Ofelia B. Oña

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.

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.

Theoretical study of the adsorption of H on Sin clusters, (n=3–10)

A recently proposed local Fukui function is used to predict the binding site of atomic hydrogen on silicon clusters. To validate the predictions, an extensive search for the more stable SinH (n=3-10) clusters has been done using a modified genetic algorithm. In all cases, the isomer predicted by the Fukui function is found by the search, but it is not always the most stable one. It is discussed that in the cases where the geometrical structure of the bare silicon cluster suffers a considerable change due to the addition of one hydrogen atom, the situation is more complicated and the relaxation effects should be considered.

Fukui and dual-descriptor matrices within the framework of spin-polarized density functional theory

This work deals with the Fukui and dual reactivity descriptors within the framework of the spin-polarized density functional theory. The first and second derivatives of the electron density and the spin density with respect to the total number of electrons N = Nα + Nβ and with respect to the spin number NS = Nα-Nβ have been formulated by means of reduced density matrices in the representation of the spin-orbitals of a given basis set, providing the matrix extension of those descriptors. The analysis of the eigenvalues and eigenvectors of the Fukui and dual-descriptor matrices yields information on the role played by the molecular orbitals in charge-transfer and spin-polarization processes. This matrix formulation enables determining similarity indices which allows one to evaluate quantitatively the quality of the simple frontier molecular orbital model in conceptual density functional theory. Selected closed- and open-shell systems in different spin symmetries have been studied with this matrix formalism at several levels of electronic correlation. The results confirm the suitability of this approach.

Performance of Shannon-entropy compacted N -electron wave functions for configuration interaction methods

The coefficients of full configuration interaction wave functions (FCI) for N-electron systems expanded in N-electron Slater determinants depend on the orthonormal one-particle basis chosen although the total energy remains invariant . Some bases result in more compact wave functions, i.e. result in fewer determinants with significant expansion coefficients. In this work, the Shannon entropy, as a measure of information content, is evaluated for such wave functions to examine whether there is a relationship between the FCI Shannon entropy of a given basis and the performance of that basis in truncated CI approaches. The results obtained for a set of randomly picked bases are compared to those obtained using the traditional canonical molecular orbitals, natural orbitals, seniority minimising orbitals and a basis that derives from direct minimisation of the Shannon entropy. FCI calculations for selected atomic and molecular systems clearly reflect the influence of the chosen basis. However, it is found that there is no direct relationship between the entropy computed for each basis and truncated CI energies.

Chemical bonding analysis in boron clusters by means of localized orbitals according to the electron localization function topology

A series of small planar boron clusters has extensively been studied in the past using different theoretical approximations, and their chemical bonding has been rationalized in terms of aromaticity, antiaromaticity and conflicting aromaticity. Here, we study these systems by means of our recently proposed orbital localization procedure based on the partitioning of the space according to the electron localization function (ELF) topology. The results are compared with those obtained from the adaptive natural density partitioning (AdNDP) method, which is a most extensively tested orbital localization procedure. Minor discrepancies have been found, especially in large clusters. In those cases, an alternative set of localized AdNDP orbitals recovered the representation obtained by ELF localization procedure. These results support the need for multicenter bonding incorporation into the localization models for rationalizing chemical bonding in atomic clusters. Additionally, the aromatic character of the clusters, when it is present, is adequately supported by the more classical treatment based on the ELF topological analysis.

Optimized solution procedure of the G-particle-hole hypervirial equation for multiplets: Application to doublet and triplet states

Highly accurate descriptions of the correlated electronic structure of atoms and molecules in singlet states have recently been directly obtained within the framework of the G-particle-hole hypervirial (GHV) equation method, without any reference to the wave function [Int. J. Quantum Chem. 2009, 109, 3170; ibid. 2011, 111, 245]. Here, the GHV method is optimized and applied to the direct study of doublet and triplet atomic and molecular states. A new set of spin-representability conditions for triplet states has been derived and is also reported here. The results obtained with this optimized version of the GHV method are compared with those yielded by several standard wave function methods. This analysis shows that the GHV energies are more accurate than those obtained with a single-double excitation configuration interaction as well as with a coupled-cluster singles and doubles treatment. Moreover, the resulting 2-body matrices closely satisfy a set of stringent N- and spin-representability conditions.

Theoretical prediction of atomic and electronic structure of neutral Si6Om (m=1–11) clusters

In this paper we found the most stable structures of silicon-oxide clusters of Si(6)O(m) (m = 1-11) by using the genetic algorithm. In this work the genetic algorithm uses a semiempirical energy function, MSINDO, to find the best cluster structures of Si(6)O(m) (m = 1-11). The best structures found were further optimized using the density functional theory. We report the stable geometries, binding energies, lowest unoccupied molecular orbital-highest occupied molecular orbital gap, dissociation energies for the most favorable fragmentation channels and polarizabilities of Si(6)O(m) (m = 1-11). For most of the clusters studied here we report structures not previously found using limited search approaches on common structural motifs.

Orbital Localization Criterion as a Complementary Tool in the Bonding Analysis by Means of Electron Localization Function: Study of the Sin(BH)5-n2- (n = 0–5) Clusters

A recently proposed molecular orbital localization procedure, based on the electron localization function (ELF) technique, has been used to describe chemical bonding in the cluster series Sin(BH)(5-n)(2-) (n = 0-5). The method combines the chemically intuitive information obtained from the traditional ELF analysis with the flexibility and generality of canonical molecular orbital theory. This procedure attempts to localize the molecular orbitals in regions that have the highest probability for finding a pair of electrons, providing a chemical bonding description according to the classical Lewis theory. The results confirm that conservation of the structures upon isoelectronic replacement of a B-H group by a Si atom, allowing evolution from B5H5(2-) to Si5(2-), is in total agreement with the preservation of the chemical bonding pattern.