Point group symmetry adaptation in clifford algebra unitary group approach

The symmetry adaptation procedure of Chen et al. [Sciencia Sinica 23 , 1116 (1980)], which can account for the invariance properties of the Hamiltonian with respect to any finite point group G, is both modified and adapted to the Clifford algebra unitary group approach ( CAUGA ). From orthogonal symmetry adapted Mo's, one first constructs a pure configuration many‐electron basis adapted to the chain U( n i ) ⊃ G ⊃ G( s ) in terms of the U( n i ) Gel'fand–Tsetlin ( GT ) basis, where n i is the dimension of the irrep defining a given pure configuration, and G( s ) designates the canonical chain supplying a unique labeling. The pure configuration basis is then coupled to the desired G‐adapted states using the point group Clebsch–Gordan coefficients and the U( n 1 ) ⊂ U( n 1 + n 2 ) ⊂ … ⊂ U( n ) basis by using the permutation group outer‐product reduction coefficients. This basis can be expressed in terms of the U( n ) GT basis by using the U( n ) subduction coefficients ( SAC'S ). The SDC'S are particularly simple for the highest weight states (Hess's) of various subproblems, which can be in turn represented through the U(2 n ) two‐box Weyl tableaux of CAUGA . The non‐ HWS 's are obtained by applying the U( n i ) lowering generators to the HWS 's. In this way we can directly obtain the spin and point group adapted CAUGA basis. The procedure is illustrated on a nontrivial example.