An energy decomposition and extrapolation scheme for evaluating electron transfer rate constants: a case study on electron self-exchange reactions of transition metal complexes

Abstract

A simple approach to the analysis of electron transfer (ET) reactions based on energy decomposition and extrapolation schemes is proposed. The present energy decomposition and extrapolation-based electron localization (EDEEL) method represents the diabatic energies for the initial and final states using the adiabatic energies of the donor and acceptor species and their complex. A scheme for the efficient estimation of ET rate constants is also proposed. EDEEL is semi-quantitative by directly evaluating the seam-of-crossing region of two diabatic potentials. In a numerical test, EDEEL successfully provided ET rate constants for electron self-exchange reactions of thirteen transition metal complexes with reasonable accuracy. In addition, its energy decomposition and extrapolation schemes provide all the energy values required for activation-strain model (ASM) analysis. The ASM analysis using EDEEL provided rational interpretations of the variation of the ET rate constants as a function of the transition metal complexes. These results suggest that EDEEL is useful for efficiently evaluating ET rate constants and obtaining a rational understanding of their magnitudes.

Fig. 1. Crossing of two diabatic potential energy surfaces and the relations among V₁₂, λ, ΔG⁰, ΔG^‡, and ΔG^‡_na in the rate constant expressions.

Fig. 2. The entire workflow for obtaining an electron transfer rate constant by EDEEL and the calculation programs used in each procedure.

Fig. 3. A correlation between experimental log₁₀ k_expt and calculated log₁₀ k_calc by EDEEL at the UωB97X-D/Def2-TZVP//Def2-SV(P) level (filled squares) or by the other method (red crosses). The red dotted line represents the diffusion-controlled rate constant.

Fig. 4. Strain energies and interaction energies by ASM analysis at UωB97X-D/Def2-TZVP.

Fig. 5. Changes in mean coordination bond length.