Efficient Algorithm for Many-Electron Angular Momentum and Spin Diagonalization on Atomic Subshells. (15th January 2016) - Mendl, Christian B.
Abstract: We devise an efficient algorithm for the symbolic calculation of irreducible angular momentum and spin (LS) eigenspaces within the n -fold antisymmetrized tensor product ^ n Vu, 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 Lz eigenstate with maximal eigenvalue is also an L 2 eigenstate (equivalently for Sz 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 ^ n Vu 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.