A mathematical discussion of Pons Viver's implementation of Löwdin's spin projection operator

Recently, the molecular electronic structure theories for efficiently treating static (or strong) correlation in a black‐box manner have attracted much attention. In these theories, a spin projection operator is used to recover the spin symmetry of a broken‐symmetry Slater determinant. Very recently, Pons Viver proposed the practical and exact implementation of Löwdin's spin projection operator (Int. J. Quantum Chem. 2019, 119, e25770). In the present study, we attempt to supply mathematical proofs to Pons Viver's proposals and show a condition for establishing Pons Viver's implementation. Moreover, we explicitly derive the (spin projected) extended Hartree‐Fock (EHF) equations on the basis of the model of common orbitals (ie, closed‐shell orbitals used in the restricted open‐shell Hartree‐Fock (ROHF) method), which was combined by Pons Viver with the EHF method.