Efficient Parallel All-Electron Four-Component Dirac–Kohn–Sham Program Using a Distributed Matrix Approach II

We propose a new complete memory-distributed algorithm, which significantly improves the parallel implementation of the all-electron four-component Dirac–Kohn–Sham (DKS) module of BERTHA (<i>J. Chem. Theory Comput.</i> <b>2010</b>, <i>6</i>, 384). We devised an original procedure for mapping the DKS matrix between an efficient integral-driven distribution, guided by the structure of specific G-spinor basis sets and by density fitting algorithms, and the two-dimensional block-cyclic distribution scheme required by the ScaLAPACK library employed for the linear algebra operations. This implementation, because of the efficiency in the memory distribution, represents a leap forward in the applicability of the DKS procedure to arbitrarily large molecular systems and its porting on last-generation massively parallel systems. The performance of the code is illustrated by some test calculations on several gold clusters of increasing size. The DKS self-consistent procedure has been explicitly converged for two representative clusters, namely Au₂₀ and Au₃₄, for which the density of electronic states is reported and discussed. The largest gold cluster uses more than 39k basis functions and DKS matrices of the order of 23 GB