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An interacting-pair model is considered to attain a new natural orbital functional (NOF). The new approach, which will be termed PNOF6, belongs to the JKL-only family of NOFs known in the literature as PNOFi. Accordingly, the approximated two-particle reduced density matrix (RDM) is reconstructed from the one-particle RDM, considering an explicit form of the two-particle cumulant in terms of the occupation numbers, and enforcing (2,2)-positivity conditions for the N-representability of the 2-RDM. PNOF6 is superior to its predecessor, PNOF5, which is an independent-pair approach. The functional is able to treat both dynamic and static correlations, thereby putting together the advantages of the other members of this series. The theory is applied to the dissociation of selected diatomic molecules. The equilibrium distances, dipole moments, harmonic frequencies, anharmonicity constants, and binding energies of the considered molecules are presented. Comparative potential energy curves for the deformation of benzene are given at the PNOF5 and PNOF6 levels of theory. In benzene, PNOF5 breaks the symmetry by about 1.5°, with an energy lowering of almost 3 kcal/mol, whereas PNOF6 provides the correct D6h symmetry [ABSTRACT FROM AUTHOR]

A previously proposed [M. Piris, X. Lopez, F. Ruipérez, J. M. Matxain, and J. M. Ugalde, J. Chem. Phys. 134, 164102 (2011)] formulation of the two-particle cumulant, based on an orbital-pairing scheme, is extended here for including more than two natural orbitals. This new approximation is used to reconstruct the two-particle reduced density matrix (2-RDM) constrained to the D, Q, and G positivity necessary conditions of the N-representable 2-RDM. In this way, we have derived an extended version of the Piris natural orbital functional 5 (PNOF5e). An antisymmetrized product of strongly orthogonal geminals with the expansion coefficients explicitly expressed by the occupation numbers is also used to generate the PNOF5e. The theory is applied to the homolytic dissociation of selected diatomic molecules: H2, LiH, and Li2. The Bader's theory of atoms in molecules is used to analyze the electron density and the presence of non-nuclear maxima in the case of a set of light atomic clusters: Li2, Li+3, Li2 + 4, and H+3 . The improvement of PNOF5e over PNOF5 was observed by visualizing the electron densities. [ABSTRACT FROM AUTHOR]

An antisymmetrized product of strongly orthogonal geminals with the expansion coefficients explicitly expressed by the occupation numbers is used to generate the Piris natural orbital functional 5 (PNOF5). Second-order corrections to PNOF5 are derived and implemented using the multiconfigurational perturbation theory size consistent at second-order (SC2-MCPT). A modified version of the SC2-MCPT including only doubly excited determinants from different geminals is proposed to describe the dispersion interaction in the helium dimer, and to avoid the breakdown of curves in homolytic dissociations of FH, CO, and N2. Comparisons of calculated properties to experimental data are included to verify the accuracy of the formulation. [ABSTRACT FROM AUTHOR]

An explicit formulation of the Piris cumulant [formula] matrix is described herein, and used to reconstruct the two-particle reduced density matrix (2-RDM). Then, we have derived a natural orbital functional, the Piris Natural Orbital Functional 5, PNOF5, constrained to fulfill the D, Q, and G positivity necessary conditions of the N-representable 2-RDM. This functional yields a remarkable accurate description of systems bearing substantial (near)degeneracy of one-particle states. The theory is applied to the homolitic dissociation of selected diatomic molecules and to the rotation barrier of ethylene, both paradigmatic cases of near-degeneracy effects. It is found that the method describes correctly the dissociation limit yielding an integer number of electrons on the dissociated atoms. PNOF5 predicts a barrier of 65.6 kcal/mol for the ethylene torsion in an outstanding agreement with Complete Active Space Second-order Perturbation Theory (CASPT2). The obtained occupation numbers and pseudo one-particle energies at the ethylene transition state account for fully degenerate π orbitals. The calculated equilibrium distances, dipole moments, and binding energies of the considered molecules are presented. The values obtained are accurate comparing those obtained by the complete active space self-consistent field method and the experimental data. [ABSTRACT FROM AUTHOR]

The positivity conditions for the N-representability of the reduced density matrices are considered to propose a new natural orbital functional. The Piris reconstruction functional, which is based on an explicit form of the two-particle cumulant λ(Δ,Π) is used to reconstruct the two-particle reduced density matrix. A new approach for Π matrix, satisfying rigorously D, Q, and G necessary conditions, leads to Piris Natural Orbital Functional 4 (PNOF4). The theory is applied to the dissociation of selected diatomic molecules. The equilibrium distances, dipole moments, harmonic frequencies, anharmonicity constants, and binding energies of the considered molecules are presented. The values we have obtained are very accurate results comparing with the experimental data. [ABSTRACT FROM AUTHOR]

