@Article{CiCP-19-192,
author = {Christian B. Mendl},
title = {Efficient Algorithm for Many-Electron Angular Momentum and Spin Diagonalization on Atomic Subshells},
journal = {Communications in Computational Physics},
year = {2018},
volume = {19},
number = {1},
pages = {192--204},
abstract = {<p style="text-align: justify;">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$$V_u$, where n is the number of electrons and $u$ = s,p,d,··· denotes the
atomic subshell. This is an essential step for dimension reduction in configuration-interaction
(CI) methods applied to atomic many-electron quantum systems. The algorithm
relies on the observation that each $L_z$ eigenstate with maximal eigenvalue is
also an $L^2$ eigenstate (equivalently for $S_z$ and $S^2$ ), as well as the traversal of LS eigenstates
using the lowering operators $L_−$ and $S_−$. Iterative application to the remaining
states in <span style="text-align: justify;">$Λ^n$$V_u$</span> leads to an implicit simultaneous diagonalization. A detailed complexity
analysis for fixed $n$ and increasing subshell number $u$ yields run time&nbsp;$\mathcal{O}$($u^{3n−2}$). A
symbolic computer algebra implementation is available online.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.281014.190615a},
url = {http://global-sci.org/intro/article_detail/cicp/11085.html}
}