EXPLICIT FORMULAS FOR THE MATRIX-ELEMENTS OF A SYMMETRIZED COMBINATION OF 2 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) generato rs (also known as a two-electron spin-orbital replacement operator) ar e derived in a spin-orbital basis. [A basis symmetry adapted to the su bgroup U(n)X U(2) of U(2n).] The matrix elements of a single U(2n) gen erator are also determined. Using the above-mentioned matrix elements, all the spin-dependent terms of the Pauli-Breit Hamiltonian can be in cluded into quantum chemistry calculations. The matrix elements are ev aluated by first expressing the spin-orbital states as Yamanouchi-Kota ni states and then applying a graphical form of Wick's theorem and the graphical method of spin algebras.