Taming the combinatorics of antisymmetrized product of geminals

Patrick Cassam-Chenaï (LJAD, Université de Nice)

Mercredi 26 juin, 11h00, salle Coriolis (Galois).

Abstract. Quantum Chemistry is mainly concerned with solving the Schrödinger equation for the electrons of a molecule, that is to say, by solving the so-called “molecular electronic structure” problem. Getting inspiration from the Lewis pair model of Classical Chemistry, some quantum chemists have been looking for approximate wave functions in the form of an antisymmetrized product of geminals (APG), the latter term designing wave functions of electron pairs. However, the computational cost of the general APG model, without further constraints, scales exponentially with the size of the system.

A new geminal ansatz called antisymmetrized product of 2D-block geminals has been introduced recently to limit the cost of the APG Hamiltonian expectation value calculation (P. Cassam-Chenaï, Thomas Perez, Davide Accomasso, The Journal of Chemical Physics 158 (2023) 074106). It builds on an antisymmetrized product of strongly orthogonal geminals (APSG) while lifting the “strong orthogonality” and “seniority zero” restrictions. The combinatorics to select the terms, which can be added to each geminal of the product, to break these two constraints, grows exponentially with the number of geminals. However, we will show that the number of terms able to lower significantly the electronic energy in variational calculations, can be drastically reduced. This makes the method quite practical to use. Moreover, in most cases, the APSG geminals can be easily related to classical Lewis structures of chemistry. The improvement of the 2D-block APG model with respect to APSG is illustrated by comparing potential energy curve calculations for diatomic molecules, which is the quantity driving the vibrational motion of the nuclei.