Hartree-Fock theory half-electron

DFT has come to the fore in molecular calculations as providing a relatively cheap and effective method for including important correlation effects in the initial and final states. ADFT methods have been used, but by far the most popular approach is that based on Slater s half electron transition state theory [73] and its developments. Unlike Hartree-Fock theory, DFT has no Koopmans theorem that relates the orbital energies to an ionisation potential, instead it has been shown that the orbital energy (e,) is related to the gradient of the total energy E(N) of an N-electron system, with respect to the occupation number of the 2th orbital ( , ) [74],... 

Note this resembles the (iV-particle) Fock operator that appears in Hartree-Fock theory, but the contribution of the two-electron term is only half the normal contribution in the Fock operator. However, if we consider making the energy stationary w.r.t. variations in the reference, we must also consider the second term in Eq. (34), where we find... 

Bakhshi and Ladik [27] used ab initio Hartree-Fock crystal orbital theory and a geometry derived from that of isothianaphthene (3) with an inter-ring distance of 1.49 A, to calculate the band gaps of 1 (4.52 eV) and 12 (8.14 eV), both of which are much too high, along with other electronic properties. The observation that the band gap of 1 is half that of 12 is mirrored in these calculations. 

An approach for treating open-shell molecular systems by a closed-shell formalism which utilizes the similarity between the SCF equations (see Density Functional Theory (DFT), Hartree Fock (HF), and the Self-consistent Field) and those for a fictitious closed-shell system in which the odd electron is replaced by two half-electrons. 

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