Electronic coupling calculation and pathway analysis of electron transfer reaction using ab initio fragment-based method. I. FMO-LCMO approach

By making use of an ab initio fragment-based electronic structure method, fragment molecular orbital-linear combination of MOs of the fragments (FMO-LCMO), developed by Tsuneyuki et al. [Chem. Phys. Lett. 476, 104 (2009)], we propose a novel approach to describe long-distance electron transfer (ET) in large system. The FMO-LCMO method produces one-electron Hamiltonian of whole system using the output of the FMO calculation with computational cost much lower than conventional all-electron calculations. Diagonalizing the FMO-LCMO Hamiltonian matrix, the molecular orbitals (MOs) of the whole system can be described by the LCMOs. In our approach, electronic coupling T(DA) of ET is calculated from the energy splitting of the frontier MOs of whole system or perturbation method in terms of the FMO-LCMO Hamiltonian matrix. Moreover, taking into account only the valence MOs of the fragments, we can considerably reduce computational cost to evaluate T(DA). Our approach was tested on four different kinds of model ET systems with non-covalent stacks of methane, non-covalent stacks of benzene, trans-alkanes, and alanine polypeptides as their bridge molecules, respectively. As a result, it reproduced reasonable T(DA) for all cases compared to the reference all-electron calculations. Furthermore, the tunneling pathway at fragment-based resolution was obtained from the tunneling current method with the FMO-LCMO Hamiltonian matrix.