Abstract
Standard bipolar expansions contain radial functions Jl1l2 L(r1, r2, R) which depend on three variables, r1, r2, R. Using representations of Bessel functions as series of Laguerre polynomials, the J's are expanded in terms of functions of the individual variables. As a result, the inverse distance between two points is brought into the form r12−1 = ∑ nlllml ∑ n2l2m2 Fn1l1m1, n2l2m2(R, θ, Ψ) Yl1m1(θ1, φ1)fn1l1(r1)Yl2m2(θ2, θ2)fn2l2(r2). This modified bipolar expansion is used to derive expressions for multicenter electron repulsion and nuclear attraction integrals. The method is particularly suitable for Gaussian orbitals expressed with spherical harmonics and yields compact expressions directly. For Slater-type orbitals, the multicenter energy integrals appear as series involving only integrals of the two-center overlap type. The one-center and multipole limits of the bipolar expansion are examined.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
