(labeled LPSCl in bottom panel), where a general shift to lower frequencies can be observed in the Li projected density of states of Li compared to Li. The average lithium vibrational frequency in each compound is indicated. (B) The activation barrier dependence of the isotope effect, which is suggested to be a function of the critical phonon occupation numbers (Eq. 3), resulting in an approximately linear function of the frequency ratio (𝜔 7 /𝜔 6 ) and activation barrier according to Eq. 5 (shaded grey region shows the uncertainty in the slope depending on the 𝜔 7 /𝜔 6 ratio) and Eq. 6 (dashed line, using the theoretical value of 𝜔 7 /𝜔 6 , Eq. 1, and 𝐶 = 2). (C) A schematic of two harmonic oscillators embedded within an energetic landscape. Here, the oscillator with the higher frequency (green curve, Li) requires less phonons (i.e. the number of levels above the zeropoint energy) to overcome the energetic barrier than the oscillator with lower frequency (purple curve, Li), which must ultimately attain a higher energy to overcome the same nominal barrier.