Solid harmonics addition theorem

The second line made use of the fact that V C/m(r) = 0, and the third line used Eq. (1.27). This result is known as the addition theorem of solid harmonics. Applying this same procedure to the other harmonics produces... [Pg.20]

Abstract A new compact two-range addition theorem for Coulomb Sturmians is presented. This theorem has been derived by breaking up the exponential-type orbitals into convenient elementary functions the Yukawa potential (e /r) and evenly-loaded solid harmonics, for which translation formulas are... [Pg.71]

Using the addition theorem for regular solid harmonics... [Pg.25]

Recalling the addition theorem for regular solid harmonics (Eq. [63]), we see that a multipole expansion centered at a can be translated by a vector t to a new center A = a — t as... [Pg.27]

The next step in the derivation of the multipole expansion of the two-electron integrals is to separate the electronic coordinates according to (9.13.4). Invoking the addition theorem for the regular solid harmonics [24]... [Pg.407]

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