Ultra-large-scale electronic structure theory and numerical algorithm

TL;DR

This paper reviews ultra-large-scale electronic structure theory, focusing on its numerical algorithms and mathematical foundations, and discusses its significance in nano-material science.

Contribution

It provides a comprehensive review of the numerical algorithms and mathematical basis underlying ultra-large-scale electronic structure theory, highlighting its role in nano-material research.

Findings

Detailed overview of numerical algorithms for large-scale electronic structure calculations

Discussion of mathematical foundations supporting these algorithms

Insights into the application of theory in nano-material science

Abstract

This article is composed of two parts; In the first part (Sec. 1), the ultra-large-scale electronic structure theory is reviewed for (i) its fundamental numerical algorithm and (ii) its role in nano-material science. The second part (Sec. 2) is devoted to the mathematical foundation of the large-scale electronic structure theory and their numerical aspects.