Xabier Lopez

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.

Pro-oxidant activity of aluminum: Promoting the Fenton reaction by reducing Fe(III) to Fe(II)

The possibility for an Al-superoxide complex to reduce Fe(III) to Fe(II), promoting oxidative damage through the Fenton reaction, is investigated using highly accurate ab initio methods and density functional theory in conjunction with solvation continuum methods to simulate bulk solvent effects. It is found that the redox reaction between Al-superoxide and Fe(III) to produce Fe(II) is exothermic. Moreover, the loss of an electron from the superoxide radical ion in the Al-superoxide complex leads to a spontaneous dissociation of molecular oxygen from aluminum, recovering therefore an Al(3+) hexahydrated complex. As demonstrated in previous studies, this complex is again prone to stabilize another superoxide molecule, suggesting a catalytic cycle that augments the concentration of Fe(II) in the presence of Al(III). Similar results are found for Al(OH)(2+) and Al(OH)(2)(+) hydrolytic species. Our work reinforces the idea that the presence of aluminum in biological systems could lead to an important pro-oxidant activity through a superoxide formation mechanism.

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.

Dispersion interactions within the Piris natural orbital functional theory: the helium dimer.

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, Delta and Lambda. The functional forms of these matrices are obtained from the generalization of the two-particle system expressions, except for the off-diagonal elements of Delta. The mean value theorem and the partial sum rule obtained for the off-diagonal elements of Delta 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 Delta 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 Lambda 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 Lambda 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.

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.

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.

Pro-oxidant Activity of Aluminum: Stabilization of the Aluminum Superoxide Radical Ion

The pro-oxidant activity of aluminum, a nonredox metal, through superoxide formation is studied by theoretical methods, determining the ESR g-tensor values of O2(•–) with a variety of metals and the reaction energies for Al3+ superoxide affinity in solution. First, the intrinsic ability of aluminum to induce a splitting of the πg levels is compared to that of other significant biological metals, such as Na+, K+, Mg2+, and Ca2+. Additional properties such as bond lengths, ionization potentials, and electron affinities are also determined, and the coherency with the trends observed from ESR g-tensor values is analyzed. As it corresponds to the high charge and its small size, there is a strong interaction between Al3+ and the superoxide. We predict that this strong inherent interaction remains when aluminum is microsolvated. Finally, we analyze the possibility of Al3+ superoxide formation in solution, leading to the conclusion that substitution of the first coordination shell water molecules is plausible, but not of hydroxides. This points to the possibility of Al3+ superoxide formation in solution, which would be pH-dependent. Taking into account the earlier established linear relationship between metal–superoxide interactions and promoting effects in electron-transfer reactions, our work reinforces the idea that the presence of aluminum in biological systems could lead to an important pro-oxidant activity through a superoxide formation mechanism.

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.