverse to the FD integral of order
. It plays an important role in physical problems related to the electron
gas at finite temperature. From direct evaluation, the quality of these
improved representations is shown to be substantially superior to existing
ones, many of which were developed before the era of large-scale computation or
early in the era
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