97 research outputs found
Density-functional theory for systems with noncollinear spin: orbital-dependent exchange-correlation functionals and their application to the Hubbard dimer
A new class of orbital-dependent exchange-correlation (xc) potentials for
applications in noncollinear spin-density-functional theory is developed.
Starting from the optimized effective potential (OEP) formalism for the exact
exchange potential - generalized to the noncollinear case - correlation effects
are added via a self-consistent procedure inspired by the
Singwi-Tosi-Land-Sjolander (STLS) method. The orbital-dependent xc potentials
are applied to the Hubbard dimer in uniform and noncollinear magnetic fields
and compared to exact diagonalization and to the Bethe-ansatz local
spin-density approximation. The STLS gives the overall best performance for
total energies, densities and magnetizations, particularly in the weakly to
moderately correlated regime.Comment: Manuscript: 13 pages with 10 figures. Supplemental material: 12 page
(Spin-)density-functional theory for open-shell systems: exact magnetization density functional for the half-filled Hubbard trimer
According to the Hohenberg-Kohn theorem of density-functional theory (DFT),
all observable quantities of systems of interacting electrons can be expressed
as functionals of the ground-state density. This includes, in principle, the
spin polarization (magnetization) of open-shell systems; the explicit form of
the magnetization as a functional of the total density is, however, unknown. In
practice, open-shell systems are always treated with spin-DFT, where the basic
variables are the spin densities. Here, the relation between DFT and spin-DFT
for open-shell systems is illustrated and the exact magnetization density
functional is obtained for the half-filled Hubbard trimer. Errors arising from
spin-restricted and -unrestricted exact-exchange Kohn-Sham calculations are
analyzed and partially cured via the exact magnetization functional.Comment: 10 pages, 7 figure
The particle-hole map: a computational tool to visualize electronic excitations
We introduce the particle-hole map (PHM), a visualization tool to analyze
electronic excitations in molecules in the time or frequency domain, to be used
in conjunction with time-dependent density-functional theory (TDDFT) or other
ab initio methods. The purpose of the PHM is to give detailed insight into
electronic excitation processes which is not obtainable from local
visualization methods such as transition densities, density differences, or
natural transition orbitals. The PHM is defined as a nonlocal function of two
spatial variables and provides information about the origins, destinations, and
connections of charge fluctuations during an excitation process; it is
particularly valuable to analyze charge-transfer excitonic processes. In
contrast with the transition density matrix, the PHM has a statistical
interpretation involving joint probabilities of individual states and their
transitions, it satisfies several sum rules and exact conditions, and it is
easier to read and interpret. We discuss and illustrate the properties of the
PHM and give several examples and applications to excitations in
one-dimensional model systems, in a hydrogen chain, and in a benzothiadiazole
based molecule.Comment: 33 pages, 13 figure
Three- to two-dimensional crossover in time-dependent density-functional theory
Quasi-two-dimensional (2D) systems, such as an electron gas confined in a
quantum well, are important model systems for many-body theories. Earlier
studies of the crossover from 3D to 2D in ground-state density-functional
theory showed that local and semilocal exchange-correlation functionals which
are based on the 3D electron gas are appropriate for wide quantum wells, but
eventually break down as the 2D limit is approached. We now consider the
dynamical case and study the performance of various linear-response exchange
kernels in time-dependent density-functional theory. We compare approximate
local, semilocal and orbital-dependent exchange kernels, and analyze their
performance for inter- and intrasubband plasmons as the quantum wells approach
the 2D limit. 3D (semi)local exchange functionals are found to fail for quantum
well widths comparable to the 2D Wigner-Seitz radius, which implies in practice
that 3D local exchange remains valid in the quasi-2D dynamical regime for
typical quantum well parameters, except for very low densities.Comment: 13 pages, 9 figure
Direct calculation of exciton binding energies with time-dependent density-functional theory
Excitons are electron-hole pairs appearing below the band gap in insulators
and semiconductors. They are vital to photovoltaics, but are hard to obtain
with time-dependent density-functional theory (TDDFT), since most standard
exchange-correlation (xc) functionals lack the proper long-range behavior.
