Towards the High Performance Method for Large-Scale Electronic Structure Calculations

Density functional theory is a method for calculation of electronic structure of physical systems with a large number of atoms. In an effort to produce parallel implementation capable of solving systems with tens of thousands of atoms, in the first steps, we use Gaussian orbitals that allow relevant integrals to be calculated analytically. The main goal of this paper is the serial implementation of these integral calculations using C programming language. The analytical solutions consist of a very complex nested summations whose efficient implementation is the main contribution of this paper. We describe challenges encountered during implementation and their solutions. Results show that the given C implementation is at least three orders of magnitude faster than numerical solutions in the best available computational software programs.