Mark A. Iron, Grażyna Staszewska, Tiqing Liu, Ahren W. Jasper, and Donald G. Truhlar
Department of Chemistry and Supercomputing Institute
University of Minnesota, Minneapolis, Minnesota 55455-0431
TBPAC is a complete package for tight binding calculations on molecules containing selected metal atoms (Al, Ni, Cu, Pd, Ag, Pt, and Au) plus carbon and hydrogen. This implementation combines the capabilities of TB 1.0 and TB 2.0 plus it adds tight-binding with a Hubbard-like term (TB+U), and tight binding with configuration interaction (TBCI). As a result, it includes orthogonal and nonorthogonal Slater-Koster tight binding, penalty energies, orthogonal and nonorthogonal many-body tight binding, tight-binding with a Hubbard-like term, and tight binding with configuration interaction. (None of the methods is supported for all possible combinations of the supported elements.) Analytical gradients are available for all methods.
TBPAC is a FORTRAN 77 computer program for the calculation of potential energy surfaces and analytical gradients of systems involving H, C, Al, Ni, Cu, Pd, Ag, Pt, Au, using tight binding theory; not all combinations of these elements are supported by current parameters in the code. TBPAC was originally designed for treating the adsorption of hydrocarbon fragments on group-10 and group-11 clusters, nanoparticles, and bulk surfaces, and the current version also contains an especially large number of options for homonuclear systems composed of Al atoms. For Al, the valence electronic wave function (3 electrons per atom) is expanded in a basis of 4 atomic orbitals: 3s,3p_x,3p_y and 3p_z. Therefore dimension of the tight-binding matrix for Al clusters and nanoparticles is 4*N, where N is the number of Al atoms in the particle. Parameters may be added for other elements or combinations of elements, if desired.
Tight binding theory is a highly parametrized extended Hueckel theory, and the present implementation includes an explicit term representing the pairwise repulsion between atomic cores. The present code also includes two different ways to include a Hubbard-type penalty term. The overlap integral is not included in the secular equation. The radial parts of the Hamiltonian matrix elements are parametrized using the functional forms of Lathiotakis et al. and Wang and Mak or the Wolfberg-Holmholz scheme; the angular parts are evaluated by the Slater-Koster scheme. The program is built as a subroutine accepting the coordinates of the system from the caller and returning the energy of the system and the first derivatives of the energy with respect to the Cartesian coordinates of each atom in the system. The code may be applied to both neutral and charged systems; the same formalism is used for both open-shell and closed-shell calculations.
For Al, the radial parts of the Hamiltonian matrix elements are parametrized in 6 different ways as described in:
Grażyna Staszewska, Przemysław Staszewski, Nathan E. Schultz and Donald G. Truhlar, "Many-body tight binding model for aluminum nanoparticles," Physical Review B, 71, 045423 (2005) (Read at APS)
(1) MBTB-S - many-body tight-binding based on screening,
(2) MBTB-CN - many-body tight-binding based on coordination number,
(3) MBTB-BA - Many-body tight-binding based on bond-angle correction,
and three versions of pair-wise tight binding:
(4) TB-OWH - optimized Wolfsberg-Helmholz approximation
(5) TB-EWH - extended Wolfsberg-Helmholz approximation
(6) TB-WH - Wolfsberg-Helmholz approximation.
The angular parts are evaluated by the Slater-Koster scheme. The current version is available for energies only and does not include analytical gradients.