Gegenbauer expansions for three-electron integrals

摘要

An arbitrary power of vertical bar r(i)-r(j)vertical bar can be expanded in terms of the magnitudes of r(i) and r(j) and Gegenbauer polynomials whose argument is the cosine of the angle between these two vectors. The Gegenbauer expansion has seen little use in the evaluation of three-electron integrals because the Gegenbauer polynomials are not orthogonal when integrated over the angular variables of a spherical coordinate system. It is shown here that this disadvantage is easily overcome and that the resulting formulas are not only simple and compact but also particularly suitable for the application of truncation and/or convergence acceleration schemes. (c) 2005 Wiley Periodicals, Inc.