A Local Charge State Fixation Approach for Resolving Charge-Flow Problems in Reorganization Energy Calculations of...

Marcus theory provides a fundamental framework for describing hopping-type charge transport, and donor-bridge-acceptor (D-B-A) dimer models are widely used to evaluate reorganization energies and electron transfer rates. In practice, constrained density functional theory (CDFT) has been extensively employed to construct charge-localized states because the direct evaluation of diabatic states using post-Hartree-Fock (post-HF) methods is computationally demanding. However, in systems containing π-conjugated bridges, maintaining charge-localized states within CDFT can become more difficult, which may affect the evaluated reorganization energies. Standard remedies, including partial geometry fixation and ONIOM-based approaches, do not sufficiently resolve this limitation. In this study, we propose a local charge state fixation (LCSF) method for calculating reorganization energies in D-B-A dimers without imposing explicit constraints on the electronic density. Charged donor and acceptor monomers are optimized independently and subsequently translated and rotated to satisfy the Eckart condition with respect to the corresponding fragments of the neutral dimer. These monomers are then grafted to construct charge-localized dimer geometries, enabling reorganization energy evaluation without charge flow. The method was applied to 1,4-diphenylbutane (PS), trans,trans-1,4-diphenyl-1,3-butadiene (PD), and 1,4-diphenylbutadiyne (PT). For the PS, reorganization energies obtained from LCSF and CDFT are comparable, whereas for PD and PT, LCSF yields consistently larger values, indicating reduced electron delocalization effects. The applicability of the method was further demonstrated using Hartree-Fock and MP2 calculations. In addition, LCSF was applied to zinc oxo cluster dimers, allowing electron transfer rates to be evaluated. Although the method introduces structural constraints, it offers a computationally efficient strategy for reorganization energy calculations in dimer systems, particularly within post-HF frameworks.