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Updated: Dec 2, 2025

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
Published on: April 8, 2020
Generation of spin-adapted and spin-complete substitution operators for (high spin) open-shell coupled cluster of
Nils Herrmann1, Michael Hanrath1
1Institute for Theoretical Chemistry, University of Cologne, Greinstraße 4, 50939 Cologne, Germany.
Abstract:
A rigorous generation of spin-adapted (spin-free) substitution operators for high spin (S = Sz) references of an arbitrary substitution order and spin quantum number S is presented. The generated operators lead to linearly independent but non-orthogonal configuration state functions (CSFs) when applied to the reference and span the complete spin space. To incorporate spin completeness, spectating substitutions (e.g., Êiv va) are introduced. The presented procedure utilizes Löwdin's projection operator method of spin eigenfunction generation to ensure spin completeness. The generated operators are explicitly checked for (i) their linear independence and (ii) their spin completeness for up to tenfold substitutions and up to a multiplicity of 2S + 1 = 11. A proof of concept implementation utilizing the generated operators in a coupled cluster (CC) calculation was successfully applied to the high spin states of the boron atom. The results show pure spin states and small effects on the correlation energy compared to spin orbital CC. A comparison to spin-adapted but spin-incomplete CC shows a significant spin-incompleteness error.
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