Exploring the Linear Energy Relationships between Activation Energy and Reaction Energy under an Electric Field

Electric-field (EF)-mediated chemistry has recently garnered increasing attention partly owing to its capability to catalyze a broad range of chemical reactions. How the EF affects the kinetics and thermodynamics of target reactions is a critical question. Herein, both density functional theory (DFT) and MP2 calculations suggest that the change of activation energy ΔΔ<i>E</i>^‡ and the change of reaction energy ΔΔ<i>E</i>_rxn under an EF display a linear energy relationship (LER) ΔΔ<i>E</i>^‡ = <i>m</i>ΔΔ<i>E</i>_rxn. This has been tested against several reactions such as S_N2 and proton transfer reactions, including neutral and charged systems and endothermic and exothermic processes. The linear coefficient <i>m</i> approximates to the ratio of the dipole moment change, i.e., Δμ^‡/Δμ_rxn, of the studied reactions. The LER holds well at EF strengths up to ≈1 V/nm but deviates from the DFT-calculated results at larger EFs. Such deviations are mainly caused by the molecular geometry changes under an EF. Systems with larger polarizability experience greater geometry changes under an EF, thus leading to larger deviations. In addition, we propose that the reaction barrier can be predicted by -Δμ^‡<i>F</i> - 0.5Δα^‡<i>F</i>², while it is well approximated by -Δμ^‡<i>F</i> for small EF strengths. The proposed LER and the field-dependent barrier estimation promise broad applicability in EF-mediated chemical reactions.