UNITARY-GROUP TENSOR OPERATOR-ALGEBRAS FOR MANY-ELECTRON SYSTEMS .3. MATRIX-ELEMENTS IN U(N(1)-OF-U(N(1))XU(N(2)) PARTITIONED BASIS(N(2))SUPERSET)

Exploiting our earlier results [J. Math. Chem. 4 (1990) 295-353 and 13 (1993) 273-316] on the unitary group U(n) Racah-Wigner algebra, speci fically designed for quantum chemical calculations of molecular electr onic structure, and the related tenser operator formalism that enabled us to introduce spin-free orbital equivalents of the second quantizat ion-like creation and annihilation operators as well as higher rank sy mmetric, antisymmetric and adjoint tensors, we consider the problem of U(n) basis partitioning that is required for group-function type appr oaches to the many-electron problem. Using the U(n) superset of U(n(1) ) x U(n(2)), n = n(1) + n(2) adapted basis, we evaluate all required m atrix elements of U(n) generators and their products that arise in one - and two-body components of non-relativistic electronic Hamiltonians. The formalism employed naturally leads to a segmented form of these m atrix elements, with many of the segments being identical to those of the standard unitary group approach. Relationship with similar approac hes described earlier is briefly pointed out.