Interpolation density values on a cartesian grid: Improving the efficiency of Lebedev based numerical integration in Kohn-Sham density functional algorithms

Most modern Kohn-Sham density functional theory algorithms utilize atom-centered numerical quadrature techniques for integration. To take advantage of the Fourier Transform Coulomb method in the Q-Chem package, which utilizes an evenly-spaced Cartesian grid to perform highly efficient numerical integration, divided difference interpolation is explored as a means of translating the electron density and its gradients from the Cartesian grid to atom-centered grid points. Aspects of accuracy, error control through the use of the grid density, and efficiency estimations are explored and the method is shown to provide an accurate means to link the FTC method and numerical DFT integration.