Overview of finite difference Hartree-Fock method algorithm, implementation and application

Two-dimensional, finite difference Hartree-Fock method has been in constant usage and development over the last two decades. The method has proved stable and efficient enough to be applied to dozens of diatomic molecules, even to systems as large as the thorium fluoride. Its latest version is presented and the dependence of its accuracy on the grid size and efficiency on the overrelaxation parameters are discussed. The method has been mainly used to develop and calibrate sequences of universal even-tempered and polarization-consistent basis sets and assess basis set truncation and superposition errors. Its modified version has proved useful in testing various exchange-correlation potentials within the density functional theory. The method has turned out to be a valuable source of reference values of total energies, multipole moments, static polarizabilities and hyperpolarizabilities (α_zz, β_zzz, γ_zzzz, A_z,zz and B_zz,zz) for atoms, diatomic molecules and their ions. Recently, it has been modified to allow to calculate the electrical properties of homonuclear molecules and the results for the $Li2$⁠, $N2$⁠, $F2$ and $O2$ systems are presented. Electrical properties of the AlF, CS, KCl diatomics and of highly ionized krypton atom (⁠$Kr+32$⁠) are reported as well. Accuracy of both the matrix Hartree-Fock employing universal even-tempered basis sets and the finite difference Hartree-Fock methods is discussed and the basis set superposition errors of the dipole polarizability and the first hyperpolarizability of the FH molecule is reexamined. Basis set superposition errors are also discussed in case of the dipole polarizability and the second hyperpolarizability of the $F2$ system.