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

Quantum tunneling in degenerate double-well molecular systems has two mutually exclusive observables: the delocalized, coherent energy splitting ( Δ E 01 ) 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 Δ E 01 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. • Empirical relation between tunneling rate constant and splitting energy in decoherent tunneling. • Findings show conflicts in linear or quadratic models for tunneling rates vs. splitting energies. • Our empirical formula through an unbiased approach aligns with the quadratic theoretical model. • The accuracy between experimental and computational results reflects tunneling protocol quality.