(untitled) (Communications in Computational Physics, 2018)
We devise an efficient algorithm for the symbolic calculation of irreducible angular momentum and spin (LS) eigenspaces within the n-fold antisymmetrized tensor product Λ^nV_u, where n is the number of electrons and u = s,p,d,··· denotes the atomic subshell. This is an essential step for dimension reduction in configuration-interaction (CI) methods applied to atomic many-electron quantum systems. The algorithm relies on the observation that each L_z eigenstate with maximal eigenvalue is also an L^2 eigenstate (equivalently for S_z and S^2 ), as well as the traversal of LS eigenstates using the lowering operators L_− and S_−. Iterative application to the remaining states in Λ^nV_u leads to an implicit simultaneous diagonalization. A detailed complexity analysis for fixed n and increasing subshell number u yields run time O(u^3n−2). A symbolic computer algebra implementation is available online.