Programs in Physics & Physical Chemistry
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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.
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.
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.
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.
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