Molecular orbital analysis in evaluation of electron-transfer matrix element by Koopmans' theory

There are several approaches to evaluation of an electron-transfer (ET) matrix element. Among them, Koopmans' theory is a relatively simple one and can be used for large molecules. However, a limitation of this method is the application to some cases of a small donor-acceptor distance. In such cases, Koopmans' theory has been found to behave badly. The reasons of the failure are discussed in the present work. Investigation shows that the two orbitals included must be properly selected in evaluating the ET matrix element. It has been concluded that the sum of two relevant orbitals should be localized on the donor (acceptor), but the difference between them should be localized on the acceptor (donor). Different types of ET systems have been selected to show how to correctly employ Koopmans' theory to small donor-acceptor distance cases. According to our work, one can find what is the reason leading to the failure of Koopmans' theory, and it is suggested that such failures can be avoided by tracing the energy change of the frontier molecular orbitals against the donor-acceptor distance.