106 research outputs found
Performance of one-body reduced density matrix functionals for the homogeneous electron gas
The subject of this study is the exchange-correlation-energy functional of
reduced density matrix functional theory. Approximations of this functional are
tested by applying them to the homogeneous electron gas. We find that two
approximations recently proposed by Gritsenko, Pernal, and Baerends, J. Chem.
Phys., {\bf 122}, 204102 (2005), yield considerably better correlation energies
and momentum distributions than previously known functionals. We introduce
modifications to these functionals which, by construction, reproduce the exact
correlation energy of the homogeneous electron gas
Benchmark calculations for reduced density-matrix functional theory
Reduced density-matrix functional theory (RDMFT) is a promising alternative
approach to the problem of electron correlation. Like standard density
functional theory, it contains an unknown exchange-correlation functional, for
which several approximations have been proposed in the last years. In this
article, we benchmark some of these functionals in an extended set of molecules
with respect to total and atomization energies. Our results show that the most
recent RDMFT functionals give very satisfactory results compared to more
involved quantum chemistry and density functional approaches.Comment: 17 pages, 1 figur
Discontinuity of the chemical potential in reduced-density-matrix-functional theory
We present a novel method for calculating the fundamental gap. To this end,
reduced-density-matrix-functional theory is generalized to fractional particle
number. For each fixed particle number, , the total energy is minimized with
respect to the natural orbitals and their occupation numbers. This leads to a
function, , whose derivative with respect to the particle
number has a discontinuity identical to the gap. In contrast to density
functional theory, the energy minimum is generally not a stationary point of
the total-energy functional. Numerical results, presented for alkali atoms, the
LiH molecule, the periodic one-dimensional LiH chain, and solid Ne, are in
excellent agreement with CI calculations and/or experimental data.Comment: 9 pages, 3 figures, version as publishe
Open shells in reduced-density-matrix-functional theory
Reduced-density-matrix-functional theory is applied to open-shell systems. We
introduce a spin-restricted formulation by appropriately expressing approximate
correlation-energy functionals in terms of spin-dependent occupation numbers
and spin-independent natural orbitals. We demonstrate that the additional
constraint of total-spin conservation is indispensable for the proper treatment
of open-shell systems. The formalism is applied to the first-row open-shell
atoms. The obtained ground-state energies are in very good agreement with the
exact values as well as other state of the art quantum chemistry calculationsComment: 4 pages, 2 figures, corrected typo
Reduced Density Matrix Functional for Many-Electron Systems
Reduced density matrix functional theory for the case of solids is presented
and a new exchange correlation functional based on a fractional power of the
density matrix is introduced. We show that compared to other functionals, this
produces more accurate results for both finite systems. Moreover, it captures
the correct band gap behavior for conventional semiconductors as well as
strongly correlated Mott insulators, where a gap is obtained in absence of any
magnetic ordering.Comment: 4 figs and 1 tabl
Local reduced-density-matrix-functional theory: Incorporating static correlation effects in Kohn-Sham equations
We propose a novel scheme to bring reduced density matrix functional theory
(RDMFT) into the realm of density functional theory (DFT) that preserves the
accurate density functional description at equilibrium, while incorporating
accurately static and left-right correlation effects in molecules and keeping
the good computational performance of DFT-based schemes. The key ingredient is
to relax the requirement that the local potential is the functional derivative
of the energy with respect to the density. Instead, we propose to restrict the
search for the approximate natural orbitals within a domain where these
orbitals are eigenfunctions of a single-particle hamiltonian with a local
effective potential. In this way, fractional natural occupation numbers are
accommodated into Kohn-Sham equations allowing for the description of molecular
dissociation without breaking spin symmetry. Additionally, our scheme provides
a natural way to connect an energy eigenvalue spectrum to the approximate
natural orbitals and this spectrum is found to represent accurately the
ionization potentials of atoms and small molecules
Quasi-particle energy spectra in local reduced density matrix functional theory
Recently, we introduced [N. N. Lathiotakis, N. Helbig, A. Rubio, and N. I. Gidopoulos, Phys. Rev. A90, 032511 (2014)] local reduced density matrix functional theory (local RDMFT), a theoretical scheme capable of incorporating static correlation effects in Kohn-Sham equations. Here, we apply local RDMFT to molecular systems of relatively large size, as a demonstration of its computational efficiency and its accuracy in predicting single-electron properties from the eigenvalue spectrum of the single-particle Hamiltonian with a local effective potential. We present encouraging results on the photoelectron spectrum of molecular systems and the relative stability of C20 isotopes. In addition, we propose a modelling of the fractional occupancies as functions of the orbital energies that further improves the efficiency of the method useful in applications to large systems and solidsN.N.L. acknowledges financial support from the GSRT action KPHΠIΣ, project “New multifunctional Nanostructured Materials and Devices – POLYNANO” No. 447963, N.H. from a DFG Emmy-Noether grant, and A.R. from the European Research Council Advanced Grant No. ERC-2010-AdG-267374, Spanish Grant No. FIS2010-21282-C02-01, Grupo Consolidado UPV/EHU (IT578-13), and European Commission Project No. CRONOS(280879-2).Peer Reviewe
A functional of the one-body-reduced density matrix derived from the homogeneous electron gas: Performance for finite systems
An approximation for the exchange-correlation energy of
reduced-density-matrix-functional theory was recently derived from a study of
the homogeneous electron gas (N.N. Lathiotakis, N. Helbig, E.K.U. Gross, Phys.
Rev. B 75, 195120 (2007)). In the present work, we show how this approximation
can be extended appropriately to finite systems, where the Wigner Seitz radius
r_s, the parameter characterizing the constant density of the electron gas,
needs to be replaced. We apply the functional to a variety of molecules at
their equilibrium geometry, and also discuss its performance at the
dissociation limit. We demonstrate that, although originally derived from the
uniform gas, the approximation performs remarkably well for finite systems.Comment: 5 pages, 2 figuere
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