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Manuscript Title: A Reduce package for exact Coulomb interaction matrix elements.
Authors: N. Bogdanova, H. Hogreve
Program title: R12 INTERACTION MATRIX ELEMENTS
Catalogue identifier: ABBN_v1_0 Distribution format: gz
Journal reference: Comput. Phys. Commun. 48(1988)319
Programming language: Reduce.
Computer: IBM compatible PC, CRAY 1M.
Operating system: MS DOS 3.X, COS 1.15.
RAM: 512K words
Word size: 64
Keywords: Computer algebra, Atomic physics, Coulomb interaction, Inverse interaction, Integrals, Hydrogenic wavefunctions, Slater-functions, Slater-Condon parameters, Condon Shortley coefficients.
Classification: 2.7, 5.
Nature of problem: With atomic physics and quantum chemistry numerous numerical computations and also recent theoretical investigations require the evaluation of the quantum mechanical expectation values for the Coulomb interaction 1/r12 or inverse interaction operator r12 = \|r1 - r2\|. For Slater-functions and hydrogenic wavefunctions such expectation values can in principle be determined exactly. This fact is used in a package of Reduce procedures which calculate the wanted matrix elements and other related quantities of interest in the form of a rational expression (eventually times a square root factor). Since Reduce performs integer arithmetics to arbitrary precision, the results are exact and free of any round-off errors. They can be applied as input to further Reduce manipulations or for high precision floating point calculations in programs written in other programming languages.
Solution method: The strategy for the calculation of the matrix elements of 1/r 12 is wellknown and can be modified appropriately to apply to the inverse operator r 12. Its basic ingredient is the so - called Laplace expansion of 1/r 12. Although a priori this has the form of an infinite series, almost all coefficients involving the angular integrals vanish so that finally the result is reduced to a sum over relatively few terms.
Restrictions: The possibility of using the program on a PC to compute matrix elements for hydrogenic states associated with principal quantum numbers n >= 4 depends heavily on the available memory.
Running time: On the Cray for small quantum numbers 1-10 seconds for <1/r 12>, 2-4 times longer for <r 12; on a PC the running time is of the order of at least some minutes.