814 research outputs found
Hellman-Feynman operator sampling in Diffusion Monte Carlo calculations
Diffusion Monte Carlo (DMC) calculations typically yield highly accurate
results in solid-state and quantum-chemical calculations. However, operators
that do not commute with the Hamiltonian are at best sampled correctly up to
second order in the error of the underlying trial wavefunction, once simple
corrections have been applied. This error is of the same order as that for the
energy in variational calculations. Operators that suffer from these problems
include potential energies and the density. This paper presents a new method,
based on the Hellman-Feynman theorem, for the correct DMC sampling of all
operators diagonal in real space. Our method is easy to implement in any
standard DMC code
Non-empirical hyper-generalized-gradient functionals constructed from the Lieb-Oxford bound
A simple and completely general representation of the exact
exchange-correlation functional of density-functional theory is derived from
the universal Lieb-Oxford bound, which holds for any Coulomb-interacting
system. This representation leads to an alternative point of view on popular
hybrid functionals, providing a rationale for why they work and how they can be
constructed. A similar representation of the exact correlation functional
allows to construct fully non-empirical hyper-generalized-gradient
approximations (HGGAs), radically departing from established paradigms of
functional construction. Numerical tests of these HGGAs for atomic and
molecular correlation energies and molecular atomization energies show that
even simple HGGAs match or outperform state-of-the-art correlation functionals
currently used in solid-state physics and quantum chemistry.Comment: v2: Major revison. Added information on relation to the gradient
expansion and to local hybrids, improved discussion of size consistency and
of performance relative to other functional
Interaction-Induced Spin Polarization in Quantum Dots
The electronic states of lateral many electron quantum dots in high magnetic
fields are analyzed in terms of energy and spin. In a regime with two Landau
levels in the dot, several Coulomb blockade peaks are measured. A zig-zag
pattern is found as it is known from the Fock-Darwin spectrum. However, only
data from Landau level 0 show the typical spin-induced bimodality, whereas
features from Landau level 1 cannot be explained with the Fock-Darwin picture.
Instead, by including the interaction effects within spin-density-functional
theory a good agreement between experiment and theory is obtained. The absence
of bimodality on Landau level 1 is found to be due to strong spin polarization.Comment: 4 pages, 5 figure
Quantum Monte Carlo modelling of the spherically averaged structure factor of a many-electron system
The interaction and exchange-correlation contributions to the ground-state
energy of an arbitrary many-electron system can be obtained from a spherical
average of the wavevector-dependent diagonal structure factor (SF). We model
the continuous-k spherically averaged SF using quantum Monte Carlo calculations
in finite simulation cells. We thus derive a method that allows to
substantially reduce the troublesome Coulomb finite-size errors that are
usually present in ground-state energy calculations. To demonstrate this, we
perform variational Monte Carlo calculations of the interaction energy of the
homogeneous electron gas. The method is, however, equally applicable to
arbitrary inhomogeneous systems.Comment: 4 pages, 5 figure
Dimensional-scaling estimate of the energy of a large system from that of its building blocks: Hubbard model and Fermi liquid
A simple, physically motivated, scaling hypothesis, which becomes exact in
important limits, yields estimates for the ground-state energy of large,
composed, systems in terms of the ground-state energy of its building blocks.
The concept is illustrated for the electron liquid, and the Hubbard model. By
means of this scaling argument the energy of the one-dimensional half-filled
Hubbard model is estimated from that of a 2-site Hubbard dimer, obtaining
quantitative agreement with the exact one-dimensional Bethe-Ansatz solution,
and the energies of the two- and three-dimensional half-filled Hubbard models
are estimated from the one-dimensional energy, recovering exact results for
and and coming close to Quantum Monte Carlo data for
intermediate .Comment: 3 figure
Relativistic model for nuclear matter and atomic nuclei with momentum-dependent self-energies
The Lagrangian density of standard relativistic mean-field (RMF) models with
density-dependent meson-nucleon coupling vertices is modified by introducing
couplings of the meson fields to derivative nucleon densities. As a
consequence, the nucleon self energies, that describe the effective in-medium
interaction, become momentum dependent. In this approach it is possible to
increase the effective (Landau) mass of the nucleons, that is related to the
density of states at the Fermi energy, as compared to conventional relativistic
models. At the same time the relativistic effective (Dirac) mass is kept small
in order to obtain a realistic strength of the spin-orbit interaction.
Additionally, the empirical Schroedinger-equivalent central optical potential
from Dirac phenomenology is reasonably well described. A parametrization of the
model is obtained by a fit to properties of doubly magic atomic nuclei. Results
for symmetric nuclear matter, neutron matter and finite nuclei are discussed.Comment: 14 pages, 7 figures, 5 tables, extended introduction and conclusions,
additional references, minor corrections, accepted for publication in Phys.
Rev.
Extracting convergent surface energies from slab calculations
The formation energy of a solid surface can be extracted from slab
calculations if the bulk energy per atom is known. It has been pointed out
previously that the resulting surface energy will diverge with slab thickness
if the bulk energy is in error, in the context of calculations which used
different methods to study the bulk and slab systems. We show here that this
result is equally relevant for state-of-the-art computational methods which
carefully treat bulk and slab systems in the same way. Here we compare
different approaches, and present a solution to the problem that eliminates the
divergence and leads to rapidly convergent and accurate surface energies.Comment: 3 revtex pages, 1 figure, in print on J. Phys. Cond. Mat
Van der Waals Coefficients of Atoms and Molecules from a Simple Approximation for the Polarizability
A simple and computationally efficient scheme to calculate approximate
imaginary-frequency dependent polarizability, hence asymptotic van der Waals
coefficient, within density functional theory is proposed. The dynamical
dipolar polarizabilities of atoms and molecules are calculated starting from
the Thomas-Fermi-von Weizs\"acker (TFvW) approximation for the
independent-electron kinetic energy functional. The van der Waals coefficients
for a number of closed-shell ions and a few molecules are hence calculated and
compared with available values obtained by fully first-principles calculations.
The success in these test cases shows the potential of the proposed TFvW
approximate response function in capturing the essence of long range
correlations and may give useful information for constructing a functional
which naturally includes van der Waals interactions.Comment: 6 pages, 4 figures. To appear in Phys. Rev.
Momentum distributions in time-dependent density functional theory: Product phase approximation for non-sequential double ionization in strong laser fields
We investigate the possibility to deduce momentum space properties from
time-dependent density functional calculations. Electron and ion momentum
distributions after double ionization of a model Helium atom in a strong
few-cycle laser pulse are studied. We show that, in this case, the choice of
suitable functionals for the observables is considerably more important than
the choice of the correlation potential in the time-dependent Kohn-Sham
equations. By comparison with the solution of the time-dependent Schroedinger
equation, the insufficiency of functionals neglecting electron correlation is
demonstrated. We construct a functional of the Kohn-Sham orbitals, which in
principle yields the exact momentum distributions of the electrons and the ion.
The product-phase approximation is introduced, which reduces the problem of
approximating this functional significantly.Comment: 8 pages, 5 figures, RevTeX
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