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.
This research was supported by the National Science Foundation (NSF), USA under Award No. 1450280. This research used resources of the National Energy Research Scientific Computing Center (NERSC), a U.S. Department of Energy (DOE) Office of Science User Facility operated under Contract No. DE-AC02-05CH11231. This research also used resources of the Argonne Leadership Computing Facility, a DOE, USA Office of Science User Facility supported under Contract No. DE-AC02-06CH11357. We appreciate the constructive feedback from many fellow researchers in the electronic structure community, including developers and users of the BigDFT, CP2K, DFTB+, DGDFT, FHI-aims, NTChem, SIESTA projects and of CECAM’s Electronic Structure Library project. Yu was additionally supported by a fellowship from the Molecular Sciences Software Institute under NSF, USA Award No. 1547580. García thanks EU H2020, European Union grant 824143 (“MaX: Materials at the eXascale” CoE), Spain’s AEI (PGC2018-096955-B-C44 and “Severo Ochoa” grant SEV-2015-0496), and GenCat, Spain 2017SGR1506.