Efficient Algorithm for Many-Electron Angular Momentum and Spin Diagonalization on Atomic Subshells (Communications in Computational Physics, 2018)
We devise an efficient algorithm for the symbolic calculation of irreducibleangular momentum and spin (LS) eigenspaces within the $n$-fold antisymmetrized tensorproduct $Λ^n$$V_u$, where n is the number of electrons and $u$ = s,p,d,··· denotes theatomic subshell. This is an essential step for dimension reduction in configuration-interaction(CI) methods applied to atomic many-electron quantum systems. The algorithmrelies on the observation that each $L_z$ eigenstate with maximal eigenvalue isalso an $L^2$ eigenstate (equivalently for $S_z$ and $S^2$ ), as well as the traversal of LS eigenstatesusing the lowering operators $L_−$ and $S_−$. Iterative application to the remainingstates in $Λ^n$$V_u$ leads to an implicit simultaneous diagonalization. A detailed complexityanalysis for fixed $n$ and increasing subshell number $u$ yields run time $\mathcal{O}$($u^{3n−2}$). Asymbolic computer algebra implementation is available online.