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ACB~ By the choice of the fixed numbers ~i ~ we have to take care that Rj~R k if ~ j ~ & . Since this mapping is biJective, we have ~ = ~ A . Therefore the triangular SA~C coefficients of the set ~ are equal to the ordinary SALC coefficients of the set R: In principlejthis relation would allow the total elimination of the triangles ~ by the vectors R. 8)# an integral with the three centres Ak, , and can be regarded as a function of one vector ~ . Although this interpretation is valid, it might be confusing.
Three-centre nuclear attraction integrals Thedescription of the three-centre integrals is complicated by the following dilemma: The theorem can be formulated in two different versions, the more effective of which being at the same time the more difficult. Because of the translation invariance~only the internal coordinates of the concerned triangle can appear; but there remain many possibilities o f choosing distances and internal angles. Furthermore different choices may be appropriate to different radial functions, GTOs or STOs for instance.
4) ensures the regular behavior for ~ = ~ . 3). 3) by 6J symbols. 3) yields the simple conjugation relation: