Spin-Unrestricted Calculations in Quantum Chemistry

The unrestricted complete active space self-consistent field (UCASSCF) function is defined, and a proof that a UCASSCF eigenfunction of the spin operator S2 is a CASSCF function is given. The spin-contamination for an unrestricted Hartree-Fock (UHF) function is evaluated by using Araki angle operators, and the UHF function is then projected on the restricted open-shell Hartree-Fock (ROHF) space. The present analysis has deep consequences since it implies that the only non-spin-contaminated UHF functions are the ROHF functions. This is illustrated in a calculation of the spin density of He2+.