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Journal
2003 | 1 | 3 | 432-439
Article title

Two-electron coulomb integrals with minimal group theory. Direct analytic solution and computer program

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EN
Abstracts
EN
A general closed-form analytic solution is developed for two-electron Coulomb integrals such as those that appear in perturbative treatments of multielectron atoms. In developing this solution, no recourse is necessary to group theory, Clebsch-Gordan coefficients, or specialized coordinate transformations: only familiar properties of hydrogenic wavefunctions and standard integrals are employed. One constraint from group theory is adopted for the purpose of establishing an upper limit on an index of summation for computational purposes. An accurate and efficient computer program for evaluating such integrals is made available.
Publisher

Journal
Year
Volume
1
Issue
3
Pages
432-439
Physical description
Dates
published
1 - 9 - 2003
online
1 - 9 - 2003
Contributors
  • Department of Physics, Alma College, 48801, Alma, MI, reed@alma.edu
References
  • [1] I.N. Levine: Quantum Chemistry, 2nd ed., Ch. 9, Allyn and Bacon, Boston, 1974.
  • [2] G. Arfken: Mathematical Methods for Physicists, 3rd ed, Ch. 12, Academic Press, Orlando, 1985.
  • [3] J.C. Slater: “The Theory of Complex Spectra”, Phys. Rev., Vol. 34, (1929), pp. 1293–1322. http://dx.doi.org/10.1103/PhysRev.34.1293[Crossref]
  • [4] J.J.C. Mulder: “Closed-Form Spherical harmonics: Explicit Polynomial Expression for the Associated Legendre Functions”, J. Chem. Educ., Vol. 77, (2000), pp. 244. Note that Mulder's result is in error in that his coefficients b lmk carry an extra multiplicative factor of (1)l. http://dx.doi.org/10.1021/ed077p244[Crossref]
Document Type
Publication order reference
Identifiers
YADDA identifier
bwmeta1.element.-psjd-doi-10_2478_BF02475854
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