Pseudospherical integration scheme for electronic-structure calculations.

Contemporary electronic-structure methods avoid shape approximations but in doing so encounter the difficult problem of integral evaluation over complicated interstitial volumes. In this paper, we present a simple and efficient technique for applying rapidly convergent Gaussian product formulas to general interstitial regions. Like the recent methods of Boerrigter, te Velde, and Baerends, it is based upon partitioning space into Voronoi cells and atomic spheres. In the present work, introduction of a general pseudospherical local-coordinate system unifies the integration procedures and effects a simplified approach. A systematic procedure is derived for determining the number of Gaussian points required for a specified level of numerical precision.