Review of the finite difference Hartree-Fock method for atoms and diatomic molecules, and its implementation in the x2dhf program

Abstract

We present an extensive review of the two-dimensional finite difference Hartree--Fock (FD HF) method, and present its implementation in the newest version of X2DHF, the FD HF program for atoms and diatomic molecules. The program was originally published in Comput. Phys. Commun. in 1996, and was last revised in 2013. X2DHF can be used to obtain HF limit values of total energies and multipole moments for a wide range of diatomic molecules and their ions, using either point nuclei or a finite nuclear model. Polarizabilities ($α_{zz}$) and hyperpolarizabilities ($β_{zzz}$, $γ_{zzzz}$, ${A}_{z,zz}$, ${B}_{zz,zz}$) can also be computed by the program with the finite-field method. X2DHF has been extensively used in the literature to assess the accuracy of existing atomic basis sets and to help in developing new ones. As a new feature since the last revision, the program can now also perform Kohn-Sham density functional calculations with local and generalized gradient exchange-correlation functionals with the Libxc library of density functionals, enabling new types of studies. Furthermore, the initialization of calculations has been greatly simplified. As before, X2DHF can also perform one-particle calculations with (smooth) Coulomb, Green-Sellin-Zachor and Krammers-Henneberger potentials, while calculations with a superposition of atomic potentials have been added as a new feature. The program is easy to install from the GitHub repository and build via CMake using the x2dhfctl script that facilitates creating its single- and multiple-threaded versions, as well as building in Libxc support. Calculations can be carried out with X2DHF in double- or quadruple-precision arithmetic.