Jesus M. Ugalde

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.

On the directionality of halogen bonding

The origin of the high directionality of halogen bonding was investigated quantum chemically by a detailed comparison of typical adducts in two different orientations: linear (most stable) and perpendicular. Energy decomposition analyses revealed that the synergy between charge-transfer interactions and Pauli repulsion are the driving forces for the directionality, while electrostatic contributions are more favourable in the less-stable, perpendicular orientation.

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.

Unexpected trends in halogen-bond based noncovalent adducts.

Unexpected trends in the strengths of halogen-bond based adducts of CY(3)I (Y = F, Cl, Br, I) with two typical Lewis bases (chloride and trimethylamine) show that the halogen-bond donor strength (Lewis acidity) of a compound R-X is not necessarily increased with higher electronegativity of the (carbon-based) group R.

Designing 3-D molecular stars.

We have explored in detail the potential energy surfaces of the Si(5)Li(n)(5-6) (n = 5-7) systems. We found that it is feasible to design three-dimensional star-like silicon structures using the appropriate ligands. The global minimum structure for Si(5)Li(7)(+) has a perfect seven-peak star-like structure. The title compounds comprise, essentially, the Si(5)(6-) ring interacting with lithium cations. The ionic character of the Si-Li interactions induces the formation of a bridged structure. Concomitantly, our calculations show that the reduction of the Pauli repulsion and the maximization of the orbital contribution are also significant for the star-like structure formation. Additionally, the MO analysis of the systems suggests that the role of the lithium atoms is to provide the precise number of electrons to the central Si(5) unit. This is confirmed by the magnetic properties, which show that electron delocalization enhances the stability of the star-like structures proposed here.

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.

Iterative diagonalization for orbital optimization in natural orbital functional theory.

A challenging task in natural orbital functional theory is to find an efficient procedure for doing orbital optimization. Procedures based on diagonalization techniques have confirmed its practical value since the resulting orbitals are automatically orthogonal. In this work, a new procedure is introduced, which yields the natural orbitals by iterative diagonalization of a Hermitian matrix F. The off‐diagonal elements of the latter are determined explicitly from the hermiticity of the matrix of the Lagrange multipliers. An expression for diagonal elements is absent so a generalized Fockian is undefined in the conventional sense, nevertheless, they may be determined from an aufbau principle. Thus, the diagonal elements are obtained iteratively considering as starting values those coming from a single diagonalization of the matrix of the Lagrange multipliers calculated with the Hartree‐Fock orbitals after the occupation numbers have been optimized. The method has been tested on the G2/97 set of molecules for the Piris natural orbital functional. To help the convergence, we have implemented a variable scaling factor which avoids large values of the off‐diagonal elements of F. The elapsed times of the computations required by the proposed procedure are compared with a full sequential quadratic programming optimization, so that the efficiency of the method presented here is demonstrated.

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.

Benchmark Assessment of Density Functional Methods on Group II–VI MX (M = Zn, Cd; X = S, Se, Te) Quantum Dots

In this work, we build a benchmark data set of geometrical parameters, vibrational normal modes, and low-lying excitation energies for MX quantum dots, with M = Cd, Zn, and X = S, Se, Te. The reference database has been constructed by ab initio resolution-of-identity second-order approximate coupled cluster RI-CC2/def2-TZVPP calculations on (MX)6 model molecules in the wurtzite structure. We have tested 26 exchange-correlation density functionals, ranging from local generalized gradient approximation (GGA) and hybrid GGA to meta-GGA, meta-hybrid, and long-range corrected. The best overall functional is the hybrid PBE0 that outperforms all other functionals, especially for excited state energies, which are of particular relevance for the systems studied here. Among the DFT methodologies with no Hartree-Fock exchange, the M06-L is the best one. Local GGA functionals usually provide satisfactory results for geometrical structures and vibrational frequencies but perform rather poorly for excitation energies. Regarding the CdSe cluster, we also present a test of several basis sets that include relativistic effects via effective core potentials (ECPs) or via the ZORA approximation. The best basis sets in terms of computational efficiency and accuracy are the SBKJC and def2-SV(P). The LANL2DZ basis set, commonly employed nowadays on these types of nanoclusters, performs very disappointingly. Finally, we also provide some suggestions on how to perform calculations on larger systems keeping a balance between computational load and accuracy.