Parallel Implementation of Large-Scale Linear Scaling Density Functional Theory Calculations With Numerical Atomic Orbitals in HONPAS

Abstract

Linear-scaling density functional theory (DFT) is an efficient method to describe the electronic structures of molecules, semiconductors, and insulators to avoid the high cubic-scaling cost in conventional DFT calculations. Here, we present a parallel implementation of linear-scaling density matrix trace correcting (TC) purification algorithm to solve the Kohn–Sham (KS) equations with the numerical atomic orbitals in the HONPAS package. Such a linear-scaling density matrix purification algorithm is based on the Kohn's nearsightedness principle, resulting in a sparse Hamiltonian matrix with localized basis sets in the DFT calculations. Therefore, sparse matrix multiplication is the most time-consuming step in the density matrix purification algorithm for linear-scaling DFT calculations. We propose to use the MPI_Allgather function for parallel programming to deal with the sparse matrix multiplication within the compressed sparse row (CSR) format, which can scale up to hundreds of processing cores on modern heterogeneous supercomputers. We demonstrate the computational accuracy and efficiency of this parallel density matrix purification algorithm by performing large-scale DFT calculations on boron nitrogen nanotubes containing tens of thousands of atoms.

Computational and data driven molecular material design assisted by low scaling quantum mechanics calculations and machine learning

“… 169 Recently, Hu and co-workers have applied pole expansion and selected inversion (PEXSI) to calculate the electronic structures of boron nitrogen nanotubes. 170 Our aim is not only to show the potential and applicability of different methods and techniques and, by discussing some representative calculations, but also to help the reader to select an appropriate approach for particular molecular material systems.…”

Accurate Hellmann-Feynman forces with optimized atom-centered Gaussian basis sets

“…Regarding periodic systems, accurate simulation of the correlated electronic structure of van der Waals materials like twisted bilayer graphene would require force calculations on superlattices surpassing 40,000 atoms [10][11][12][13]. Even with adaptations for increased efficiency [14][15][16], traditional first principles methods, that is, density functional theory (DFT) [17,18] is unable to efficiently and accurately compute forces for such large-scale systems.…”