First, it should be noted that the quantity (𝜔 ̅ 7 -𝜔 ̅ 6 ) is negative, meaning that (𝜕𝐸 A /𝜕𝜔 ̅ 6 ) must also be negative for Δ𝐸 A to be positive. Considering the theory of Rice and Roth, where the activation barrier can be written as 𝐸 A = 𝐴𝜔 2 (𝐴 is a frequency-independent factor), the derivative (𝜕𝐸 A /𝜕𝜔) = 2𝐴𝜔 is still positive. Thus, the Rice and Roth theory cannot explain the observed isotope effect as it predicts Δ𝐸 A should decrease. This is not surprising since the frequency in the Rice and Roth model effectively describes the force constant 𝐾, which is constant during isotopic substitution. In the theory by Mahan, the activation barrier can be written as 𝐸 A = 𝜆ℏ𝜔, which results in (𝜕𝐸 A /𝜕𝜔) = 𝜆ℏ if the phonon-ion coupling constant 𝜆 is frequency-independent. In this case, Mahan's theory also cannot explain the increase in Δ𝐸 A , however the true nature of 𝜆 and its frequency dependence are not known at this time. Nevertheless, in neither the Rice and Roth theory or Mahan theory is there any indication that Δ𝐸 A should also depend on the inherent magnitude of a reference 𝐸 A .