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.