Jon M. Matxain

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.

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.

Evidence of High •OH Radical Quenching Efficiency by Vitamin B6

Molecules acting as antioxidants capable of scavenging reactive oxygen species (ROS) are of the utmost importance in the living cell. The antioxidative properties of pyridoxine (vitamin B6) have recently been discovered. Previous theoretical calculations have shown a high reactivity of pyridoxine toward hydroxyl radicals, where the latter preferably abstract H from either carbon of the two methanol substituents (C8 or C9). In this study, we have explored the reactivity of pyridoxine toward further hydroxyl radicals, considering as the first step the H abstraction from either C8 or C9, also including addition reactions and cyclization. Many of the reactions display similar DeltaG, and hence, the quenching of hydroxyl radicals by pyridoxine may undergo different pathways leading to a mix of products. In addition, we observe that pyridoxine, under high hydroxyl radical concentrations, may scavenge up to eight radicals, supporting its observed high antioxidant activity.

A DFT/TDDFT study on the optoelectronic properties of the amine-capped magic (CdSe)13 nanocluster

Motivated by the recent experiments by Wang et al. (Angew. Chem., Int. Ed. 2012, 51, 6154-6157), in which the alkylamine-capped magic-size (CdSe)13 has been isolated for the first time, we report on the computational modeling of the putative low-lying isomers of (CdSe)13, both bare and ligand-protected. According to Density Functional Theory (DFT) calculations, the core@cage configuration Se@Cd13Se12, consisting of a Se atom incarcerated in the center of a puckered Cd13Se12 cage, lies lower in energy than fullerene- and wurtzite-like structures. Methylamine-capped nanoclusters present average bond energies per ligand of about 20 kcal mol(-1), while bond energy decomposition schemes show this interaction to be mostly electrostatically-driven. The computed Time-Dependent-DFT (TDDFT) spectrum of the lowest-lying methylamine-protected (CdSe)13 isomer essentially coincides with the experiment, with a notable blueshift of the absorption features induced by the ligands. The LUMO has been found to be the acceptor orbital for all the lowest-lying electronic excitations, in both the bare and methylamine-capped clusters, which could explain the narrow emission profiles inherent in semiconductor nanostructures. In addition, the attachment of pyridine and aniline molecules has been evaluated. Interestingly, the molecular orbitals of these aromatic amines located on the edges of the valence and conduction bands may act as trap states, in agreement with experimental evidences. In the particular case of pyridine molecules, unoccupied orbitals intrude into the HOMO-LUMO gap of the cluster.

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 Baders 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.

Communication: Chemical bonding in carbon dimer isovalent series from the natural orbital functional theory perspective

The natural orbital functional theory admits two unique representations in the orbital space. On the one hand, we have the natural orbitals themselves that minimize the energy functional, and which afford for a diagonal one-particle reduced density matrix but not for a diagonal Lagrangian orbital energy multipliers matrix. On the other hand, since it is possible to reverse the situation but only once the energy minimization has been achieved, we have the so-called canonical representation, where the Lagrangian orbital energy multipliers matrix is diagonal but the one-particle reduced density matrix is not. Here it is shown that the former representation, the natural orbital representation, accounts nicely for the quadrupole bond character of the ground states of C2, BN, CB(-), and CN(+), and for the double bond order character of the isovalent (1)Σg (+) state of Si2. Similarly, the canonical orbital representation accounts correctly for the ionization spectra of all these species.

Quantum chemical assessment of the binding energy of CuO

We present a detailed theoretical investigation on the dissociation energy of CuO(+), carried out by means of coupled cluster theory, the multireference averaged coupled pair functional (MR-ACPF) approach, diffusion quantum Monte Carlo (DMC), and density functional theory (DFT). At the respective extrapolated basis set limits, most post-Hartree-Fock approaches agree within a narrow error margin on a D(e) value of 26.0 kcal mol(-1) [coupled-cluster singles and doubles level augmented by perturbative triples corrections, CCSD(T)], 25.8 kcal mol(-1) (CCSDTQ via the high accuracy extrapolated ab initio thermochemistry protocol), and 25.6 kcal mol(-1) (DMC), which is encouraging in view of the disaccording data published thus far. The configuration-interaction based MR-ACPF expansion, which includes single and double excitations only, gives a slightly lower value of 24.1 kcal mol(-1), indicating that large basis sets and triple excitation patterns are necessary ingredients for a quantitative assessment. Our best estimate for D(0) at the CCSD(T) level is 25.3 kcal mol(-1), which is somewhat lower than the latest experimental value (D(0) = 31.1 ± 2.8 kcal mol(-1)[semicolon] reported by the Armentrout group) [Int. J. Mass Spectrom. 182/183, 99 (1999)]. These highly correlated methods are, however, computationally very demanding, and the results are therefore supplemented with those of more affordable DFT calculations. If used in combination with moderately-sized basis sets, the M05 and M06 hybrid functionals turn out to be promising candidates for studies on much larger systems containing a [CuO](+) core.

Performance of PNOF5 Natural Orbital Functional for Radical Formation Reactions: Hydrogen Atom Abstraction and C-C and O-O Homolytic Bond Cleavage in Selected Molecules.

Radical formation through hydrogen abstraction and C-C and O-O homolytic bond cleavage from selected molecules is investigated by use of natural orbital functional theory in its PNOF5 natural orbital functional implementation, and the results are compared to high-level ab initio complete active space self-consistent field (CASSCF) and complete active space with second-order perturbation theory (CASPT2) methods and experimental data. It is observed that PNOF5 is able to treat the strong electron correlation effects along the homolysis of X-H (X = C, N, O) and X-X (X = C, O) bonds, leading, in general, to the correct trends in the corresponding bond strengths and a good description of the resultant electronic structure for these radicals. In general, PNOF5 bond energies are lower than the experimental ones, because of partial lack of dynamical electron correlation. However, the part of dynamical electron correlation recovered by PNOF5 allows it to give more accurate results than CASSCF methods with a minimum window required to treat near-degeneracy effects. In addition, inspection of the natural orbital occupancies with respect to the CASSCF ones shows an outstanding performance of PNOF5 in treating degenerate and quasidegenerate states, giving a correct description of diradicals and diradicaloids formed upon C-C cleavage in cyclopropane and derivatives.