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, $M$, the total energy is minimized with respect to the natural orbitals and their occupation numbers. This leads to a function, $E_{\mathrm{tot}}^M$, 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, $S_z=\pm 1$, and the $S_z=0$ 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 $N$-representability conditions. Recently, the topic of pure-state $N$-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 $N$-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