Direct Calculation of Electronic Coupling

However, the Hartree-Fock method may be nsed in a simplified way, which usually gives accurate results. Instead of calculating the total energies, we calculate the ionization energies via Koopmans theorem. According to the latter theorem, we have in the hole case 

Notice that we obtain the total energy difference for a system with N - 1 electrons, as we want. The orbital energies though belong to a system with filled orbitals (N electrons). 

The main cyclohexane part of the molecule serves as a bridge. The two k MOs (27 and 28) are split because of interaction through the bridge. In Fig. 10.15, we see 

In the neutral molecule, the orbital energies correspond to the symmetric (e+) and antisymmetric (e ) orbitals, respectively. The HOMO and HOMO - 1 are symmetric or antisymmetric and their energy difference is A. 

In the case of ET (not hole transfer), we instead use Koopmans theorem for electron affinities. It is weU known that the theorem is less accurate in this case. However, in this particular application, the errors seem to cancel ont very well, according to experience. We thns obtain A as the orbital difference between the LUMO and LUMO -I-1, calculated for the neutral system. 

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