Racah’s normalization

To remove the constant fraction in front of each term, the solid harmonics in Racah s normalization are used ... 

To develop the multipole expansion of the two-electron integral (9.13.1), we invoke the addition theorem for the spherical harmonics (7.3.3). In Racah s normalization of the spherical harmonics (6.4.10), the addition theorem takes the form... 

It should be realized that the real regular solid harmonics Rj O ) and f (r) introduced here differ from the real solid harmonics Si r) of Section 6.4.2. Thus, whereas the real functions in Section 6.4.2 were obtained by a unitary transformation of the complex ones (in Racah s normalization), the transformation in (9.13.45) and (9.13.46) is not unitary. It is adopted here since it leads to simpler expressions for the multipole expansions. 

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