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

Abstract

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.

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

“…Our adaptation of the procedure of Subotnik et al 23 to minimise the seniority number proceeds as follows. 12 1. Start with a set of orthonormal orbitals, e.g., the RHF molecular orbitals.…”

“…Some of us have previously shown that the orbital basis that minimises the seniority number of a FCI wave function can be used to achieve a more compact determinantal expansion, where the determinants with zero seniority number are the dominant contributions to the FCI wave function. 12 In practice, this means that this orbital basis can be used as a good approximation to the energy optimised DOCI orbitals. As FCI wave functions are hardly tractable for larger systems, we examine whether a seniority number minimising basis derived from a truncated CI wave function serves equally well.…”

Configuration interaction wave functions: A seniority number approach

“…Three types of molecular orbital bases have been utilized in this study: (i) the canonical Hartree-Fock molecular orbitals (CMO), (ii) the natural orbitals (NO) in which the FCI spinfree first-order reduced density matrix is diagonal (generally considered as the one yielding the fastest CI convergence but whose behavior has been questioned, 5,17 and (iii) the orbitals (M min ) which minimize the expectation value FCI |ˆ | FCI for a given FCI wave function (N, S). 15 The Hartree-Fock reference energies, the Hartree-Fock molecular orbital basis sets, and the one-and two-electron integrals have been obtained from a modified version of the PSI 3.3 package. 27 We have used our own codes to calculate the spin-free secondorder reduced density matrix elements required to determine the orbitals of the basis set M min .…”

“…15 In this reference we have shown that the expectation value of the seniority number operator for an N-electron spin-adapted space is an invariant with respect to any unitary transformation of the basis set, while its expectation value for a determined wave function which describes a state is an orbital basis dependent magnitude. This dependence has allowed us to propose transformations of the orbital basis set in order to achieve a minimum value for the seniority number of the FCI N-electron wave function.…”

“…The compactness of the FCI wave functions has been studied by means of an analysis of their expansions in the basis sets of the canonical molecular orbitals (CMO), in the natural orbitals (NO), 16,17 and in the molecular orbital sets in which the seniority number possesses a minimum value (M min ). 15 Since the energies and the convergence of the CI expansions depend upon the orbitals from which the configurations are formed, another purpose of the present work is to study the performance of these three types of molecular orbital basis in the seniority-number-based CI expansions, in order to identify the basis which leads to the energy values closer to the FCI results.…”