A finite difference Hartree–Fock program for atoms and diatomic molecules

Abstract

The newest version of the two-dimensional finite difference Hartree–Fock program for atoms and diatomic molecules is presented. This is an updated and extended version of the program published in this journal in 1996. It can be used to obtain reference, Hartree–Fock limit values of total energies and multipole moments for a wide range of diatomic molecules and their ions in order to calibrate existing and develop new basis sets, calculate (hyper)polarizabilities (αzz, βzzz, γzzzz, Az,zz, Bzz,zz) of atoms, homonuclear and heteronuclear diatomic molecules and their ions via the finite field method, perform DFT-type calculations using LDA or B88 exchange functionals and LYP or VWN correlations ones or the self-consistent multiplicative constant method, perform one-particle calculations with (smooth) Coulomb and Krammers–Henneberger potentials and take account of finite nucleus models. The program is easy to install and compile (tarball+configure+make) and can be used to perform calculations within double- or quadruple-precision arithmetic. Program summaryProgram title: 2dhfCatalogue identifier: ADEB_v2_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADEB_v2_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: GNU General Public License version 2No. of lines in distributed program, including test data, etc.: 171196No. of bytes in distributed program, including test data, etc.: 9481802Distribution format: tar.gzProgramming language: Fortran 77, C.Computer: any 32- or 64-bit platform.Operating system: Unix/Linux.RAM: Case dependent, from few MB to many GBClassification: 16.1.Catalogue identifier of previous version: ADEB_v1_0Journal reference of previous version: Comput. Phys. Comm. 98(1996)346Does the new version supersede the previous version?: YesNature of problem: The program finds virtually exact solutions of the Hartree–Fock and density functional theory type equations for atoms, diatomic molecules and their ions. The lowest energy eigenstates of a given irreducible representation and spin can be obtained. The program can be used to perform one-particle calculations with (smooth) Coulomb and Krammers–Henneberger potentials and also DFT-type calculations using LDA or B88 exchange functionals and LYP or VWN correlations ones or the self-consistent multiplicative constant method.Solution method: Single-particle two-dimensional numerical functions (orbitals) are used to construct an antisymmetric many-electron wave function of the restricted open-shell Hartree–Fock model. The orbitals are obtained by solving the Hartree–Fock equations as coupled two-dimensional second-order (elliptic) partial differential equations (PDEs). The Coulomb and exchange potentials are obtained as solutions of the corresponding Poisson equations. The PDEs are discretized by the eighth-order central difference stencil on a two-dimensional single grid, and the resulting large and sparse system of linear equations is solved by the (multicolour) successive overrelaxation ((MC)SOR) method. The self-consistent-field iterations are interwoven with the (MC)SOR ones and orbital energies and normalization factors are used to monitor the convergence. The accuracy of solutions depends mainly on the grid and the system under consideration, which means that within double precision arithmetic one can obtain orbitals and energies having up to 12 significant figures. If more accurate results are needed, quadruple-precision floating-point arithmetic can be used.Reasons for new version: Additional features, many modifications and corrections, improved convergence rate, overhauled code and documentation.Summary of revisions: see ChangeLog found in tar.gz archiveRestrictions: The present version of the program is restricted to 60 orbitals. The maximum grid size is determined at compilation time.Unusual features: The program uses two C routines for allocating and deallocating memory. Several BLAS (Basic Linear Algebra System) routines are emulated by the program. When possible they should be replaced by their library equivalents.Additional comments: automake and autoconf tools are required to build and compile the program; checked with f77, gfortran and ifort compilersRunning time: Very case dependent — from a few CPU seconds for the H2 defined on a small grid up to several weeks for the Hartree–Fock-limit calculations for 40–50 electron molecules.