Unrestricted Hartree—Fock Calculations. I. An Improved Method of Computing Spin Properties

Abstract

Spin properties calculated using a spin-polarized single-determinant wavefunction in the unrestricted Hartree—Fock method can be unreliable because the wavefunction is not a spin eigenstate and contains unwanted spin components. New expressions are derived for the spin properties after the most important of these has been removed by an annihilator. Expressions are given for 〈S2〉 and for the spin- and charge-density functions, all in terms of the unrestricted bond-order matrices for electrons of α spin and of β spin. The cases of orthogonal and nonorthogonal atomic orbitals are included. The role of corresponding orbitals in the derivations is outlined. The results are illustrated by calculations on the pi-electron radicals, allyl, pentadienyl, naphthalene positive and negative ions, and the lowest-energy naphthalene triplet configuration. An estimate is made of the error due to the unwanted components which still remain in the wavefunction, and this will usually be small. A simple, approximate expression for the spin-density function is obtained.