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\begin{document}

\title{A Recursive Formulation of One-Electron Coupling Coefficients for
Spin-Adapted Configuration Interaction Calculations Featuring Many
Unpaired Electrons}



\author[1]{Mihkel Ugandi}%
\author[1]{Michael Römelt}%
\affil[1]{Humboldt-Universität zu Berlin}%


\vspace{-1em}



  
  \date{May 22, 2024}


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\begin{abstract}
This work reports on a novel computational approach to the efficient
evaluation of one-electron coupling coefficients as they are required
during spin-adapted electronic structure calculations of the
configuration interaction type. The presented approach relies on the
equivalence of the representation matrix of excitation operators in the
basis of configuration state functions and the representation matrix of
permutation operators in the basis of genealogical spin eigenfunctions.
After the details of this connection are established for every class of
one-electron excitation operator, a recursive scheme to evaluate
permutation operator representations originally introduced by Yamanouchi
and Kotani is recapitulated. On the basis of this scheme we have
developed an efficient algorithm that allows the evaluation of all
nonredundant coupling coefficients for systems with 20 unpaired
electrons and a total spin of S = 0 within only a few hours on a simple
Desktop-PC. Furthermore, a full-CI implementation that utilizes the
presented approach to one-electron coupling coefficients is shown to
perform well in terms of computational timings for CASCI calculations
with comparably large active spaces. More importantly, however, this
work paves the way to spin-adapted and configuration driven selected
configuration interaction calculations with many unpaired electrons.%
\end{abstract}%



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