Vectorization of Direct Fock Matrix Construction in DIRAC-DHF Calculations

Abstract

Iterations of the Fock matrix construction from two-electron integrals completely dominates the total cost of direct self-consistent-field (DSCF) calculations, especially for the four-component Dirac-Hartree-Fock (DHF) relativistic molecular-orbital method. We revive here the notion of vectorization as helpful to accelerate DSCF-DHF calculations. DIRAC is a representative state-of-the-art DHF code on which we consider the vectorized Fock matrix construction. While the integral generation is straightforwardly vectorizable, the contraction of generated integrals with associated densities into the Fock matrix elements is unable to vectorize simply due to frequent address conflicts. In this report, we present a vectorization of the direct Fock matrix construction by introducing a working-array technique. Total vectorization efficiency for DHF runs is improved from 50–60% by the original DIRAC to more than 90% by the modified version.

KEYWORDS:

• relativistic molecular-orbital calculations
• Dirac-Hartree-Fock
• integral-direct method
• vectorization
• earth simulator
• Fock method