Multiresolution computational chemistry

Multiresolution techniques in multiwavelet bases, made practical in three and higher dimensions by separated representations, have enabled significant advances in the accuracy and manner of computation of molecular electronic structure. The mathematical and numerical techniques are described in the article by Fann. This paper summarizes the major accomplishments in computational chemistry which represent the first substantial application of most of these new ideas in three and higher dimensions. These include basis set limit computation with linear scaling for Hartree-Fock and Density Functional Theory with a wide variety of functionals including hybrid and asymptotically corrected forms. Current capabilities include energies, analytic derivatives, and excitation energies from linear response theory. Direct solution in 6-D of the two-particle wave equation has also been demonstrated. These methods are written using MADNESS which provides a high level of composition using functions and operators with guarantees of speed and precision.