Furthermore, optical spectra of bulk solids calculated with TDDFT often lack
the required resolution to distinguish discrete, weakly bound excitons from the
continuum. We adapt the Casida equation formalism for molecular excitations to
periodic solids, which allows us to obtain exciton binding energies directly.
We calculate exciton binding energies for both small- and large-gap
semiconductors and insulators, study the recently proposed bootstrap xc kernel
[S. Sharma et al., Phys. Rev. Lett. 107, 186401 (2011)], and extend the
formalism to triplet excitons
A brief compendium of time-dependent density-functional theory
Time-dependent density-functional theory (TDDFT) is a formally exact approach
to the time-dependent electronic many-body problem which is widely used for
calculating excitation energies. We present a survey of the fundamental
framework, practical aspects, and applications of TDDFT. This paper is mainly
intended for non-experts (students or researchers in other areas) who would
like to learn about the present state of TDDFT without going too deeply into
formal details.Comment: 33 pages, 18 figures; updated version, including additional
reference
Assessment of long-range-corrected exchange-correlation kernels for solids: accurate exciton binding energies via an empirically scaled Bootstrap kernel
In time-dependent density-functional theory, a family of exchange-correlation
kernels, known as long-range-corrected (LRC) kernels, have shown promise in the
calculation of excitonic effects in solids. We perform a systematic assessment
of existing static LRC kernels (empirical LRC, Bootstrap, and
jellium-with-a-gap model) for a range of semiconductors and insulators,
focusing on optical spectra and exciton binding energies. We find that no LRC
kernel is capable of simultaneously producing good optical spectra and
quantitatively accurate exciton binding energies for both semiconductors and
insulators. We propose a simple and universal, empirically scaled Bootstrap
kernel which yields accurate exciton binding energies for all materials under
consideration, with low computational cost
Application of object-oriented programming in a time-dependent density-functional theory calculation of exciton binding energies
This paper discusses the benefits of object-oriented programming to
scientific computing, using our recent calculations of exciton binding energies
with time-dependent density-functional theory (arXiv: 1302.6972) as a case
study. We find that an object-oriented approach greatly facilitates the
development, the debugging, and the future extension of the code by promoting
code reusing. We show that parallelism is added easily in our code in a
object-oriented fashion with ScaLAPACK, Boost::MPI and OpenMP.Comment: 3 figure
Optical properties of CsCuX (X=Cl, Br and I): A comparative study between hybrid time-dependent density-functional theory and the Bethe-Salpeter equation
The cesium copper halides CsCuX (X=Cl, Br and I) are a class of
all-inorganic perovskites with interesting and potentially useful optical
properties, characterized by distinct excitonic features. We present a
computational study of the optical absorption spectra of CsCuX,
comparing time-dependent density-functional theory (TDDFT) and the
Bethe-Salpeter equation (BSE), using quasiparticle band structures as
input. The TDDFT calculations are carried out using several types of global
hybrid exchange-correlation functionals. It is found that an admixture of
nonlocal exchange determined by the dielectric constant produces optical
spectra in excellent agreement with the BSE. Thus, hybrid TDDFT emerges as a
promising first-principles approach for excitonic effects in solids
Direct extraction of excitation energies from ensemble density-functional theory
A very specific ensemble of ground and excited states is shown to yield an
exact formula for any excitation energy as a simple correction to the energy
difference between orbitals of the Kohn-Sham ground state. This alternative
scheme avoids either the need to calculate many unoccupied levels as in
time-dependent density functional theory (TDDFT) or the need for many
self-consistent ensemble calculations. The symmetry-eigenstate Hartree-exchange
(SEHX) approximation yields results comparable to standard TDDFT for atoms.
With this formalism, SEHX yields approximate double-excitations, which are
missed by adiabatic TDDFT.Comment: 6 pages, 2 figure
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