The Integral Screened Configuration Interaction Method

TL;DR

The paper introduces the Integral-Screened Configuration-Interaction (ISCI) method, which achieves near-linear scaling for large quantum systems through rigorous integral screening, enabling efficient and accurate CI calculations on large orbital spaces.

Contribution

The ISCI method provides a novel integral screening approach that significantly reduces computational scaling while maintaining high accuracy in CI calculations.

Findings

Achieves linear or near-linear scaling for large systems

Retains energy accuracy of 10^{-14} or better

Enables large orbital space calculations on a single CPU

Abstract

We present the formulation and implementation of the Integral-Screened Configuration-Interaction method (ISCI). The ISCI is a minimal-operational count integral-driven direct Configuration-Interaction (CI) method with a simple and rigorous integral screening (IS). With a novel derivation of the CI equations we show that the time consuming $\sigma$-vector calculation is separable up to an overall sign and that this separability can lead to a rigorous IS. The rigorous IS leads to linear scaling in the $\sigma$-vector step for large systems but can also lead to near linear scaling for smaller systems for the standard CISD, CISDT and CISDTQ methods, where the exponent for the scaling is 1.27, 1.48 and 1.98, respectively, even while retaining an accuracy of $10^{-14}$ or less in the energy. In the ISCI the non-relativistic CI problem can be broken into 42 generalized-matrix-vector products in the $\sigma$-vector calculation, which can be separately optimized. Due to the IS the ISCI can use dramatically larger orbital spaces combined with large CI expansions, on a single cpu, as compared with traditional CI methods. Further, it offers an intrinsic possibility for parallelization on modern computing architectures. We show examples of how IS leads to linear or near linear scaling with respect to the size of the simulation box in calculations on the Beryllium atom.