Phenomenological manifestations of quantum-mechanical tunneling. I. Curvature in Arrhenius plots

The extent of nonlinearity that quantum-mechanical tunneling, through one-dimensional Eckart barriers, can produce in Arrhenius plots is calculated as a function of barrier height (V*), barrier ``frequency'' (ν*), and temperature range. It is shown that Arrhenius-plot curvature is not a simple function of the extent of tunneling but is favored by high barriers and values of u*=h ν*/k T around 8. The experimental significance of the predicted extent of nonlinearity is discussed in general and with regard to actual cases for which curved Arrhenius plots have been interpreted as manifestations of tunneling.