164 research outputs found
Structure of the first order Reduced Density Matrix in three electron systems: A Generalized Pauli Constraints assisted study
We investigate the structure of the one-body Reduced Density Matrix (1RDM) of
three electron systems, i.e. doublet and quadruplet spin configurations,
corresponding to the smallest interacting system with an open-shell ground
state. To this end, we use Configuration Interaction (CI) expansions of the
exact wave function in Slater determinants built from natural orbitals in a
finite dimensional Hilbert space. With the exception of maximally polarized
systems, the natural orbitals of spin eigenstates are generally spin dependent,
i.e. the spatial parts of the up and down natural orbitals form two different
sets. A measure to quantify this spin dependence is introduced and it is shown
that it varies by several orders of magnitude depending on the system. We also
study the ordering issue of the spin-dependent occupation numbers which has
practical implications in Reduced Density Matrix Functional Theory minimization
schemes when Generalized Pauli Constraints are imposed and in the form of the
CI expansion in terms of the natural orbitals. Finally, we discuss the
aforementioned CI expansion when there are GPCs that are almost "pinned"
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
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
Constraining density functional approximations to yield self-interaction free potentials
Self-interactions (SIs) are a major problem in density functional approximations and the source of serious divergence from experimental results. Here, we propose to optimize density functional total energies in terms of the effective local potential, under constraints for the effective potential that guarantee it is free from SI errors and consequently asymptotically correct. More specifically, we constrain the Hartree, exchange and correlation potential to be the electrostatic potential of a non-negative effective repulsive density of N − 1 electrons. In this way, the optimal effective potentials exhibit the correct asymptotic decay, resulting in significantly improved one-electron properties
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
Conditions for describing triplet states in reduced density matrix functional theory
We consider necessary conditions for the one-body-reduced density matrix
(1RDM) to correspond to a triplet wave-function of a two electron system. The
conditions concern the occupation numbers and are different for the high spin
projections, , and the projection. Hence, they can be used
to test if an approximate 1RDM functional yields the same energies for both
projections. We employ these conditions in reduced density matrix functional
theory calculations for the triplet excitations of two-electron systems. In
addition, we propose that these conditions can be used in the calculation of
triplet states of systems with more than two electrons by restricting the
active space. We assess this procedure in calculations for a few atomic and
molecular systems. We show that the quality of the optimal 1RDMs improves by
applying the conditions in all the cases we studied
Generalized Pauli constraints in reduced density matrix functional theory
Functionals of the one-body reduced density matrix (1-RDM) are routinely
minimized under Coleman's ensemble -representability conditions. Recently,
the topic of pure-state -representability conditions, also known as
generalized Pauli constraints, received increased attention following the
discovery of a systematic way to derive them for any number of electrons and
any finite dimensionality of the Hilbert space. The target of this work is to
assess the potential impact of the enforcement of the pure-state conditions on
the results of reduced density-matrix functional theory calculations. In
particular, we examine whether the standard minimization of typical 1-RDM
functionals under the ensemble -representability conditions violates the
pure-state conditions for prototype 3-electron systems. We also enforce the
pure-state conditions, in addition to the ensemble ones, for the same systems
and functionals and compare the correlation energies and optimal occupation
numbers with those obtained by the enforcement of the ensemble conditions
alone
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
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