Fast and accurate 3D tensor calculation of the Fock operator in a general basis Original Research Article

The present paper contributes to the construction of a “black-box” 3D solver for the Hartree–Fock equation by the grid-based tensor-structured methods. It focuses on the calculation of the Galerkin matrices for the Laplace and the nuclear potential operators by tensor operations using the generic set of basis functions with low separation rank, discretized on a fine image Cartesian grid. We prove the image error estimate in terms of mesh parameter, image, that allows to gain a guaranteed accuracy of the core Hamiltonian part in the Fock operator as image. However, the commonly used problem adapted basis functions have low regularity yielding a considerable increase of the constant image, hence, demanding a rather large grid-size image of about several tens of thousands to ensure the high resolution. Modern tensor-formatted arithmetics of complexity image, or even image, practically relaxes the limitations on the grid-size. Our tensor-based approach allows to improve significantly the standard basis sets in quantum chemistry by including simple combinations of Slater-type, local finite element and other basis functions. Numerical experiments for moderate size organic molecules show efficiency and accuracy of grid-based calculations to the core Hamiltonian in the range of grid parameter image.