With the state of the system being described by a single Slater determinant, the Hartree–Fock (HF) wave function is given as that which minimizes the electronic energy in a variational sense with respect to variations in the spin orbitals. It represents a cornerstone in quantum chemistry and provides total electronic energies that are within 1% of the exact results and a wide range of molecular properties that are within 5–10% accuracy. Moreover, the Hartree–Fock method serves as starting points for the formulation of many other, more accurate, wave function methods as well as the Kohn–Sham formulation of density functional theory.

In this section, we will discuss:

  • The theory underlying the Hartree–Fock method, as well as many other methods in quantum chemistry

  • The implementation of a self-consistent field procedure

  • Examples on how to diagonalize the Fock matrix, and removing linear dependencies in the basis set

  • An example of how to use the HF implementation in VeloxChem, as well as visualizing molecular orbitals