Abstract
The general two-center Dalitz integral of the form: $$I_{if} = \frac{1}{{2\pi ^2 }}\smallint \frac{{dq}}{{q^2 }}\tilde \varphi _f^* (q - \alpha )\tilde \varphi _i (q - \beta )$$ is calculated analytically and numerically for an arbitrary set {i,f} of indices associated with the Fourier transforms\(\tilde \varphi _i (q + \beta )\) and\(\tilde \varphi _f (q - \alpha )\) of exponential-type orbitals. The analytical results for hydrogenic, Sturmian and other related functions, as well as for Slater-type orbitals with an arbitrary quantization axis, are presented as concise, closed expressions. These contain only a few finite summations of easily available quantities, such as Gaunt coefficients, Clausen hypergeometric polynomials of unit argument, spherical harmonics, etc. .... The present closed formulae are also valid for all scaling parameters of the orbitals involved. Furthermore, an additional angular momentum decomposition of the final result can readily be accomplished.
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 callMore From: Zeitschrift für Physik D Atoms, Molecules and Clusters
Disclaimer: 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.
