An improvement of the grid generation algorithm in density functional method

Abstract

We are developing a density functional method program ProteinDF for all-electron calculation on proteins. ProteinDF adopts the fuzzy cell method to evaluate exchange-correlation potential so that grids and their weights are estimated for numerical integrals before self-consistent field (SCF) calculation. Because this task is depending on the 3rd power of the number of atoms, it becomes one of the time-consuming routines when the system size is very large. Recently we achieved the 26766 canonical orbitals calculation of a protein, where the grid generation routine cost 22% of all calculations. In order to calculate larger proteins and achieve structure updated calculations such as geometry optimization and ab initio molecular dynamics, it is very important to improve this routine. In this study, we modify the loop structure in the grid generating routine and improve the computational cost by compensating memory. As a result, the performance is increased 4 times, and the share of the grid generation was reduced to 5% for 26766 orbitals calculations. Now, we modify the fuzzy cell algorithm for the further speed-up.