Tunneling splitting energy vs. tunneling rate constant: An empirical computational corroboration

Abstract

Quantum tunneling in degenerate double-well molecular systems has two mutually exclusive observables: the delocalized, coherent energy splitting ($\Delta$E₀₁) and the localized, decoherent, non-stationary rearrangement rate constant (k). Although incompatible, both depend on similar factors, with sources suggesting linear or quadratic relationships. Our comparison between the experimental $\Delta$E₀₁ values and small-curvature tunneling computed k values supports the quadratic model. The agreement between experimental and computational results also supports the applied tunneling protocol. We discuss how the quadratic formula applies to the decoherent regime, typical in “chemical” tunneling, while the linear model describes quantum probability fluctuations between wells under coherent tunneling.