Alicia Torre

On the definition of bond orders at correlated level

Most often bond orders have heuristically been defined. In this work we follow a rigorous theoretical procedure looking for an appropriate definition of this concept. The study points out the exchange part of the pair density as a suitable starting point to set up a bond order definition, while the definitions based on the fluctuation of electron populations should be restricted to noncorrelated state functions. Numerical calculations are reported to illustrate these conclusions.

On the density matrix of effectively unpaired electrons

This Letter describes the relationships between the density of effectively unpaired electrons and other tools as the cumulant of the second-order reduced density matrix and the statistical population analysis. A topological population analysis, based on the atoms in molecules (AIM) theory, is incorporated in to the framework of the density of effectively unpaired electrons. Numerical determinations are carried out within this analysis in several systems and the results are compared with those of a more traditional Mulliken approach.

Energy decompositions according to physical space partitioning schemes

This work describes simple decompositions of the energy of molecular systems according to schemes that partition the three-dimensional space. The components of those decompositions depend on one and two atomic domains thus providing a meaningful chemical information about the nature of different bondings among the atoms which compose the system. Our algorithms can be applied at any level of theory (correlated or uncorrelated wave functions). The results reported here, obtained at the Hartree-Fock level in selected molecules, show a good agreement with the chemical picture of molecules and require a low computational cost in comparison with other previously reported decompositions.

Configuration interaction wave functions: A seniority number approach

This work deals with the configuration interaction method when an N-electron Hamiltonian is projected on Slater determinants which are classified according to their seniority number values. We study the spin features of the wave functions and the size of the matrices required to formulate states of any spin symmetry within this treatment. Correlation energies associated with the wave functions arising from the seniority-based configuration interaction procedure are determined for three types of molecular orbital basis: canonical molecular orbitals, natural orbitals, and the orbitals resulting from minimizing the expectation value of the N-electron seniority number operator. The performance of these bases is analyzed by means of numerical results obtained from selected N-electron systems of several spin symmetries. The comparison of the results highlights the efficiency of the molecular orbital basis which minimizes the mean value of the seniority number for a state, yielding energy values closer to those provided by the full configuration interaction procedure.

Seniority number in spin-adapted spaces and compactness of configuration interaction wave functions

This work extends the concept of seniority number, which has been widely used for classifying N-electron Slater determinants, to wave functions of N electrons and spin S, as well as to N-electron spin-adapted Hilbert spaces. We propose a spin-free formulation of the seniority number operator and perform a study on the behavior of the expectation values of this operator under transformations of the molecular basis sets. This study leads to propose a quantitative evaluation for the convergence of the expansions of the wave functions in terms of Slater determinants. The non-invariant character of the seniority number operator expectation value of a wave function with respect to a unitary transformation of the molecular orbital basis set, allows us to search for a change of basis which minimizes that expectation value. The results found in the description of wave functions of selected atoms and molecules show that the expansions expressed in these bases exhibit a more rapid convergence than those formulated in the canonical molecular orbital bases and even in the natural orbital ones.

On the definition of the spin-free cumulant of the second-order reduced density matrix

This note deals with the appropriate definition for the spin-free cumulant of the second-order reduced density matrix. Our approach leads to a direct derivation of one of the proposals reported by Kutzelnigg and Mukherjee [J. Chem. Phys. 116, 4787 (2002)] and it points out its suitability.

Atomic valence in molecular systems

Abstract Atomic valence in molecular systems is described as a partitioning of the hole distribution, the complementary part of the particle distribution. In this scheme, valence splits into three contributions, related to electron spin density, nonuniform occupancy of orbitals (nonpairing terms) and exchange density (pairing terms), respectively, and whose importance depends on the nature of the state of the system. Calculations carried out for correlated CI and Hartree–Fock state functions in both Mulliken and topological AIM type partitionings as well as theoretical results show the suitability of this formulation for describing valence concepts.

A hybrid configuration interaction treatment based on seniority number and excitation schemes

We present a configuration interaction method in which the Hamiltonian of an N-electron system is projected on Slater determinants selected according to the seniority-number criterion along with the traditional excitation-based procedure. This proposed method is especially useful to describe systems which exhibit dynamic (weak) correlation at determined geometric arrangements (where the excitation-based procedure is more suitable) but show static (strong) correlation at other arrangements (where the seniority-number technique is preferred). The hybrid method amends the shortcomings of both individual determinant selection procedures, yielding correct shapes of potential energy curves with results closer to those provided by the full configuration interaction method.

Determination of Local Spins by Means of a Spin-Free Treatment.

This work describes a Mulliken-type partitioning of the expectation value of the spin-squared operator corresponding to an N-electron system. Our algorithms, which are based on a spin-free formulation, predict appropriate spins for the molecular fragments (at equilibrium geometries and at dissociation limits) and can be applied to any spin symmetry. Numerical determinations performed in selected closed- and open-shell systems at correlated level are reported. A comparison between these results and their counterpart ones arising from other alternative approaches is analyzed in detail.

A study of the partitioning of the first-order reduced density matrix according to the theory of atoms in molecules.

This work describes a simple spatial decomposition of the first-order reduced density matrix corresponding to an N-electron system into first-order density matrices, each of them associated to an atomic domain defined in the theory of atoms in molecules. A study of the representability of the density matrices arisen from this decomposition is reported and analyzed. An appropriate treatment of the eigenvectors of the matrices defined over atomic domains or over unions of these domains allows one to describe satisfactorily molecular properties and chemical bondings within a determined molecule and among its fragments. Numerical determinations, performed in selected molecules, confirm the reliability of our proposal.