Last Modified 23 January 2002

Notes on the Tight-Binding parameters

These are the tight-binding parameter files associated with the paper Applications of a tight-binding total energy method for transition and noble metals: Elastic Constants, Vacancies, and Surfaces of Monatomic Metals by Michael J. Mehl and Dimitrios A. Papaconstantopoulos of the Complex Systems Theory Branch, Naval Research Laboratory, Washington, DC 20375-5345 USA.

The labels associated with the tight-binding parameters reference the equations found in the above paper.

Comments or questions about these parameters should be addressed (Privacy Advisory) to the authors.

Notes:

• As outlined in our paper, the Slater-Koster Hamiltonian and overlap parameters have the form

  \[ P(R) = [e + fR +\bar{f}R^2]exp(-(g^2)R) F(R) \]

  where the distances are in atomic units (1 a.u. = 0.529177249 Å) and where e, f, fbar and g can be found in these pages.

  The function F(R) is a smooth cutoff function. In the top right-hand corner of each parametrization file are two quantities,

  \[R_{cut} \text{ and } SCREENL \]
  . The cutoff function has the form

  \[F(R) = \frac{1}{(1 + exp((R - R_{cut} + 5SCREENL)/SCREENL}, \ R < R_{cut}\]

  \[F(R) = 0, R > R_{cut}\]

  At the moment SCREENL is 0.5 for all parameters, so the width of the smoothing region is approximately 5 a.u.

• The parameters for vanadium have a slightly different form than those for the other elements, as explained in the text (see the discussion around equation 11).
• Our current generation of tight-binding codes uses the parameter format which we developed for vanadium. This represents a slight change from the original form of the parameters. The new format is discussed in our paper. See the discussion around equation 11. Old tight-binding parameter files may be converted to the new version with a Fortran filter.
• The parameters for the magnetic transition metals (chromium through nickel) were fit to non-magnetic ("paramagnetic") first-principles calculations, again as described in the text.
• All parameters are subject to change as we improve our fits.
• The form of the tight-binding parametrization has changed slightly. Each parameter file now has a header which describes the style of parameterization, the elements in the file, their atomic weights and orbital occupation numbers, and the cutoff ranges for each type of interaction. The idea is to move all parameter-dependent information into the parameter file. More details are available in the documentation for the static program.
  The actual parameters have not changed. If you are using an older version of our tight-binding codes, simply strip off the new header to get a version of the parameters which runs with your code. Note, however, that we recommend upgrading to a newer version of the code.

References:

1. Tight-binding total-energy method for transition and noble metals, Phys. Rev. B Rapid Comm. 50, 14694 (1994).
2. Application of a new tight-binding method for transition metals: manganese, Europhysics. Lett. 31, 537 (1995).
3. Applications of a tight-binding total energy method for transition and noble metals: Elastic Constants, Vacancies, and Surfaces of Monatomic Metals, Phys. Rev. B 54, 4519 (1996).
4. Tight-Binding Parametrization of First-Principles Results in Computational Materials Science, C. Fong, ed. (World Scientific Publishing, Singapore, 1998).
5. Applications of a New Tight-Binding Total Energy Method, Proceedings of the International Symposium on Novel Materials, Bhubaneswar, India, March 3-7, 1997, edited by B.K. Rao (1998), pp. 393-403.
6. Application of a tight-binding total-energy method for Al, Ga, and In, Phys. Rev. B 57 R2013-R2016, (15 Jan 1998).
7. Tight-Binding Hamiltonians for Carbon and Silicon, Tight-Binding Approach to Computational Materials Science, P. E. A. Turchi, A. Gonis, and L. Columbo, eds., MRS Proceedings 491, 221, (Materials Research Society, Warrendale PA, 1998).
8. Ab Initio Based Tight-Binding Hamiltonian for the Dissociation of Molecules at Surfaces, Axel Gross, Matthias Scheffler, Michael J. Mehl and Dimitrios A. Papaconstantopoulos, Phys. Rev. Lett. 82, 1209-12 (1999).
9. Tight-binding study of stacking fault energies and the Rice criterion of ductility in the fcc metals, M. J. Mehl, D. A. Papaconstantopoulos, N. Kioussis, and M. Herbranson, Phys. Rev. B 61, 4894 (2000).
10. ``Energetic, vibrational, and electronic properties of silicon using a nonorthogonal tight-binding model,'' N. Bernstein, M. J. Mehl, D. A. Papaconstantopoulos, N. I. Papanicolaou, M. Z. Bazant, and E. Kaxiras, Phys. Rev. B 62, 4477 (2000).
11. ``The Slater-Koster Tight-Binding Method: A Computationally Efficient and Accurate Approach,'' (preprint) Dimitrios A. Papaconstantopoulos and Michael J. Mehl, to appear in Tight-Binding Hamiltonians and their Applications, P. Turchi, ed. (Springer-Verlag). (Review Article).
12. ``Transferable tight binding parameters for ferromagnetic and paramagnetic iron,'' N.C. Bacalis, D.A. Papaconstantopoulos, M.J. Mehl, and M Lach-hab, Physica B 296, 125 (2001).
13. ``Tight-binding Hamiltonians for realistic electronic structure calculations,'' D. A. Papaconstantopoulos, M. Lach-hab, and M. J. Mehl, Physica B 296, 129 (2001).
14. ``Dynamical properties of Au from tight-binding molecular-dynamics simulations,'' F. Kirchhoff, M. J. Mehl, N. I. Papanicolaou, D. A. Papaconstantopoulos, and F. S. Khan, Phys. Rev. B 63, 195101 (2001). (A hypertext PDF preprint is also available.)
15. ``Structural stability and lattice defects in copper: Ab initio, tight-binding, and embedded-atom methods,'' Y. Mishin, M. J. Mehl, D. A. Papaconstantopoulos, A. F. Voter, and J. D. Kress, Phys. Rev. B 63, 224106 (2001).
16. ``Tight-binding description of the electronic structure and total energy of tin,'' Brahim Akdim, D. A. Papaconstantopoulos, and M. J. Mehl, Phil. Mag. B 82, 47 (2002).

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