Study of Practical Approach for Grid-free XC Computational Method

Abstract

The current density functional calculations adopt numerical integration to estimate exchange-correlation (XC) term, which brings numerical instability in case of huge molecule and massively multipoint calculations. The grid-free method developed in 1993 was capable of calculating XC term analytically and conquering brittleness but could not have given reliable computational values so far. In this paper, we clarified that the cause of this problem was in the basis set used to calculate the matrix representation of density (MRD). From this knowledge, we proposed the new grid-free method which greatly improved the computational values, where rich basis sets were applied to MRD basis. In addition, we proposed an application of Cholesky decomposition method to the grid-free method in order to reduce the computational cost safely and effectively.