Diego R. Alcoba

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.

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.

Relationships between cumulant and spin-density matrices: application to the decomposition of spin.

This paper reports the derivation of a relationship between some elements of the cumulant matrix of the second-order reduced density matrix and the elements of the spin-density matrix. This relationship turns out to be very useful to determine local spins through the partitioning of the spin expectation value of an N-electron system. The procedure enables expression of both one- and two-center contributions only in terms of one-electron matrix elements, the elements of the spin-density matrix. We report numerical determinations of local spins in the Hilbert space of atomic orbitals in selected molecules and radicals in triplet and doublet states.

On the measure of electron correlation and entanglement in quantum chemistry based on the cumulant of the second-order reduced density matrix

In this paper we propose a functional of the many-body cumulant of the second-order reduced density matrix within the spin-free formalism of quantum chemistry which quantifies the idea of electron correlation and allows one to detect spin entanglement. Its properties are rigorously stated and discussed for spin-adapted pure states. Numerical determinations are performed for both equilibrium conformations and dissociation processes in molecular systems.

Variational Optimization of the Second-Order Density Matrix Corresponding to a Seniority-Zero Configuration Interaction Wave Function.

We perform a direct variational determination of the second-order (two-particle) density matrix corresponding to a many-electron system, under a restricted set of the two-index N-representability P-, Q-, and G-conditions. In addition, we impose a set of necessary constraints that the two-particle density matrix must be derivable from a doubly occupied many-electron wave function, i.e., a singlet wave function for which the Slater determinant decomposition only contains determinants in which spatial orbitals are doubly occupied. We rederive the two-index N-representability conditions first found by Weinhold and Wilson and apply them to various benchmark systems (linear hydrogen chains, He, N2, and CN(-)). This work is motivated by the fact that a doubly occupied many-electron wave function captures in many cases the bulk of the static correlation. Compared to the general case, the structure of doubly occupied two-particle density matrices causes the associate semidefinite program to have a very favorable scaling as L(3), where L is the number of spatial orbitals. Since the doubly occupied Hilbert space depends on the choice of the orbitals, variational calculation steps of the two-particle density matrix are interspersed with orbital-optimization steps (based on Jacobi rotations in the space of the spatial orbitals). We also point to the importance of symmetry breaking of the orbitals when performing calculations in a doubly occupied framework.

Topology of the electron density in open-shell systems.

This work describes the decomposition of the electron density field of open-shell molecular systems into physically meaningful contributions. The new features that the open-shell nature of the wave function introduces into these fields are topologically studied and discussed, showing the charge concentration and depletion regions within the system. The localized character (field concentration only close to the nuclear positions of the system) or the nonlocalized character (concentration in other regions of the system) is used to study the reliability of the Lewis model of bonding to describe chemical bonding phenomenon in open-shell systems. Numerical examples are reported for molecular systems at a correlated level of approximation, in the single-double configuration interaction wave function approach.