Distance Dependence of Electronic Coupling through Trans Alkyl Chains: Effects of Electron Correlation

Abstract

Electronic coupling between CH2 π donor/acceptor groups at the termini of trans alkyl chains [H2C−(CH2)n-2−CH2, n = 4−16] was investigated using Hartree−Fock (HF) theory, second-order Moller−Plesset perturbation theory (MP2), and density functional theory (DFT). For each method the couplings in the ions were calculated in two ways: (1) the difference in donor/acceptor orbital energies [Koopmans' theorem (KT)] and (2) the difference between the ground state and first excited state energy of the ions (ΔE). The distance dependence of the coupling in anions was found to be independent of the method used, indicating that electron correlation has little effect. In contrast, the distance dependence of the couplings in cations was very dependent on the method used. For cations, couplings from ΔDFT calculations have a weak distance dependence (β < 0.4) similar to that found previously for KT couplings from HF (β ∼ 0.4), while couplings from KT(DFT) and ΔMP2 calculations have a stronger distance dependence (β ∼ 0.6−0.7) similar to that found previously from ΔHF calculations. When energetics are examined, it appears that the weak distance dependence for some of the methods may arise from small energy differences between the donor/acceptor levels and the energies of the filled orbitals. This was confirmed by calculations on a series of trans alkyls with different donor/acceptor groups (NH2, SiH2, PH2). The couplings for the anions have a stronger distance dependence (β ∼ 0.6−0.7) in all of the methods. Finally, it is found that the inclusion of diffuse functions in the basis set does not introduce problems for the calculation of anion couplings by density functional theory, in contrast to ab initio molecular orbital calculations where erratic results are obtained.