A few theories exist that relate phonons to the activation barrier directly, and those typically make use of a single phonon mode approximation, which projects ion dynamics onto one effective vibrational frequency. This is justified considering that the aim is to characterize the lowest-order phonon description of 𝐸 A . A theory from Rice and Roth proposes a quadratic relationship between the activation barrier and the oscillating frequency of the mobile ion (𝐸 A ∝ 𝜔 2 ). In this approach, the magnitude of 𝐸 A can be considered as the linear-elastic strain energy of the mobile ion at the transition state. Thus, the phonon frequency effectively characterizes the strength of bonding interactions. Conversely, a theory by Mahan proposes that the activation barrier has a linear frequency dependence (𝐸 A ∝ 𝜔), such that it is proportional to the energy of the phonon mode (ℏ𝜔). Mahan's theory, however, makes use of an ion-phonon coupling parameter that makes it difficult to ascertain the full frequency dependence or to make quantitative predictions. Furthermore, while both theories have their merits, there has not yet been convincing experimental or computational evidence to support one or the other. There appears to be a predominantly linear correlation of 𝐸 A with characteristic phonon frequency (e.g. Debye frequency), but it should be noted that measurement uncertainties, combined with the limited range wherein vibrational frequencies can be tuned, inhibits any overarching conclusion at this point. It should also be noted that these theories do not consider phonon occupation as a relevant factor to define the activation energy. The explicit importance of phonon occupation for ionic transport has recently been suggested, has not yet been tied to the activation barrier.