# Efficient methods for computing integrals in electronic structure calculations

## TL;DR

This paper introduces efficient numerical methods for computing integrals in electronic structure calculations by representing them as contour integrals and evaluating with Clenshaw-Curtis quadrature, demonstrating improved performance.

## Contribution

The paper presents a novel approach combining contour integral representation with Clenshaw-Curtis quadrature for faster integral computation in electronic structure methods.

## Key findings

- Significant reduction in computational time.
- High accuracy demonstrated in numerical experiments.
- Applicable to large-scale electronic structure problems.

## Abstract

Efficient methods are proposed, for computing integrals appeaing in electronic structure calculations. The methods consist of two parts: the first part is to represent the integrals as contour integrals and the second one is to evaluate the contour integrals by the Clenshaw-Curtis quadrature. The efficiency of the proposed methods is demonstrated through numerical experiments.