An efficient deterministic perturbation theory for selected configuration interaction methods

TL;DR

This paper introduces a highly efficient, fully deterministic second-order perturbation theory algorithm for selected configuration interaction methods, significantly outperforming stochastic approaches and enabling large-scale quantum chemistry calculations.

Contribution

The authors develop a fast, deterministic PT2 algorithm for SCI methods that leverages sorting techniques and is optimized for modern parallel computing architectures.

Findings

Deterministic PT2 is orders of magnitude faster than stochastic methods.

Using accurate search algorithms like ASCI improves energy calculations.

The method enables evaluation of trillions of PT2 contributions with modest resources.

Abstract

The interplay between advances in stochastic and deterministic algorithms has recently led to development of interesting new selected configuration interaction (SCI) methods for solving the many body Schr\"{o}dinger equation. The performance of these SCI methods can be greatly improved with a second order perturbation theory (PT2) correction, which is often evaluated in a stochastic or hybrid-stochastic manner. In this work, we present a highly efficient, fully deterministic PT2 algorithm for SCI methods and demonstrate that our approach is orders of magnitude faster than recent proposals for stochastic SCI+PT2. We also show that it is important to have a compact reference SCI wave function, in order to obtain optimal SCI+PT2 energies. This indicates that it advantageous to use accurate search algorithms such as 'ASCI search' rather than more approximate approaches. Our deterministic PT2 algorithm is based on sorting techniques that have been developed for modern computing architectures and is inherently straightforward to use on parallel computing architectures. Related architectures such as GPU implementations can be also used to further increase the efficiency. Overall, we demonstrate that the algorithms presented in this work allow for efficient evaluation of trillions of PT2 contributions with modest computing resources.