Spin-adapted selected configuration interaction in a determinant basis

TL;DR

This paper introduces an efficient algorithm to generate spin-adapted wave functions in selected configuration interaction methods, ensuring spin purity without complex manipulations, thereby improving accuracy for magnetic and excited states.

Contribution

The authors develop a novel algorithm that generates all missing determinants for spin adaptation directly from a determinant space, avoiding the use of configuration state functions.

Findings

Efficient generation of spin-adapted determinants with minimal CPU cycles

Maintains determinant-based selection while ensuring spin purity

Reduces memory footprint using configuration state function basis

Abstract

Selected configuration interaction (SCI) methods, when complemented with a second-order perturbative correction, provide near full configuration interaction (FCI) quality energies with only a small fraction of the Slater determinants of the FCI space. However, a selection criterion based on determinants alone does not ensure a spin-pure wave function. In other words, such SCI wave functions are not eigenfunctions of the $S^2$ operator. In many situations (bond breaking, magnetic system, excited state, etc), having a spin-adapted wave function is essential for a quantitatively correct description of the system. Here, we propose an efficient algorithm which, given an arbitrary determinant space, generates all the missing Slater determinants allowing one to obtain spin-adapted wave functions while avoiding manipulations involving configuration state functions. For example, generating all the possible determinants with 6 spin-up and 6 spin-down electrons in 12 open shells takes 21 CPU cycles per generated Slater determinant. The selection is still done with individual determinants, and one can take advantage of the basis of configuration state functions in the diagonalization of the Hamiltonian to reduce significantly the memory footprint.