Explicit formulas for the matrix elements of a symmetrized combination of two U(2n) generators in the unitary-group approach

Explicit segment level formulas (in terms of 3-j and 6-j symbols) for the matrix elements of a symmetrized combination of two U(2n) generators (also known as a two-electron spin-orbital replacement operator) are derived in a spin-orbital basis. [A basis symmetry adapted to the subgroup U(n)×U(2) of U(2n).] The matrix elements of a single U(2n) generator are also determined. Using the above-mentioned matrix elements, all the spin-dependent terms of the Pauli-Breit Hamiltonian can be included into quantum chemistry calculations. The matrix elements are evaluated by first expressing the spin-orbital states as Yamanouchi-Kotani states and then applying a graphical form of Wick’s theorem and the graphical method of spin algebras