Skip to main content
SpringerLink
Log in

Transformation of Bloch representation into atomic orbital representation and combined matrix element calculation technique for spatially bounded basis functions in crystals

  • Published:
Journal of Structural Chemistry Aims and scope Submit manuscript

Abstract

A method is proposed for transforming the Hamiltonian from Bloch to atomic function representation. For spatially bounded functions, this is a rigorous method based on solution of a certain algebraic system of equations. Unlike the conventional procedure based on integration over the Brillouin zone, the new method requires knowledge of the matrix elements of the Bloch representation only at several points of the Brillouin zone. The number of these points is determined by the trimming radius for the spatially bounded functions and by the lattice constant. The method can be used for calculating matrix elements in a basis of atomic functions and for reducing computations in matrix element calculations of the Bloch representation for procedures using numerical integration.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. M. J. Frisch, G. W. Trucks, H. B. Schlegel, et al., Gaussian 98, Revision A.11, Gaussian, Inc., Pittsburg, PA (2001).

    Google Scholar 

  2. H. L. Skriver, The LMTO Method. Muffin-Tin Orbitals and Electronic Structure, Springer, New York (1984).

    Google Scholar 

  3. V. M. Tapilin, Zh. Strukt. Khim., 44, 587–592 (2003).

    Google Scholar 

  4. J. C. Slater and G. F. Koster, Phys. Rev., 94, 1498–1524 (1954).

    Article  CAS  Google Scholar 

  5. G. Te Velde and E. J. Baerends, ibid., B44, 7888–7903 (1991).

    Google Scholar 

  6. J. R. A. Collado, J. F. Rico, M. Paniagua, and G. Ramirez, Comp. Phys. Commun., 52, 323–331 (1989).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. G. K. Boreskov Institute of Catalysis, Siberian Branch, Russian Academy of Sciences, Russia

    V. M. Tapilin

Authors
  1. V. M. Tapilin
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Original Russian Text Copyright © 2005 by V. M. Tapilin

__________

Translated from Zhurnal Strukturnoi Khimii, Vol. 46, No. 1, pp. 3–10, January–February, 2005.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Tapilin, V.M. Transformation of Bloch representation into atomic orbital representation and combined matrix element calculation technique for spatially bounded basis functions in crystals. J Struct Chem 46, 1–8 (2005). https://doi.org/10.1007/s10947-006-0001-9

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10947-006-0001-9

Keywords

Search

Navigation