Extended Numerov method for the numerical solution of the Hartree–Fock equations

Abstract

To match the intrinsic accuracy of an expanded basis set solution of atomic orbitals by numerical orbitals requires integration formulas of comparable intrinsic accuracy. Integration of the coupled, integro‐differential, Hartree–Fock equations is most easily done using Numerov’s formula. without increasing the number of mesh points, one must extend the basic formula to include more points. Herein is presented the derivation of the general (2N+1)‐point Numerov formula, including the error term, as well as suggestions for numerical determination with specific formulas of 3‐, 5‐, 7‐, and 9‐ point fits.