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Canonical two‐range addition theorem for slater‐type orbitals
Author(s) -
Gebremedhin Daniel,
Weatherford Charles
Publication year - 2012
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.24319
Subject(s) - slater type orbital , yukawa potential , exponential type , coulomb , physics , spherical harmonics , atomic orbital , mathematical physics , type (biology) , canonical transformation , parametric statistics , range (aeronautics) , quantum mechanics , linear combination of atomic orbitals , mathematics , mathematical analysis , materials science , quantum , ecology , statistics , composite material , biology , electron
Abstract The radial Slater‐type orbitals (STO) ${r^\mu }{e^{ - \alpha r}}$ can be simply obtained by repeated parametric differentiation of the Yukawa Potential $({e^{ - \alpha r}}/r)$ with respect to α. A new compact two‐range addition theorem (AdT) for the STO is herein derived by explicit parametric differentiation of the well‐known Yukawa AdT. The resulting addition formula is combined with the single‐range AdT for solid spherical harmonics $({r^l}Y_l^m(\hat r))$ to present a new AdT for three‐dimensional spherical coordinate STOs. We advance the proposition that this formula is “canonical” in the same sense that the Laplace expansion of the Coulomb potential is considered canonical. We demonstrate how this procedure can be employed for all exponential‐type orbitals. © 2012 Wiley Periodicals, Inc.