The expectation value of the spin operator Ŝ2 as a diagnostic tool in coupled cluster theory: The advantages of using UHF-CCSD theory for the description of homolytic dissociation

Coupled cluster (CC) theory carried out with a spin-unrestricted Hartree–Fock (UHF) reference wave function suffers less from spin contamination because infinite order electron correlation effects covered by the CC method in question reduce spin contamination. For example, UHF-CCSD, contrary to UHF, is not contaminated by a S+1 state. However, the value of 〈Ŝ2〉CCSD, is strongly influenced by the response of the UHF-CCSD wave function on the spin contamination present at UHF and, therefore, adopts a relatively large value. A reliable diagnostic tool correctly reflecting the influence of spin contamination on the UHF-CCSD energy is obtained by just considering the energy related part of 〈Ŝ2〉CCSD.