TY - JOUR T1 - Efficient Algorithm for Many-Electron Angular Momentum and Spin Diagonalization on Atomic Subshells AU - Christian B. Mendl JO - Communications in Computational Physics VL - 1 SP - 192 EP - 204 PY - 2018 DA - 2018/04 SN - 19 DO - http://doi.org/10.4208/cicp.281014.190615a UR - https://global-sci.org/intro/article_detail/cicp/11085.html KW - AB -

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^n$$V_u$, where n is the number of electrons and $u$ = s,p,d,··· denotes the atomic subshell. This is an essential step for dimension reduction in configuration-interaction (CI) methods applied to atomic many-electron quantum systems. The algorithm relies on the observation that each $L_z$ eigenstate with maximal eigenvalue is also an $L^2$ eigenstate (equivalently for $S_z$ and $S^2$ ), as well as the traversal of LS eigenstates using the lowering operators $L_−$ and $S_−$. Iterative application to the remaining states in $Λ^n$$V_u$ leads to an implicit simultaneous diagonalization. A detailed complexity analysis for fixed $n$ and increasing subshell number $u$ yields run time $\mathcal{O}$($u^{3n−2}$). A symbolic computer algebra implementation is available online.