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

An efficient and accurate analytic gradient method for Hartree-Fock (HF) and density functional calculations using multiresolution analysis in multiwavelet bases was presented. The derivative was computed as an inner product between compressed forms of the density and the differentiated nuclear potential through the Hellmann-Feynman theorem. The derivatives of N ₂ molecule were shown using multiresolution calculation for various accuracies with comparison to correlation consistent Gaussisan-type basis sets. It was observed that a highly precise Hartree-Fock optimization for the H ₂O molecule produced six digits for the geometric parameters.