Multiresolution quantum chemistry in multiwavelet bases: Analytic derivatives for Hartree–Fock and density functional theory

An efficient and accurate analytic gradient method is presented for Hartree–Fock and density functional calculations using multiresolution analysis in multiwavelet bases. The derivative is efficiently computed as an inner product between compressed forms of the density and the differentiated nuclear potential through the Hellmann–Feynman theorem. A smoothed nuclear potential is directly differentiated, and the smoothing parameter required for a given accuracy is empirically determined from calculations on six homonuclear diatomic molecules. The derivatives of $N2$ molecule are shown using multiresolution calculation for various accuracies with comparison to correlation consistent Gaussian-type basis sets. The optimized geometries of several molecules are presented using Hartree–Fock and density functional theory. A highly precise Hartree–Fock optimization for the $H2O$ molecule produced six digits for the geometric parameters.