432 research outputs found
Trivial Constraints on Orbital-free Kinetic Energy Density Functionals
Kinetic energy density functionals (KEDFs) are central to orbital-free
density functional theory. Limitations on the spatial derivative dependencies
of KEDFs have been claimed from differential virial theorems. We point out a
central defect in the argument: the relationships are not true for an arbitrary
density but hold only for the minimizing density and corresponding chemical
potential. Contrary to the claims therefore, the relationships are not
constraints and provide no independent information about the spatial derivative
dependencies of approximate KEDFs. A simple argument also shows that validity
for arbitrary -representable densities is not restored by appeal to the
density-potential bijection.Comment: 5 page
Accurate Anisotropic Gaussian Type Orbital Basis Sets for Atoms in Strong Magnetic Fields
In high magnetic field calculations, anisotropic Gaussian type orbital (AGTO)
basis functions are capable of reconciling the competing demands of the
spherically symmetric Coulombic interaction and cylindrical magnetic (
field) confinement. However, the best available {\it a priori} procedure for
composing highly accurate AGTO sets for atoms in a strong field [Phys.\
Rev. A {\bf 90}, 022504 (2014)] yields very large basis sets. Their size is
problematical for use in any calculation with unfavorable computational cost
scaling. Here we provide an alternative constructive procedure. It is based
upon analysis of the underlying physics of atoms in fields that allows
identification of several principles for the construction of AGTO basis sets.
Aided by numerical optimization and parameter fitting, followed by fine tuning
of fitting parameters, we devise formulae for generating accurate AGTO basis
sets in an arbitrary field. For the hydrogen iso-electronic sequence, a set
depends on field strength, nuclear charge, and upon orbital quantum
numbers. For multi-electron systems, the basis set formulae also include
adjustment to account for orbital occupations. Tests of the new basis sets for
atoms H through C (), and ions Li, Be, and B, in a
wide field range ( a.u.), show an accuracy better than a
few H for single-electron systems, and a few hundredths to a few mHs for
multi-electron atoms. The relative errors are similar for different atoms and
ions in a large field range, from a few to a couple of tens of millionths,
thereby confirming rather uniform accuracy across the nuclear charge and
field strength values. Residual basis set errors are two to three orders of
magnitude smaller than the electronic correlation energies in muti-electron
atoms ..
Revised Thomas-Fermi Approximation for Singular Potentials
Approximations to the many-fermion free energy density functional that
include the Thomas-Fermi (TF) form for the non-interacting part lead to
singular densities for singular external potentials (e.g. attractive Coulomb).
This limitation of the TF approximation is addressed here by a formal map of
the exact Euler equation for the density onto an equivalent TF form
characterized by a modified Kohn-Sham potential. It is shown to be a
"regularized" version of the Kohn-Sham potential, tempered by convolution with
a finite-temperature response function. The resulting density is non-singular,
with the equilibrium properties obtained from the total free energy functional
evaluated at this density. This new representation is formally exact.
Approximate expressions for the regularized potential are given to leading
order in a non-locality parameter and the limiting behavior at high and low
temperatures is described. The non-interacting part of the free energy in this
approximation is the usual Thomas-Fermi functional. These results generalize
and extend to finite temperatures the ground-state regularization by Parr and
Ghosh (Proc. Nat. Acad. Sci. 83, 3577 (1986)) and by Pratt, Hoffman, and Harris
(J. Chem. Phys. 92, 1818 (1988)) and formally systematize the
finite-temperature regularization given by the latter authors.Comment: Version 2 clarifies notation issue identified by reviewer. Arguments
and conclusions are unchanged from version
Deorbitalized meta-GGA Exchange-Correlation Functionals in Solids
A procedure for removing explicit orbital dependence from
meta-generalized-gradient approximation (mGGA) exchange-correlation functionals
by converting them into Laplacian-dependent functionals recently was developed
by us and shown to be successful in molecules. It uses an approximate kinetic
energy density functional (KEDF) parametrized to Kohn-Sham results (not
experimental data) on a small training set. Here we present extensive
validation calculations on periodic solids that demonstrate that the same
deorbitalization with the same parametrization also is successful for those
extended systems. Because of the number of stringent constraints used in its
construction and its recent prominence, our focus is on the SCAN meta-GGA.
