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.
The Energetics of Hut-Cluster Self-Assembly in Ge/Si(001) from Linear-Scaling DFT Calculations
