Q-Next: A Fast, Parallel, and Diagonalization-Free Alternative to Direct Inversion of the Iterative Subspace

As computer systems dedicated to scientific calculations become massively parallel, the poor parallel performance of the Fock matrix diagonalization becomes a major impediment to achieving larger molecular sizes in self-consistent field (SCF) calculations. In this Article, a novel, highly parallel, and diagonalization-free algorithm for the accelerated convergence of the SCF procedure is presented. The algorithm, called Q-Next, draws on the second-order SCF, quadratically convergent SCF, and direct inversion of the iterative subspace (DIIS) approaches to enable fast convergence while replacing the Fock matrix diagonalization SCF bottleneck with higher parallel efficiency matrix multiplications. Performance results on both parallel multicore CPU and GPU hardware for a variety of test molecules and basis sets are presented, showing that Q-Next achieves a convergence rate comparable to the DIIS method while being, on average, one order of magnitude faster.