ELSI — An open infrastructure for electronic structure solvers

Routine applications of electronic structure theory to molecules and periodic systems need to compute the electron density from given Hamiltonian and, in case of non-orthogonal basis sets, overlap matrices. System sizes can range from few to thousands or, in some examples, millions of atoms. Different discretization schemes (basis sets) and different system geometries (finite non-periodic vs. infinite periodic boundary conditions) yield matrices with different structures. The ELectronic Structure Infrastructure (ELSI) project provides an open-source software interface to facilitate the implementation and optimal use of high-performance solver libraries covering cubic scaling eigensolvers, linear scaling density-matrix-based algorithms, and other reduced scaling methods in between. In this paper, we present recent improvements and developments inside ELSI, mainly covering (1) new solvers connected to the interface, (2) matrix layout and communication adapted for parallel calculations of periodic and/or spin-polarized systems, (3) routines for density matrix extrapolation in geometry optimization and molecular dynamics calculations, and (4) general utilities such as parallel matrix I/O and JSON output. The ELSI interface has been integrated into four electronic structure code projects (DFTB+, DGDFT, FHI-aims, SIESTA), allowing us to rigorously benchmark the performance of the solvers on an equal footing. Based on results of a systematic set of large-scale benchmarks performed with Kohn–Sham density-functional theory and density-functional tight-binding theory, we identify factors that strongly affect the efficiency of the solvers, and propose a decision layer that assists with the solver selection process. Finally, we describe a reverse communication interface encoding matrix-free iterative solver strategies that are amenable, e.g., for use with planewave basis sets.

电子结构理论在分子与周期性体系中的常规应用，需从给定的哈密顿量（Hamiltonian）以及非正交基组场景下的重叠矩阵（overlap matrices）中计算电子密度。体系规模可覆盖数个原子至数千乃至数百万原子不等。不同的离散化方案（基组）与体系几何结构（有限非周期性与无限周期性边界条件）会生成结构各异的矩阵。电子结构基础设施（ELSI，Electronic Structure Infrastructure）项目提供了一套开源软件接口，以助力高性能求解器库的实现与优化应用，涵盖三次标度本征求解器、线性标度基于密度矩阵的算法，以及介于二者之间的其他低标度计算方法。本文介绍了ELSI内部的最新改进与进展，主要包括以下四方面：(1) 接入该接口的新型求解器；(2) 适配周期性和/或自旋极化体系并行计算的矩阵布局与通信机制；(3) 用于几何优化与分子动力学计算的密度矩阵外推程序；(4) 并行矩阵输入输出（I/O）、JSON输出等通用工具集。ELSI接口已集成至四个电子结构代码项目（DFTB+、DGDFT、FHI-aims、SIESTA），使得我们能够在同等基准条件下严格对标各类求解器的性能表现。基于利用科恩-沈吕九密度泛函理论（Kohn–Sham density-functional theory）与密度泛函紧束缚理论（density-functional tight-binding theory）开展的系统性大规模基准测试结果，我们识别出了对求解器效率影响显著的关键因素，并提出了一个可辅助求解器选择的决策层模块。最后，本文还介绍了一种反向通信接口，其封装了无矩阵迭代求解器策略，可适配例如平面波基组（planewave basis sets）的应用场景。