Unitary group approach to the many-electron correlation problem: spin-dependent operators

Following a brief overview of the unitary group approach (UGA) to the many-electron correlation problem, focusing in particular on Shavitt’s contribution via his graphical unitary group approach, we present a short review of our earlier results for the evaluation of matrix elements (MEs) of unitary group generators or products of generators in the electronic Gel’fand–Tsetlin basis with the help of spin-adapted second-quantization-like creation and annihilation vector operators at the unitary group level. This formalism is then extended to a spin-dependent case that is required when accounting for relativistic effects by developing explicit expressions for MEs of spin-orbital creation and annihilation operators in terms of the standard spin-adapted UGA basis. This leads naturally to a segmentation of these MEs and enables the evaluation of spin-dependent one-body operators while relying largely on the segment values of the standard spin-independent UGA.