1,173 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
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
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
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
Exact Kohn-Sham potential of strongly correlated finite systems
The dissociation of molecules, even the most simple hydrogen molecule, cannot
be described accurately within density functional theory because none of the
currently available functionals accounts for strong on-site correlation. This
problem has led to a discussion of properties that the local Kohn-Sham
potential has to satisfy in order to correctly describe strongly correlated
systems. We derive an analytic expression for this potential at the
dissociation limit and show that the numerical calculations for a
one-dimensional two electron model system indeed approach and reach this limit.
It is shown that the functional form of the potential is universal, i.e.
independent of the details of the system.Comment: 17 pages, 3 figures, submitted to JC
Local reduced-density-matrix-functional theory: Incorporating static correlation effects in Kohn-Sham equations
We propose a scheme to bring reduced-density-matrix-functional theory 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.N.N.L. acknowledges financial support from the GSRT, Greece, Polynano-Kripis project (Grant No. 447963); N.H. from an Emmy-Noether grant from Deutsche Forschungsgemeinschaft; and A.R. from the European Community’s FP7 through the CRONOS project, grant agreement no. 280879, the European Research Council Advanced Grant DYNamo (ERC-2010-AdG-267374), and Grupos Consolidados UPV/EHU del Gobierno Vasco (Grant: IT578-13).Peer Reviewe
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
Understanding Genotypes and Phenotypes in Epileptic Encephalopathies
Epileptic encephalopathies are severe often intractable seizure disorders where epileptiform abnormalities contribute to a progressive disturbance in brain function. Often, epileptic encephalopathies start in childhood and are accompanied by developmental delay and various neurological and non-neurological comorbidities. In recent years, this concept has become virtually synonymous with a group of severe childhood epilepsies including West syndrome, Lennox-Gastaut syndrome, Dravet syndrome, and several other severe childhood epilepsies for which genetic factors are increasingly recognized. In the last 5 years, the field has seen a virtual explosion of gene discovery, raising the number of bona fide genes and possible candidate genes for epileptic encephalopathies to more than 70 genes, explaining 20-25% of all cases with severe early-onset epilepsies that had otherwise no identifiable causes. This review will focus on the phenotypic variability as a characteristic aspect of genetic epilepsies. For many genetic epilepsies, the phenotypic presentation can be broad, even in patients with identical genetic alterations. Furthermore, patients with different genetic etiologies can have seemingly similar clinical presentations, such as in Dravet syndrome. While most patients carry mutations in SCN1A, similar phenotypes can be seen in patients with mutations in PCDH19, CHD2, SCN8A, or in rare cases GABRA1 and STXBP1. In addition to the genotypic and phenotypic heterogeneity, both benign phenotypes and severe encephalopathies have been recognized in an increasing number of genetic epilepsies, raising the question whether these conditions represent a fluid continuum or distinct entities
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