329 research outputs found
Exchange and correlation as a functional of the local density of states
A functional is presented, in which the exchange
and correlation energy of an electron gas depends on the local density of
occupied states. A simple local parametrization scheme is proposed, entirely
from first principles, based on the decomposition of the exchange-correlation
hole in scattering states of different relative energies. In its practical
Kohn-Sham-like form, the single-electron orbitals become the independent
variables, and an explicit formula for the functional derivative is obtained.Comment: 5 pages. Expanded version. Will appear in Phys. Rev.
Expansion algorithm for the density matrix
A purification algorithm for expanding the single-particle density matrix in
terms of the Hamiltonian operator is proposed. The scheme works with a
predefined occupation and requires less than half the number of matrix-matrix
multiplications compared to existing methods at low (90%)
occupancy. The expansion can be used with a fixed chemical potential in which
case it is an asymmetric generalization of and a substantial improvement over
grand canonical McWeeny purification. It is shown that the computational
complexity, measured as number of matrix multiplications, essentially is
independent of system size even for metallic materials with a vanishing band
gap.Comment: 5 pages, 4 figures, to appear in Phys. Rev.
Density-functional calculation of ionization energies of current-carrying atomic states
Current-density-functional theory is used to calculate ionization energies of
current-carrying atomic states. A perturbative approximation to full
current-density-functional theory is implemented for the first time, and found
to be numerically feasible. Different parametrizations for the
current-dependence of the density functional are critically compared. Orbital
currents in open-shell atoms turn out to produce a small shift in the
ionization energies. We find that modern density functionals have reached an
accuracy at which small current-related terms appearing in open-shell
configurations are not negligible anymore compared to the remaining difference
to experiment.Comment: 7 pages, 2 tables, accepted by Phys. Rev.
Spin Resolution of the Electron-Gas Correlation Energy: Positive same-spin contribution
The negative correlation energy per particle of a uniform electron gas of
density parameter and spin polarization is well known, but its
spin resolution into up-down, up-up, and down-down contributions is not.
Widely-used estimates are incorrect, and hamper the development of reliable
density functionals and pair distribution functions. For the spin resolution,
we present interpolations between high- and low-density limits that agree with
available Quantum Monte Carlo data. In the low-density limit for ,
we find that the same-spin correlation energy is unexpectedly positive, and we
explain why. We also estimate the up and down contributions to the kinetic
energy of correlation.Comment: new version, to appear in PRB Rapid Communicatio
Striped periodic minimizers of a two-dimensional model for martensitic phase transitions
In this paper we consider a simplified two-dimensional scalar model for the
formation of mesoscopic domain patterns in martensitic shape-memory alloys at
the interface between a region occupied by the parent (austenite) phase and a
region occupied by the product (martensite) phase, which can occur in two
variants (twins). The model, first proposed by Kohn and Mueller, is defined by
the following functional: where
is periodic in and almost everywhere.
Conti proved that if then the minimal specific
energy scales like ,
as . In the regime , we improve Conti's results, by computing exactly the
minimal energy and by proving that minimizers are periodic one-dimensional
sawtooth functions.Comment: 29 pages, 3 figure
Comparative study of density functional theories of the exchange-correlation hole and energy in silicon
We present a detailed study of the exchange-correlation hole and
exchange-correlation energy per particle in the Si crystal as calculated by the
Variational Monte Carlo method and predicted by various density functional
models. Nonlocal density averaging methods prove to be successful in correcting
severe errors in the local density approximation (LDA) at low densities where
the density changes dramatically over the correlation length of the LDA hole,
but fail to provide systematic improvements at higher densities where the
effects of density inhomogeneity are more subtle. Exchange and correlation
considered separately show a sensitivity to the nonlocal semiconductor crystal
environment, particularly within the Si bond, which is not predicted by the
nonlocal approaches based on density averaging. The exchange hole is well
described by a bonding orbital picture, while the correlation hole has a
significant component due to the polarization of the nearby bonds, which
partially screens out the anisotropy in the exchange hole.Comment: 16 pages, 5 figures, RevTeX, added conten
Froth-like minimizers of a non local free energy functional with competing interactions
We investigate the ground and low energy states of a one dimensional non
local free energy functional describing at a mean field level a spin system
with both ferromagnetic and antiferromagnetic interactions. In particular, the
antiferromagnetic interaction is assumed to have a range much larger than the
ferromagnetic one. The competition between these two effects is expected to
lead to the spontaneous emergence of a regular alternation of long intervals on
which the spin profile is magnetized either up or down, with an oscillation
scale intermediate between the range of the ferromagnetic and that of the
antiferromagnetic interaction. In this sense, the optimal or quasi-optimal
profiles are "froth-like": if seen on the scale of the antiferromagnetic
potential they look neutral, but if seen at the microscope they actually
consist of big bubbles of two different phases alternating among each other. In
this paper we prove the validity of this picture, we compute the oscillation
scale of the quasi-optimal profiles and we quantify their distance in norm from
a reference periodic profile. The proof consists of two main steps: we first
coarse grain the system on a scale intermediate between the range of the
ferromagnetic potential and the expected optimal oscillation scale; in this way
we reduce the original functional to an effective "sharp interface" one. Next,
we study the latter by reflection positivity methods, which require as a key
ingredient the exact locality of the short range term. Our proof has the
conceptual interest of combining coarse graining with reflection positivity
methods, an idea that is presumably useful in much more general contexts than
the one studied here.Comment: 38 pages, 2 figure
Thermal Density Functional Theory in Context
This chapter introduces thermal density functional theory, starting from the
ground-state theory and assuming a background in quantum mechanics and
statistical mechanics. We review the foundations of density functional theory
(DFT) by illustrating some of its key reformulations. The basics of DFT for
thermal ensembles are explained in this context, as are tools useful for
analysis and development of approximations. We close by discussing some key
ideas relating thermal DFT and the ground state. This review emphasizes thermal
DFT's strengths as a consistent and general framework.Comment: Submitted to Spring Verlag as chapter in "Computational Challenges in
Warm Dense Matter", F. Graziani et al. ed
Use of the Generalized Gradient Approximation in Pseudopotential Calculations of Solids
We present a study of the equilibrium properties of -bonded solids within
the pseudopotential approach, employing recently proposed generalized gradient
approximation (GGA) exchange correlation functionals. We analyze the effects of
the gradient corrections on the behavior of the pseudopotentials and discuss
possible approaches for constructing pseudopotentials self-consistently in the
context of gradient corrected functionals. The calculated equilibrium
properties of solids using the GGA functionals are compared to the ones
obtained through the local density approximation (LDA) and to experimental
data. A significant improvement over the LDA results is achieved with the use
of the GGA functionals for cohesive energies. For the lattice constant, the
same accuracy as in LDA can be obtained when the nonlinear coupling between
core and valence electrons introduced by the exchange correlation functionals
is properly taken into account. However, GGA functionals give bulk moduli that
are too small compared to experiment.Comment: 15 pages, latex, no figure
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