Various integral estimations and screening schemes for extended systems in PySCF

TL;DR

This paper reviews and analyzes integral estimation and screening schemes in PySCF, proposing methods to optimize computational efficiency while maintaining accuracy for extended systems.

Contribution

It introduces new integral estimators and screening parameter conditions based on range-separated and Fourier transform algorithms in PySCF.

Findings

Effective integral estimators improve accuracy control

Screening parameters reduce unnecessary computations

Numerical tests validate the efficiency of proposed methods

Abstract

In this document, we briefly review the two-electron integral algorithms based on the range-separated algorithms and Fourier transform integral algorithms that are implement ed in the PySCF package. For each integral algorithm, we estimate the upper bound of relevant integrals and derive the necessary conditions for the screening parameters, including distance cutoff and energy cutoff, to reach the desired accuracy. Our numerical tests show that the proposed integral estimators and screening parameters can effectively address the required accuracy while computational efforts are not wasted on unintended accuracy.