Gustavo E. Massaccesi

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.

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.

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.

Polynomial scaling approximations and dynamic correlation corrections to doubly occupied configuration interaction wave functions

A class of polynomial scaling methods that approximate Doubly Occupied Configuration Interaction (DOCI) wave functions and improve the description of dynamic correlation is introduced. The accuracy of the resulting wave functions is analysed by comparing energies and studying the overlap between the newly developed methods and full configuration interaction wave functions, showing that a low energy does not necessarily entail a good approximation of the exact wave function. Due to the dependence of DOCI wave functions on the single-particle basis chosen, several orbital optimisation algorithms are introduced. An energy-based algorithm using the simulated annealing method is used as a benchmark. As a computationally more affordable alternative, a seniority number minimising algorithm is developed and compared to the energy based one revealing that the seniority minimising orbital set performs well. Given a well-chosen orbital basis, it is shown that the newly developed DOCI based wave functions are especially suitable for the computationally efficient description of static correlation and to lesser extent dynamic correlation.

A study of the compactness of wave functions based on Shannon entropy indices: a seniority number approach

Abstract This work reports the formulation of Shannon entropy indices in terms of seniority numbers of the Slater determinants expanding an N-electron wave function. Numerical determinations of those indices prove that they provide a suitable quantitative procedure to evaluate compactness of wave functions and to describe their configurational structures. An analysis of the results, calculated for full configuration interaction wave functions in selected atomic and molecular systems, allows one to compare and to discuss the behavior of several types of molecular orbital basis sets in order to achieve more compact wave function expansions, and to study their multiconfigurational character.

Spin contamination-free N-electron wave functions in the excitation-based configuration interaction treatment

This work deals with the spin contamination in N-electron wave functions provided by the excitation-based configuration interaction methods. We propose a procedure to ensure a suitable selection of excited N-electron Slater determinants with respect to a given reference determinant, required in these schemes. The procedure guarantees the construction of N-electron wave functions which are eigenfunctions of the spin-squared operator Sˆ(2), avoiding any spin contamination. Our treatment is based on the evaluation of the excitation level of the determinants by means of the expectation value of an excitation operator formulated in terms of spin-free replacement operators. We report numerical determinations of energies and 〈Sˆ(2)〉 expectation values, arising from our proposal as well as from traditional configuration interaction methods, in selected open-shell systems, in order to compare the behavior of these procedures and their computational costs.

Molecular magnetism in closo-azadodecaborane supericosahedrons

ABSTRACT The connection of 12 s = ½ closo-azadodecaborane radical units (NB11H11•), where a hydrogen atom is removed from the nitrogen atom, produces a supericosahedron [(NB11H6•)12](S), S being the total spin of the system. This work describes the study of the low-lying energy spin-projected states of this supericosahedron with two different geometrical arrangements, each nitrogen atom pointing (1) inwards or (2) outwards with respect to radial axes. These spin-projected states are mapped into a Heisenberg spin Hamiltonian, thus allowing the determination of coupling constants between magnetic sites. The eigenvalues of this model Hamiltonian then predict the ground spin state and the corresponding combinations of spin orientations of the magnetic centres. We show that the energy minimum in the [(Nin/outB11H6•)12](S) systems corresponds to a high-spin S = 6 state. Geometrical arrangement of the supericosahedrons.

Magnetic Properties of Mononuclear Co(II) Complexes with Carborane Ligands

We analyze the magnetic properties of three mononuclear Co(II) coordination complexes using quantum chemical complete active space self-consistent field and N-electron valence perturbation theory approaches. The complexes are characterized by a distorted tetrahedral geometry in which the central ion is doubly chelated by the icosahedral ligands derived from 1,2-(HS)2-1,2-C2B10H10 (complex I), from 1,2-(HS)2-1,2-C2B10H10 and 9,12-(HS)2-1,2-C2B10H10 (complex II), and from 9,12-(HS)2-1,2-C2B10H10 (complex III), which are two positional isomers of dithiolated 1,2-dicarba- closo-dodecaborane (complex I). Complex I was realized experimentally recently (Tu, D.; Shao, D.; Yan, H.; Lu, C. Chem. Commun. 2016, 52, 14326) and served to validate the computational protocol employed in this work, while the remaining two proposed complexes can be considered positional isomers of I. Our calculations show that these complexes present different axial and rhombic zero-field splitting anisotropy parameters and different values of the most significant components of the g tensor. The predicted axial anisotropy D = -147.2 cm-1 for complex II is twice that observed experimentally for complex I, D = -72.8 cm-1, suggesting that this complex may be of interest for practical applications. We also analyze the temperature dependence of the magnetic susceptibility and molar magnetization for these complexes when subject to an external magnetic field. Overall, our results suggest that o-carborane-incorporated Co(II) complexes are worthwhile candidates for experimental exploration as single-ion molecular magnets.

Symmetry-adapted formulation of the combined G-particle-hole hypervirial equation and Hermitian operator method

High accuracy energies of low-lying excited states, in molecular systems, have been determined by means of a procedure which combines the G-particle-hole hypervirial (GHV) equation method (Alcoba et al. in Int J Quantum Chem 109:3178, 2009) and the Hermitian operator (HO) one (Bouten et al. in Nucl Phys A 202:127, 1973). This work reports a suitable strategy to introduce the point group symmetry within the framework of the combined GHV-HO method, which leads to an improvement of the computational efficiency. The resulting symmetry-adapted formulation has been applied to illustrate the computer timings and the hardware requirements in selected chemical systems of several geometries. The new formulation is used to study the low-lying excited states torsional potentials in the ethylene molecule.