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I7) |~+6 -*i iAe~ra) , • (~j IB~b~rb) . x,. ~ABOD. • (A ~ lOTCrc). 7). dimf. ~:P'). Finally we sum up the results omitting again the multiplicity indices. -a. geminals using the coefficients of fractional parentage [27, i7], we start with the matrix elements of the geminals. 22) (~')dime. GE01 ( (AaCct), (~a, c~6),(eSe;+)) •GE01 ( (BbDdt+), (~, ~6), (fT~)) Later on from a more general point of view it will turn out, that the factor GEO 5 is even a triple combination of the factors of type GEO I • 47 ~2.
26). 25) are all of the same type and can be proved by a uniform method. We have a term of the form X(S%), qq" the left hand side of these equations, starting now from the S S Sl expression ~Dpq(g)X(q~) we shift the cperation~in X from term to term. 25). 28) Thus X would achieve a similarity transformation between irreducible representations. X(qq) where X(q~) does not depend on q. 25). 36 8. Triansular invariants The most important examples of functions defined on triangles are the molecular three-centre nuclear-attraction integrals.
3) ~ZCa~ACB~c~ACB~ .... 3). 8) have four columns of indices. A direet treatment in the sense of section 6 would lead to a parallelism with the group-theoretical 4jm symbols, which couple four irreducible representations . 15) The collective index eDe counts the multiplicity of the identical reprsentation in the direct product aX b x c X d . 8), which is achieved as follows. Instead by its three vertices! a triangle can be determined by one of its edges and the opposite vertex. The interrelation of the triangle ~i' the edge ~ ' a n d the vertex ~l is expressed by a further topological matrix.