Open shell species, potential energy

So far there have not been any restrictions on the MOs used to build the determinantal trial wave function. The Slater determinant has been written in terms of spinorbitals, eq. (3.20), being products of a spatial orbital times a spin function (a or /3). If there are no restrictions on the form of the spatial orbitals, the trial function is an Unrestricted Hartree-Fock (UHF) wave function. The term Different Orbitals for Different Spins (DODS) is also sometimes used. If the interest is in systems with an even number of electrons and a singlet type of wave function (a closed shell system), the restriction that each spatial orbital should have two electrons, one with a and one with /3 spin, is normally made. Such wave functions are known as Restricted Hartree-Fock (RHF). Open-shell systems may also be described by restricted type wave functions, where the spatial part of the doubly occupied orbitals is forced to be the same this is known as Restricted Open-shell Hartree-Fock (ROHF). For open-shell species a UHF treatment leads to well-defined orbital energies, which may be interpreted as ionization potentials. Section 3.4. For an ROHF wave function it is not possible to chose a unitary transformation which makes the matrix of Lagrange multipliers in eq. (3.40) diagonal, and orbital energies from an ROHF wave function are consequently not uniquely defined, and cannot be equated to ionization potentials by a Koopman type argument. 

Potential Energy Surfaces for Open Shell Species Hergiorgio Casavecchia... 

POTENTIAL ENERGY SURFACES FOR OPEN SHELL SPECIES... 

Semiempirical MNDO calculations have been carried out on model pyrylium and thiopyrylium systems (88MI1). The calculated HOMO-LUMO gap in the gas phase correlates well with experimental absorption maxima obtained in solution. Ionization potentials and electron affinities predicted by Koopmans theorem with MNDO orbital energies do not track the observed trends in the experimental redox values. In contrast these are paralleled by the trends predicted by A// values calculated by MNDO and AMI for the open-shell and closed-shell species. 

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