Efficient evaluation of the Coulomb force in density-functional theory calculations

The Coulomb force in density-functional theory calculations is efficiently evaluated based on a partitioning into near-field (NF) and far-field (FF) interactions. For the NF contributions, a J force engine method is developed based on our previous J matrix engine methods, and offers a significant speedup over derivative electron repulsion integral evaluation, without any approximation. In test calculations on water clusters and linear alkanes, the computer time for the NF force is reduced by a factor of 5–7 with a 3-21G basis set and 6–8 with a 6-31G** basis set. The FF force is treated by a generalization of the continuous fast multipole method, and the FF computational cost is found to be comparable to that of an energy evaluation.

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