The spin-conserving density matrix functional theory is used to propose an improved natural orbital functional. The Piris reconstruction functional, PNOF, which is based on an explicit form of the two-particle cumulant λ(Δ,Λ) satisfying necessary positivity conditions for the two-particle reduced density matrix, is used to reconstruct the latter. A new approach Λ(3), as well as an extension of the known Δαβ to spin-uncompensated systems lead to PNOF3. The theory is applied to the calculation of the total energies of the first- and second-row atoms (H–Ne) and a number of selected small molecules. The energy differences between the ground state and the lowest-lying excited state with different spin for these atoms, and the atomization energies of the considered molecules are also presented. The obtained values agree remarkably well with their corresponding both CCSD(T, full) and experimental values. [ABSTRACT FROM AUTHOR]

The natural orbital functional theory is considered for spin uncompensated systems, i.e., systems that have one or more unpaired electrons. The well-known cumulant expansion is used to reconstruct the two-particle reduced density matrix. A new condition to ensure the conservation of the total spin is obtained for the two-particle cumulant matrix. An extension of the Piris natural orbital functional 1 (PNOF1), based on an explicit form for the cumulant, to spin uncompensated systems is also considered. The theory is applied to the calculation of energy differences between the ground state and the lowest lying excited state with different spins for first-row atoms (Li, Be, B, C, N, O, and F) and diatomic oxygen molecule (O2). The values we obtained are very accurate results as compared to the CCSD(T) method and the experimental data. [ABSTRACT FROM AUTHOR]

We have investigated the dissociation behavior of the radical helium dimer He2+ using the Piris natural orbital functional (PNOF). This system is particularly challenging to be described by standard density functionals. The restricted open formulation of the PNOF-2, as well as the PNOF-2 energy plus the extended Koopmans’ vertical ionization potential calculations of the neutral helium dimer, have been tested for calculating the ground-state energies of He2+ as a function of the internuclear distance. For comparison, we present the dissociation curve obtained with the diffusion Monte Carlo method. The dissociation energies, equilibrium bond lengths, and rovibrational levels are reported. The obtained potential energy curves indicate that PNOF-2 yields a correct and accurate dissociation behavior for the helium radical dimer. [ABSTRACT FROM AUTHOR]

We have investigated the radial electron pair probability distributions (REPPDs) of the helium dimer within the Piris natural orbital functional (PNOF) theory. The analytical formulas to evaluate intracule densities, Fermi, Coulomb, and total correlation holes using our reconstruction functional PNOF-2 [J. Chem. Phys. 126, 214103 (2007)] are derived. The Löwdin’s Coulomb holes from PNOF-2 and full configuration interaction calculations are analyzed showing a very similar behavior. New definitions of the Coulomb and Fermi holes based on the cumulant expansion of the two-particle reduced density matrix are presented. The holes are defined in terms of the exact one-particle reduced density matrix and the two-particle cumulant without any reference to the Hartree–Fock state. Through these definitions, we analyze separately the contribution of each component to the total REPPD at several values of the internuclear distance. A straight connection between the Coulomb hole and dispersion interactions is observed. [ABSTRACT FROM AUTHOR]

The authors have investigated the description of the dispersion interaction within the Piris natural orbital functional (PNOF) theory. The PNOF arises from an explicit antisymmetric approach for the two-particle cumulant in terms of two symmetric matrices, Δ and Λ. The functional forms of these matrices are obtained from the generalization of the two-particle system expressions, except for the off-diagonal elements of Δ. The mean value theorem and the partial sum rule obtained for the off-diagonal elements of Δ provide a prescription for deriving practical functionals. In particular, the previous employed approximation {Jpp/2} for the mean values {Jp*} affords several molecular properties but it is incapable to account for dispersion effects. In this work, the authors analyze a new approach for Jp* obtained by factorization of the matrix Δ within the bounds on its off-diagonal elements imposed by the positivity conditions of the two-particle reduced density matrix. Additional terms for the matrix elements of Λ proportional to the square root of the holes are again introduced to describe properly the occupation numbers of the lowest occupied levels. The authors have found that the cross products between weakly occupied orbitals must be removed from the functional form of Λ to obtain a correct long-range asymptotic behavior. The PNOF is used to predict the binding energy as well as the equilibrium distance of the helium dimer. The results are compared with the full configuration-interaction calculations and the corresponding experimental data. [ABSTRACT FROM AUTHOR]

The Piris natural orbital functional (PNOF) based on a new approach for the two-electron cumulant has been used to predict adiabatic ionization potentials, equilibrium bond distances, and harmonic vibrational frequencies of 18 diatomic molecules. Vertical ionization potentials have been calculated for the same set of diatomic molecules and another set of 20 polyatomic molecules using energy-difference methods as well as the extended Koopman theorem. The PNOF properties compare favorably with the coupled-cluster-doubles results. The calculated PNOF values are in good agreement with the corresponding experimental data, considering the basis sets used (6-31G**). [ABSTRACT FROM AUTHOR]

Defines first and second order electron correlation in reduced density matrices. Examination of the Bardeen-Cooper-Schrieffer ground state for molecules with an even number of electrons; Formalism extended to molecules with an odd number of electrons.