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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., Êivva) are introduced. The presented procedure utilizes Löwdin's projection operator method of spin eigenfunction generat
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