Analytic energy gradients for the Gaussian very fast multipole method (GvFMM)

The first use of the Gaussian very fast multipole method (GvFMM) for calculating the integral derivatives that arise in the Coulomb terms of density-functional theory (DFT) energy gradients is reported. Tests of the GvFMM gradient algorithm indicate that its accuracy, speed, and near-linear scaling behavior are similar to the GvFMM molecular energy algorithm. Specifically, 10−8 hartree per Bohr accuracy in the energy gradient has been achieved, and the ratio of the computational cost for the GvFMM energy gradient to the GvFMM energy has been found to be lower than the ratio for previous state-of-the-art method.