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To predict barrier heights at low temperatures, it is not enough to employ highly accurate electronic structure methods. We discuss the influence of quantum tunnelling on the comparison of experimental and theoretical activation parameters (Ea, ΔH‡, ΔG‡, or ΔS‡), since the slope-based experimental techniques to obtain them completely neglect the tunnelling component. The intramolecular degenerate rearrangement of four fluxional molecules (bullvalene, barbaralane, semibullvalene, and norbornadienylidene) were considered, systems that cover the range between fast deep tunneling and small but significant shallow tunnelling correction. The barriers were computed with the composite W3lite-F12 method at the CCSDT(Q)/CBS level, and the tunnelling contribution with small curvature tunnelling. While at room temperature the effect is small (∼1 kJ mol-1), at low temperatures it can be considerable (in the order of tens of kJ mol-1 at ∼80 K).