177 research outputs found
Perspective on density functional theory
Density functional theory (DFT) is an incredible success story. The low
computational cost, combined with useful (but not yet chemical) accuracy, has
made DFT a standard technique in most branches of chemistry and materials
science. Electronic structure problems in a dazzling variety of fields are
currently being tackled. However, DFT has many limitations in its present form:
Too many approximations, failures for strongly correlated systems, too slow for
liquids, etc. This perspective reviews some recent progress and ongoing
challenges.Comment: submitted to J. Chem. Phy
Density functional description of Coulomb blockade: Adiabatic or dynamic exchange-correlation?
Above the Kondo temperature, the Kohn-Sham zero-bias conductance of an
Anderson junction has been shown to completely miss the Coulomb blockade.
Within a standard model for the spectral function, we deduce a parameterization
for both the onsite exchange-correlation potential and the bias drop as a
function of the site occupation that applies for all correlation strengths. We
use our results to sow doubt on the common interpretation of such corrections
as arising from dynamical exchange-correlation contributions.Comment: 9 pages, 8 figures, submitted to Phys. Rev.
Uniform semiclassical approximations for one-dimensional fermionic systems
A thorough account is given of the derivation of uniform semiclassical
approximations to the particle and kinetic energy densities of N noninteracting
bounded fermions in one dimension. The employed methodology allows the
inclusion of non-perturbative effects via an infinite resummation of the
Poisson summation formula.Comment: 21 pages, 3 figure
The Role of Exact Conditions in TDDFT
This chapter is devoted to exact conditions in time-dependent density
functional theory. Many conditions have been derived for the exact ground-state
density functional, and several have played crucial roles in the construction
of popular approximations. We believe that the reliability of the most
fundamental approximation of any density functional theory, the local density
approximation (LDA), is due to the exact conditions that it satisfies. Improved
approximations should satisfy at least those conditions that LDA satisfies,
plus others. (Which others is part of the art of functional approximation). In
the time-dependent case, as we shall see, the adiabatic LDA (ALDA) plays the
same role as LDA in the ground-state case, as it satisfies many exact
conditions. But we do not have a generally applicable improvement beyond ALDA
that includes nonlocality in time. For TDDFT, we have a surfeit of exact
conditions, but that only makes finding those that are useful to impose an even
more demanding task.Comment: 13 pages, 3 figure
Quantum critical benchmark for density functional theory
Two electrons at the threshold of ionization represent a severe test case for
electronic structure theory. A pseudospectral method yields a very accurate
density of the two-electron ion with nuclear charge close to the critical
value. Highly accurate energy components and potentials of Kohn-Sham density
functional theory are given, as well as a useful parametrization of the
critical density. The challenges for density functional approximations and the
strength of correlation are also discussed.Comment: 7 pages, 4 figure
Connection formulas for thermal density functional theory
The adiabatic connection formula of ground-state density functional theory
relates the correlation energy to a coupling-constant integral over a purely
potential contribution, and is widely used to understand and improve
approximations. The corresponding formula for thermal density functional theory
is cast as an integral over temperatures instead, ranging upward from the
system's physical temperature. We also show how to relate different different
correlation components to each other, either in terms of temperature- or
coupling-constant integrations. We illustrate our results on the uniform
electron gas
A new challenge for time-dependent density-functional theory
Time-dependent density functional theory is thought to work well for the test
cases of He and Be atoms. We perform a quantum defect analysis of the s, p, and
d Rydberg states of Be with accurate ground state Kohn-Sham potentials. The s-
and p-quantum defects are well described by the ALDA, but fails badly for the
d-quantum defect. The same failure is observed in case of He. This provides a
new challenge for functional development in time-dependent density functional
theory.Comment: 1 table, 5 figures submitted to Chemical Physics Letter
Deriving approximate functionals with asymptotics
Modern density functional approximations achieve moderate accuracy at low
computational cost for many electronic structure calculations. Some background
is given relating the gradient expansion of density functional theory to the
WKB expansion in one dimension, and modern approaches to asymptotic expansions.
A mathematical framework for analyzing asymptotic behavior for the sums of
energies unites both corrections to the gradient expansion of DFT and
hyperasymptotics of sums. Simple examples are given for the model problem of
orbital-free DFT in one dimension. In some cases, errors can be made as small
as 10 Hartree suggesting that, if these new ingredients can be applied,
they might produce approximate functionals that are much more accurate than
those in current use. A variation of the Euler-Maclaurin formula generalizes
previous results.Comment: Submitted to Faraday Discussions for the Developments in DFT
conference, Sept 2, 202
Excited states from time-dependent density functional theory
Time-dependent density functional theory (TDDFT) is presently enjoying
enormous popularity in quantum chemistry, as a useful tool for extracting
electronic excited state energies. This article explains what TDDFT is, and how
it differs from ground-state DFT. We show the basic formalism, and illustrate
with simple examples. We discuss its implementation and possible sources of
error. We discuss many of the major successes and challenges of the theory,
including weak fields, strong fields, continuum states, double excitations,
charge transfer, high harmonic generation, multiphoton ionization, electronic
quantum control, van der Waals interactions, transport through single
molecules, currents, quantum defects, and, elastic electron-atom scattering.Comment: 38 pages, 17 figures and 11 tables. Submitted to Reviews of
Computational Chemistry. Caution: Large Fil
Quantifying Density Errors in DFT
We argue that any general mathematical measure of density error, no matter
how reasonable, is too arbitrary to be of universal use. However the energy
functional itself provides a universal relevant measure of density errors. For
the self-consistent density of any Kohn-Sham calculation with an approximate
functional, the theory of density-corrected density functional theory (DC-DFT)
provides an accurate, practical estimate of this ideal measure. We show how to
estimate the significance of the density-driven error even when exact densities
are unavailable. In cases with large density errors, the amount of
exchange-mixing is often adjusted, but we show this is unnecessary. Many
chemically relevant examples are given
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