A system of many electrons (atom or molecule) possesses symmetry (invariance) under the group of all permutations on the coordinates of these indistinguishable particles. Consequently, the symmetric group Sn (of all permutations on n objects) has many applications in quantum chemistry [You can read about the general theory and application of the symmetric group in the recent book: R. Pauncz, "The Symmetric Group in Quantum Chemistry", CRC Press, 1995].
R.D. Poshusta has studied various aspects and applications of Sn. "Spin- free quantum chemistry" is the theory of electronic structure in which non- essential spin variables are removed. Spin-free SCF theory is the method for performing self-consistent-field calculations on pure multiplet states without employing Slater determinants. Algebrants are a generalization of the determinant and play an imporant computational role in spin-free quantum chemistry.