Consistency, Cancellation, and Experiment in Quasi-Harmonic Thermochemistry

Abstract

For weakly bound molecular complexes, the Gibbs energy is often limited less by the electronic interaction energy, now computed to near chemical accuracy, than by the statistical-mechanical treatment of their low-frequency intermolecular vibrations. The standard remedy, Grimme’s quasi-harmonic correction, rescales the entropy of these modes toward a free-rotor limit while leaving their energy harmonic; because both derive from the same partition function, this is thermodynamically inconsistent. Applied consistently to energy and entropy, the correction largely cancels over the dominant intermolecular modes, whereas the entropy-only form leaves a one-sided shift that grows with system size. We test this against experiments: carboxylic acid dimerization, methanol vapor association, and sulfuric acid–ammonia nucleation in the CLOUD chamber. The entropy-only correction departs from experiment in all three cases, while the plain harmonic treatment matches the dimerization data and, supplemented by a physically grounded anharmonic term, the measured alcohol vapor properties and nucleation barriers. For such complexes, thermodynamic consistency is a prerequisite that no empirical entropy correction can replace.