Skip to main content
Log in

New general formulas for matrix elements of the free-particle Green's function over Cartesian Gaussians

  • Published:
Theoretica chimica acta Aims and scope Submit manuscript

Summary

In this paper, we present new general analytical formulas for matrix elements of the free-particle Green's function over arbitrary Cartesian Gaussians and explicit formulas for Green's function matrix elements overs, p, d andf Gaussians. One-center matrix elements were obtained by direct integration and two-center matrix elements by differentiation of the integral formula fors Gaussians with respect to the position vectors ofp, d, andf Gaussians. We also present a representative set of numerical values of the matrix elements.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Ostlund NS (1975) Chem Phys Lett 34:419

    Google Scholar 

  2. Ostlund NS private communication noted in Ref. [3]

  3. Levin DA, Fliflet AW, Ma M, McKoy V (1978) J Comput Phys 28:416

    Google Scholar 

  4. Erdélyi, A, Magnus W, Oberhettinger F, Tricomi FG (1954) Tables of integral transforms, Vol 1. McGraw-Hill, New York

    Google Scholar 

  5. Abramowitz M, Stegun IA (eds) (1968) Handbook of mathematical functions, 7th edition. National Bureau of Standards, Washington

    Google Scholar 

  6. Gautschi W (1970) SIAM J Numer Anal 7:187

    Google Scholar 

  7. Gradshteyn IS, Ryzhik IM (1980) In: Jeffrey A (ed) Tables of integrals, series, and products, Corrected and Enlarged Edition, Chapters 8 and 9. Academic Press, New York

    Google Scholar 

  8. Shavitt I (1963) in: Alder B, Fernbach S, Rotenberg M (eds) Methods in computational physics, Vol 2, pp 1–45. Academic Press, New York

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

On leave from Heyrovský Institute

Rights and permissions

Reprints and permissions

About this article

Cite this article

Čársky, P., Hrouda, V. & Polášek, M. New general formulas for matrix elements of the free-particle Green's function over Cartesian Gaussians. Theoret. Chim. Acta 93, 49–59 (1996). https://doi.org/10.1007/BF01113857

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01113857

Key words

Navigation