Kinetic energy-free Hartree–Fock equations: an integral formulation

Abstract

We have implemented a self-consistent feld solver for Hartree–Fock calculations, by making use of Multiwavelets and Multiresolution Analysis. We show how such a solver is inherently a preconditioned steepest descent method and therefore a good starting point for rapid convergence. A distinctive feature of our implementation is the absence of any reference to the kinetic energy operator. This is desirable when Multiwavelets are employed, because diferential operators such as the Laplacian in the kinetic energy are challenging to represent correctly. The theoretical framework is described in detail and the implemented algorithm is both presented in the paper and made available as a Python notebook. Two simple examples are presented, highlighting the main features of our implementation: arbitrary predefned precision, rapid and robust convergence, absence of the kinetic energy operator.