Taylor expansions are commonly used in physics to test the functional dependence of experimental parameters of a theory. Since different phonon-based theories of the activation barrier have different frequency derivatives, i.e. (∂ω 𝐶 /𝜕𝜔) = 𝐶𝜔 , this is a simple way to see if they can plausibly describe the observed isotope effect Δ𝐸 A .