“Easy spin-symmetry-adaptation.” Exploitation of the Clifford algebra unitary group in correlated many-electron theories

An efficient scheme for the generation of spin-symmetry adapted matrix elements required by all correlated many electron wave function methods of electronic structure theory is briefly outlined. Matrix elements can be formulated in the Clifford algebra unitary group representation of Gel’fand-Tsetlin basis, Clifford-Weyl basis, Jeziorski-Paldus-Jankowski basis or determinant basis in order to exploit the U(2n)←↩ U(n) or U(22n)←↩ U(2n) embeddings. The former embedding, which will be the focus of this paper, ensures automatic spin adaptation for open-shell and closed-shell cases and reduces the calculation of complicated matrix elements in terms of U [u(n)] to matrix elements involving U(2n) generators acting on two-box Weyl tableaux. The advantage of such a scheme is that the action of U(2n) generators on two-box U(2n)-modules is essentially a linear combination of Kronecker deltas. This scheme, provides an alternative to Wick’s theorem for the computation of matrix elements and has been implemented with the MathematicaT M computer algebra program.