137 research outputs found
Exchange and correlation energy functionals for two-dimensional open-shell systems
We consider density functionals for exchange and correlation energies in
two-dimensional systems. The functionals are constructed by making use of exact
constraints for the angular averages of the corresponding exchange and
correlation holes, respectively, and assuming proportionality between their
characteristic sizes. The electron current and spin are explicitly taken into
account, so that the resulting functionals are suitable to deal with systems
exhibiting orbital currents and/or spin polarization. Our numerical results
show that in finite systems the proposed functionals outperform the standard
two-dimensional local spin-density approximation, still performing well also in
the important limit of the homogeneous two-dimensional electron gas
Local correlation functional for electrons in two dimensions
We derive a local approximation for the correlation energy in two-dimensional
electronic systems. In the derivation we follow the scheme originally developed
by Colle and Salvetti for three dimensions, and consider a Gaussian
approximation for the pair density. Then, we introduce an ad-hoc modification
which better accounts for both the long-range correlation, and the
kinetic-energy contribution to the correlation energy. The resulting functional
is local, and depends parametrically on the number of electrons in the system.
We apply this functional to the homogeneous electron gas and to a set of
two-dimensional quantum dots covering a wide range of electron densities and
thus various amounts of correlation. In all test cases we find an excellent
agreement between our results and the exact correlation energies. Our
correlation functional has a form that is simple and straightforward to
implement, but broadly outperforms the commonly used local-density
approximation
Construction of the B88 exchange-energy functional in two dimensions
We construct a generalized-gradient approximation for the exchange-energy
density of finite two-dimensional systems. Guided by non-empirical principles,
we include the proper small-gradient limit and the proper tail for the
exchange-hole potential. The observed performance is superior to that of the
two-dimensional local-density approximation, which underlines the usefulness of
the approach in practical applications
Orbital currents in the Colle-Salvetti correlation energy functional and the degeneracy problem
Popular density functionals for the exchange-correlation energy typically
fail to reproduce the degeneracy of different ground states of open-shell
atoms. As a remedy, functionals which explicitly depend on the current density
have been suggested. We present an analysis of this problem by investigating
functionals that explicitly depend on the Kohn-Sham orbitals. Going beyond the
exact-exchange approximation by adding correlation in the form of the
Colle-Salvetti functional we show how current-dependent terms enter the
Colle-Salvetti expression and their relevance is evaluated. A very good
description of the degeneracy of ground-states for atoms of the first and
second row of the periodic table is obtained
Exchange-energy functionals for finite two-dimensional systems
Implicit and explicit density functionals for the exchange energy in finite
two-dimensional systems are developed following the approach of Becke and
Roussel [Phys. Rev. A 39, 3761 (1989)]. Excellent agreement for the
exchange-hole potentials and exchange energies is found when compared with the
exact-exchange reference data for the two-dimensional uniform electron gas and
few-electron quantum dots, respectively. Thereby, this work significantly
improves the availability of approximate density functionals for dealing with
electrons in quasi-two-dimensional structures, which have various applications
in semiconductor nanotechnology.Comment: 5 pages, 3 figure
Universal correction for the Becke-Johnson exchange potential
The Becke-Johnson exchange potential [J. Chem. Phys. 124, 221101 (2006)] has
been successfully used in electronic structure calculations within
density-functional theory. However, in its original form the potential may
dramatically fail in systems with non-Coulombic external potentials, or in the
presence of external magnetic or electric fields. Here, we provide a
system-independent correction to the Becke-Johnson approximation by (i)
enforcing its gauge invariance and (ii) making it exact for any single-electron
system. The resulting approximation is then better designed to deal with
current-carrying states, and recovers the correct asymptotic behavior for
systems with any number of electrons. Tests of the resulting corrected exchange
potential show very good results for a Hydrogen chain in an electric field and
for a four-electron harmonium in a magnetic field
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