Abstract
Formulas are presented for efficient computation of the energy of four-body quantum-mechanical Coulomb systems with wavefunctions consisting of fully correlated exponentials premultiplied by arbitrary integer powers of the interparticle distances. Using the interparticle distances as coordinates, the potential energy is easily expressed in terms of basic integrals involving these wavefunctions. All the contributions to the kinetic energy are also expressible using the same basic integrals, but it is useful to organize the computations in ways that take advantage of the relations between integrals and that illustrate the underlying symmetry of the formulation. The utility of the formulation presented here is illustrated by an “ultra-compact” computation of the ground state of the Li atom.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
L. M. Delves, T. Kalotas, Aust. J. Phys. 21, 1 (1968)
A. J. Thakkar, V. H. Smith, Jr., Phys. Rev. A 15, 1 (1977)
E. A. Hylleraas, Z. Phys. 54, 347 (1929)
F. E. Harris, V. H. Smith, Jr., J. Phys. Chem. A 109, 11413 (2005)
F. E. Harris, V. H. Smith, Jr., Adv. Quantum Chem. 48, 407 (2005)
F. E. Harris, V. H. Smith, Jr., in Symmetry, Spectroscopy and SCHUR, ed. by R. C. King, M. Bylicki, J. Karwowski (Nicolaus Copernicus University Press, Torun, 2006), pp. 127–137
T. K. Rebane, V. S. Zotev, O. N. Yusupov, Zh. Eksp. Teor. Fiz. 110, 55 (1996) [JETP 83, 28 (1996)]
V. S. Zotev, T. K. Rebane, Opt. Spekt. 85, 935 (1998) [Opt. Spect. 85, 856 (1998)]
F. E. Harris, A. M. Frolov, V. H. Smith, Jr., Int. J. Quantum Chem. 100, 1086 (2004)
F. E. Harris, Phys. Rev. A 79, 032517 (2009)
T. K. Rebane, Opt. Spekt. 75, 945 (1993) [Opt. Spect. 75, 557 (1993)]
F. E. Harris, A. M. Frolov, V. H. Smith, Jr., J. Chem. Phys. 119, 8833 (2003)
D. M. Fromm, R. N. Hill, Phys. Rev. A 36, 1013 (1987)
F. E. Harris, Phys. Rev. A 55, 1820 (1997)
E. Remiddi, Phys. Rev. A 44, 5492 (1991)
K. Pachucki, M. Puchalski, E. Remiddi, Phys. Rev. A 70, 032502 (2004)
S. Larsson, Phys. Rev. 169, 49 (1968)
T. Koga, H. Tatewaki, A. J. Thakkar, Phys. Rev. A 47, 4510 (1993)
M. Puchalski, K. Pachucki, Phys. Rev. A 73, 022503 (2006)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer Science+Business Media B.V.
About this chapter
Cite this chapter
Harris, F.E. (2009). Energy Computation for Exponentially Correlated Four-Body Wavefunctions. In: Piecuch, P., Maruani, J., Delgado-Barrio, G., Wilson, S. (eds) Advances in the Theory of Atomic and Molecular Systems. Progress in Theoretical Chemistry and Physics, vol 19. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-2596-8_4
Download citation
DOI: https://doi.org/10.1007/978-90-481-2596-8_4
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-2595-1
Online ISBN: 978-90-481-2596-8
eBook Packages: Chemistry and Materials ScienceChemistry and Material Science (R0)