The intrapair electron correlation in natural orbital functional theory.

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, Li3(+), Li4(2+), and H3(+). The improvement of PNOF5e over PNOF5 was observed by visualizing the electron densities.

Computational study on the attack of ·OH radicals on aromatic amino acids.

The attack of hydroxyl radicals on aromatic amino acid side chains, namely phenylalanine, tyrosine, and tryptophan, have been studied by using density functional theory. Two reaction mechanisms were considered: 1) Addition reactions onto the aromatic ring atoms and 2) hydrogen abstraction from all of the possible atoms on the side chains. The thermodynamics and kinetics of the attack of a maximum of two hydroxyl radicals were studied, considering the effect of different protein environments at two different dielectric values (4 and 80). The obtained theoretical results explain how the radical attacks take place and provide new insight into the reasons for the experimentally observed preferential mechanism. These results indicate that, even though the attack of the first (·)OH radical on an aliphatic C atom is energetically favored, the larger delocalization and concomitant stabilization that are obtained by attack on the aromatic side chain prevail. Thus, the obtained theoretical results are in agreement with the experimental evidence that the aromatic side chain is the main target for radical attack and show that the first (·)OH radical is added onto the aromatic ring, whereas a second radical abstracts a hydrogen atom from the same position to obtain the oxidized product. Moreover, the results indicate that the reaction can be favored in the buried region of the protein.

The natural orbital functional theory of the bonding in Cr2, Mo2 and W2.

In this paper, we present for the first time a description based on the natural orbital functional theory (NOFT) of the group VI dimers, namely, Cr(2), Mo(2) and W(2). The PNOF5, Piris Natural Orbital Functional, has been used throughout this work, and the results are compared to multireferential perturbation theory (CASPT2) results. Both methods have been combined with effective core potentials to take into account the scalar relativistic effects. In addition, for Cr(2), an all-electron TZVP quality basis set has also been used to recover the core-valence dynamical correlation. In all cases, PNOF5 shows better behavior than CASPT2, which needs a larger basis set to recover comparable amounts of dynamical correlation. PNOF5 is able to account for the non-dynamical electron correlation, which is responsible for the multireferential nature of these dimers. However, it does not fully recover the dynamical correlation, which is crucial for the accurate description of these challenging potential energy curves. Consequently, PNOF5 predicts longer equilibrium distances and lower dissociation energies than the experimental values. Unlike CASPT2, the PNOF5 results do not significantly improve by using larger basis sets. These new findings represent a major step in the NOFT development, since PNOF5 is the first functional of the natural orbitals reported to yield a chemically balanced and accurate description of these challenging transition metal dimers.

A computational study on the intriguing mechanisms of the gas-phase thermal activation of methane by bare [Ni(H)(OH)]+.

A detailed computational study on the reaction mechanisms of the thermal activation of methane by the bare complex [Ni(H)(OH)](+) has been conducted. The experimentally observed reaction features, i.e. the ligand exchange Ni(H) → Ni(CH(3)), the H/D scrambling between the incoming methane and the hydrido ligand of the nickel complex, the spectator-like behavior of the OH ligand, and the relatively moderate reaction efficiency of 6% relative to the collision rate of the ion/molecule reaction, can be explained by considering three competing mechanisms, and a satisfactory agreement between experiment and theory has been found.

Homolytic molecular dissociation in natural orbital functional theory.

The dissociation of diatomic molecules of the 14-electron isoelectronic series N(2), O(2)(2+), CO, CN(-) and NO(+) is examined using the Piris natural orbital functional. It is found that the method describes correctly the dissociation limit yielding an integer number of electrons on the dissociated atoms, in contrast to the fractional charges obtained when using the variational two-particle reduced density matrix method under the D, Q and G positivity necessary N-representability conditions. The chemistry of the considered systems is discussed in terms of their dipole moments, natural orbital occupations and bond orders as well as atomic Mulliken populations at the dissociation limit. The values obtained agree well with accurate multiconfigurational wave function based CASSCF results and the available experimental data.

A natural orbital functional for multiconfigurational states.

An explicit formulation of the Piris cumulant λΔ,Π 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.

Communication: The role of the positivity N-representability conditions in natural orbital functional theory.

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.

Performance of PNOF3 for reactivity studies: X[BO] and X[CN] isomerization reactions (X = H, Li) as a case study.

Natural Orbital Functional Theory in its PNOF3 implementation is used to investigate the potential energy surfaces of four isomerization reactions: (i) BOH to HBO; (ii) BOLi to LiBO; (iii) CNH to HCN; and (iv) CNLi to LiCN. These reactions are taken as a case study to illustrate the potentiality of PNOF3 to yield the correct topology for reactions sensible to electron correlation. The perfomance of PNOF3 to yield accurate reaction barriers and isomerization energies is also discussed. We have found that PNOF3 shows promising behaviour in the description of these delicate PESs, and yield the correct trends in isomerization energies and reaction barriers, although the latter trends tend to be somewhat lower than the ones calculated at highly correlated levels of theory. The present results show that PNOF3 can give a balanced description of electron correlation in both equilibrium and non-equilibrium structures.

Communications: Accurate description of atoms and molecules by natural orbital functional theory.

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 lambda(Delta,Lambda) satisfying necessary positivity conditions for the two-particle reduced density matrix, is used to reconstruct the latter. A new approach Lambda((3)), as well as an extension of the known Delta(alphabeta) 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.

Spin conserving natural orbital functional theory.

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 (O(2)). The values we obtained are very accurate results as compared to the CCSD(T) method and the experimental data.

Piris natural orbital functional study of the dissociation of the radical helium dimer.

We have investigated the dissociation behavior of the radical helium dimer He(2) (+) 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 He(2) (+) 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.