Unrestricted Hartree-Fock model, spin orbitals

Here, occ means occupied and virt means virtual. In the restricted Hartree-Fock model, each orbital can be occupied by at most one a spin and one (i spin electron. That is the meaning of the (redundant) Alpha in the output. In the unrestricted Hartree-Fock model, the a spin electrons have a different spatial part to the spin electrons and the output consists of the HF-LCAO coefficients for both the a spin and the spin electrons. 

One way to overcome this difficulty is to use different orbitals for different spins (DODS model). This technique introduced, into the Hartree-Fock scheme, gave rise to the unrestricted Hartree-Fock model (UHF), the wave-function being written as an open shell single Slater determinant[2) ... 

The field of real numbers is retained for the coefficients, but now each MO is formed by linear combinations of basis functions having either an a spin factor or a. P spin factor. The most graphic name of this model is Different Orbitals for Different Spins (DODS). However, historically, this was the first Hartree-Fbck method to be used which had any of the common constraints removed and so has also come to be known as simply the Unrestricted Hartree Fock model (UHF). Obviously this name should really be used for CGUHF. 

Pople refers to a specific set of approximations as defining a theoretical model. Hence the ab initio or Hartree-Fock models employ the Born-Oppenheimer, LCAO and SCF approximations. If the system under study is a closed-shell system (even number of electrons, singlet state), the constraint that each spatial orbital should contain two electrons, one with a and one with P spin, is normally made. Such wavefunctions are known as restricted Hartree-Fock (RHF). Open-shell systems are better described by unrestricted Hartree-Fock (UHF) wavefunctions, where a and P electrons occupy different spatial orbitals. We have seen that Hartree-Fock (HF) models give rather unreliable energies. 

Sulphur Heterocyclic Radicals.—Most studies in this field have used theoretical methods to derive the spin-density distribution and hyperfine splitting constants. In a few cases the unrestricted Hartree-Fock (UHF) formalism has been applied (PPP approximation). (The inclusion of d-orbitals slightly improved the spin-density results in the p-model. )... 

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