Molecular Orbital Analysis in Evaluation of Electron-Transfer Matrix Element by Koopmans' Theory

Abstract

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.

Theoretical study of electron transfer in uranyl(VI)–uranyl(V) complexes in solution

“…(13) and (14), H ij = 〈φ i | H |φ j 〉 ( i , j = r, p), S rp = S pr = 〈φ i |φ j 〉, and H is the electronic Hamiltonian of the system. In applying KT 6, the restricted SCF method is calculated at the nuclear configuration of the transition state. The two pertinent molecular orbitals to calculate V rp should satisfy the following condition: the sum and difference of them are localized in donor or acceptor, respectively.…”

“…The reactions 2–4 belong to the inner‐sphere mechanism. In this study, we will calculate the electronic coupling matrix element with two‐state model (TM) 5 and Koopmans' theorem (KT) 6. The diabatic potential energy curves are obtained using linear reaction coordinate.…”

Thermodynamics for nonequilibrium solvation and numerical evaluation of solvent reorganization energy

“…A correct calculation of values of V DA is crucial in understanding the reaction type. Koopmans' theorem (KT) [2,26,27] is adopted to compute V DA and the transition state. Although KT approach works badly in estimating V DA for a short range ET, it works well in the case of long-distance ET [26] .…”

“…Koopmans' theorem (KT) [2,26,27] is adopted to compute V DA and the transition state. Although KT approach works badly in estimating V DA for a short range ET, it works well in the case of long-distance ET [26] . In KT approach, the value of V DA for an anion system is simply approximated as one half of the energy gap between the lowest unoccupied molecular orbital (LUMO) and the next lowest unoccupied molecular orbital (abbreviated as LUMO+1) of the neutral molecule in the transition state.…”

“…Because the accurate determination of the ET reaction path for an even small system is not practicable at present, we apply the linear reaction coordinate R to describing the nuclear configuration variation [22,26] . The nuclear rearrangement along the R can be expressed as Employing the KT approach, together with the linear reaction coordinate method, we calculate a series of eigenvalue gaps between LUMO and LUMO+1 of the neutral system Bp-spacer-Np along the reaction coordinate R. The results are given in Figure 1.…”