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

Abstract

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.

FMO3-LCMO study of electron transfer coupling matrix element and pathway: Application to hole transfer between two tryptophans through cis- and trans-polyproline-linker systems

“…The method was found to give accurate ET couplings over four orders of magnitude along the ET distance when the bond detached atoms (BDA) were not involved or when the minimal atomic basis set was used [16]. Nevertheless, the problem of degraded MO energies caused by BDAs with atomic basis sets larger than minimal set, that had been already pointed out in Ref.…”

“…In the tunneling current analysis [30,31], the ET coupling T DA is expressed as a sum of tunneling current J Ip,Jq between basis FMOs {φ I p } [16,17],…”

“…In a series of papers, we have reported calculations of ET coupling matrix element and ET pathways [16][17][18] from the linear-combination of FMOs (FMO-LCMO) [19] with the two-body correction (FMO2). The method was found to give accurate ET couplings over four orders of magnitude along the ET distance when the bond detached atoms (BDA) were not involved or when the minimal atomic basis set was used [16].…”

Charge-transfer matrix elements by FMO-LCMO approach: Hole transfer in DNA with parameter tuned range-separated DFT

“…Here we outline the FMO-LCMO method [27][28][29][30]. For simplicity, we restrict to the FMO2 version with dimer exchange, although extension to the trimer FMO3 is straightforward [28].…”

“…In this work we put forward another solution by employing the method of fragment molecular orbitals (FMO) [23][24][25][26] and their linear combinations (FMO-LCMO) [27][28][29][30]. The FMO-LCMO method was originally proposed to obtain canonical MOs of large systems [27,28].…”