Study of Numerical Multicenter Integration for Large Scale Density Functional Calculation

Abstract

Large-scale density functional (DF) calculations were made possible by both high-performance computers and an efficient quantum chemical calculation algorithm. The exchange correlation (XC) term in the DF calculation is generally estimated by numerical integral scheme. Even though the accurate scheme is proposed for small molecules, the effectiveness is not verified enough for large-scale molecules like proteins. For the analysis of molecular properties such as chemical reaction, vibration spectrum, and so on, the integral scheme is demanded on 0.01~0.1 kcal/mol accuracy. The more accurate integral scheme is assumed to be required for the calculation of the huge molecules because those have a lot of electrons to accumulate the numerical error. In our previous study, we evaluated the accuracy of the various integral schemes by a single and a few amino-acid residues, and found that increasing the number of grids did not necessarily raise accuracy, and traditional three-dimensional numerical quadrature did not keep the rotational invariance. In this study, the relation of rotation and calculation accuracy of grids was clarified in detail for the improvement in accuracy of numerical integration.