On the Unrestricted Hartree–Fock Wavefunction

The unrestricted Hartree–Fock (UHF) wavefunction is analyzed and interpreted in configuration-interaction (CI) language. The results of the present study are as follows. (i) The UHF wavefunction includes only one type of the singly excited configurations [Eq. (20)], and thus the correlation effects included are very limited ones, compared with the usual CI treatment. (ii) The weight of the lowest contaminating spin function, included in the UHF wavefunction, decreases with increasing spin multiplicity. (iii) The annihilation of the lowest contaminating spin function little affects the electron density distributions and other physical quantities, the operators of which commute with the annihilation operator. (iv) In the UHF method, the “spin-appearing” (spin-polarization and spin-delocalization) mechanisms are clearly divided, and an approximate method to separate these contributions is generalized, and some discussions about spin annihilation are made.