. 𝑅 m is the equilibrium value of 𝑅 and 𝑆 *. * is the vibrational coupling at the distance 𝑅 m . 𝛼 is the decay parameter . The behavior of proton donor and acceptor has been approximated as an ideal harmonic oscillator with mass 𝑀 and frequency 𝛺, i.e., the 'R-mode' termed by Hammes-Schiffer and co-workers , with the average distance satisfying ⟨𝑅 -𝑅 m ⟩ = 0. The strong dependence of both 𝐸 * * and 𝜆 !" ! 44 on ∆𝐺 /0& discussed above indicates that water molecules in the first hydration layer of cations are the proton donors in CO2RR. The attractive cation-water interaction (∆𝐺 /0& < 0) is expected to increase the average distance between proton donor and acceptor since cations are located at the outer Helmholtz plane (OHP) of the double layer (Fig. ). We denote the extra donor-acceptor distance caused by cations as 𝛿𝑅, and then 𝑆 *. should contain an additional exponential decay term due to the interaction between cations and proton donor: