On the full exploitation of symmetry in periodic (as well as molecular) self-consistentfield ab initio calculations

Abstract

Use of symmetry can dramatically reduce the computational cost (running time and memory allocation) of Self-Consistent-Field ab initio calculations for molecular and crystalline systems. Crucial for running time is symmetry exploitation in the evaluation of one- and two-electron integrals, diagonalization of the Fock matrix at selected points in reciprocal space, reconstruction of the density matrix. As regards memory allocation, full square matrices (overlap, Fock and density) in the Atomic Orbital (AO) basis are avoided and a direct transformation from the packed AO to the SACO (Symmetry Adapted Crystalline Orbital) basis is performed, so that the largest matrix to be handled has the size of the largest sub-block in the latter basis. Quantitative examples, referring to the implementation in the Crystal code, are given for high symmetry families of compounds such as carbon fullerenes and nanotubes.