Coded in \textsc{vasp}, the deorbitalized version, SCAN-L, can be as much as a
factor of three faster than original SCAN, a potentially significant gain for
large-scale ab initio molecular dynamics
Deorbitalization strategies for meta-GGA exchange-correlation functionals
We explore the simplification of widely used meta-generalized-gradient
approximation (mGGA) exchange-correlation functionals to the Laplacian level of
refinement by use of approximate kinetic energy density functionals (KEDFs).
Such deorbitalization is motivated by the prospect of reducing computational
cost while recovering a strictly Kohn-Sham local potential framework (rather
than the usual generalized Kohn-Sham treatment of mGGAs). A KEDF that has been
rather successful in solid simulations proves to be inadequate for
deorbitalization but we produce other forms which, with parametrization to
Kohn-Sham results (not experimental data) on a small training set, yield rather
good results on standard molecular test sets when used to deorbitalize the
meta-GGA made very simple, TPSS, and SCAN functionals. We also study the
difference between high-fidelity and best-performing deorbitalizations and
discuss possible implications for use in ab initio molecular dynamics
simulations of complicated condensed phase systems
Finite Temperature Scaling, Bounds, and Inequalities for the Non-interacting Density Functionals
Finite temperature density functional theory requires representations for the
internal energy, entropy, and free energy as functionals of the local density
field. A central formal difficulty for an orbital-free representation is
construction of the corresponding functionals for non-interacting particles in
an arbitrary external potential. That problem is posed here in the context of
the equilibrium statistical mechanics of an inhomogeneous system. The density
functionals are defined and shown to be equal to the extremal state for a
functional of the reduced one-particle statistical operators. Convexity of the
latter functionals implies a class of general inequalities. First, it is shown
that the familiar von Weizs\"acker lower bound for zero temperature functionals
applies at finite temperature as well. An upper bound is obtained in terms of a
single-particle statistical operator corresponding to the Thomas-Fermi
approximation. Next, the behavior of the density functionals under coordinate
scaling is obtained. The inequalities are exploited to obtain a class of upper
and lower bounds at constant temperature, and a complementary class at constant
density. The utility of such constraints and their relationship to
corresponding results at zero temperature are discussed.Comment: submitted for publication in Phys. Rev.
Analysis of over-magnetization of elemental transition metal solids from the SCAN Density Functional
Recent investigations have found that the strongly constrained and
appropriately normed (SCAN) meta-GGA exchange-correlation functional
significantly over-magnetizes elemental Fe, Co, and Ni solids. For the
paradigmatic case, bcc Fe, the error relative to experiment is .
Comparative analysis of magnetization results from SCAN and its
\textit{deorbitalized} counterpart, SCAN-L, leads to identification of the
source of the discrepancy. It is not from the difference between Kohn-Sham
(SCAN-L) and generalized Kohn-Sham (SCAN) procedures. The key is the
iso-orbital indicator (the ratio of the local Pauli and Thomas-Fermi
kinetic energy densities). Its \textit{deorbitalized} counterpart, ,
has more dispersion in both spin channels with respect to magnetization in an
approximate region between 0.6 Bohr and 1.2 Bohr around an Fe nucleus. The
overall effect is that the SCAN switching function evaluated with
reduces the energetic disadvantage of the down channel with respect to up
compared to the original , which in turn reduces the magnetization.
This identifies the cause of the SCAN magnetization error as insensitivity of
the SCAN switching function to values in the approximate range and oversensitivity for .Comment: 5 pages, 5 figures, revised versio
Density Response from Kinetic Theory and Time Dependent Density Functional Theory for Matter Under Extreme Conditions
The density linear response function for an inhomogeneous system of electrons
in equilibrium with an array of fixed ions is considered. Two routes to its
evaluation for extreme conditions (e.g., warm dense matter) are considered. The
first is from a recently developed short-time kinetic equation; the second is
from time-dependent density functional theory (tdDFT). The result from the
latter approach agrees with that from kinetic theory in the "adiabatic
approximation", providing support and context for each. Both provide a
connection to the phenomenological Kubo-Greenwood method for calculating
transport properties. A brief proof of the van Leeuwen theorem (an essential
underpinning of tdDFT) extended to the mixed states of equilibrium ensembles is
given.Comment: 21 page
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
- …