chrinide/x2dhf

Two-Dimensional Finite Difference Hartree-Fock Program

Two-Dimensional Finite Difference Hartree-Fock program for diatomic molecules

This program finds virtually exact solutions of the Hartree-Fock and density functional theory equations for diatomic molecules and atoms (the quality of a solution depends on grid size and arithmetic precision used). The lowest energy eigenstates of a given irreducible representation and spin can be obtained.

The program can be also be used to obtain the ground and excited states of one-electron systems with the (smoothed) Coulomb and Kramers-Hennenberger potentials.

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 in the form of the coupled two-dimensional second-order (elliptic) partial differential equations (PDE). The Coulomb and exchange potentials are obtained as solutions of the corresponding Poisson equations. The PDEs are disretized by the 8th-order central difference stencil on a two-dimensional grid and the resulting large and sparse system of linear equations is solved by the (multicolour) successive overrelaxation method ((MC)SOR). 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.

See the following articles for the detailed description of the program and examples of its usage and accuracy:

• L. Laaksonen, P. Pyykkö, and D. Sundholm, Fully numerical Hartree-Fock methods for molecules, Comp. Phys. Reports 4 (1986) 313-344. http://doi.org/10.1016/0167-7977(86)90021-3
• L. Laaksonen, D. Sundholm, and P. Pyykkö, in "Scientific Computing in Finland", Eds. K. Kankaala and R. Nieminen, Research Report R1/89, Centre for Scientific Computing, (1989) p. 183.
• P. Pyykkö, in Numerical Determination of the Electronic Structure of Atoms, Diatomic and Polyatomic Molecules (NATO ASI Series C271) Eds. M. Defranceschi and J. Delhalle, (1989) p. 161. http://doi.org/10.1007/978-94-009-2329-4
• J. Kobus, Finite-difference versus finite-element methods, Chem. Phys. Lett. 202 (1993) 7-12. http://doi.org/10.1016/0009-2614(93)85342-L
• J. Kobus, Vectorizable algorithm for the (multicolour) successive overrelaxation method, Comput. Phys. Commun. 78 (1994) 247-255. http://doi.org/10.1016/0010-4655(94)90003-5
• J. Kobus, L. Laaksonen, D. Sundholm, A numerical Hartree-Fock program for diatomic molecules, Comp. Phys. Commun. 98 (1996) 346-358. http://doi.org/10.1016/0010-4655(96)00098-7
• J. Kobus, Numerical Hartree-Fock methods for diatomic molecules, Handbook of Molecular Physics and Quantum Chemistry (Chichester), ed. S. Wilson (Wiley, 2002)
• J. Kobus, Hartree-Fock limit values of multipole moments, polarizabilities and hyperpolarizabilities for atoms and diatomic molecules, Comp. Lett. 3 (2007) 71-113. http://doi.org/10.1163/157404007782913408
• J. Kobus, A finite difference Hartree-Fock program for atoms and diatomic molecules, Comp. Phys. Commun. 184 (2013) 799-811. http://dx.doi.org/10.1016/j.cpc.2012.09.033

The last paper in the above list has an up-to-date description of the operating principles and layout of the program.

The programming language used is Fortran 90; only a Fortran compiler and CMake are necessary to compile the program. The program can be built by running ./compile.sh. See the file INSTALL for more details on installation.

The file doc/users-guide.pdf contains the description of the program's input data and examples of its usage. Examples are included in examples/

This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License version 2 as published by the Free Software Foundation.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.