Direct Elucidation of the Vibrationally Averaged Structure of Benzene: A Path Integral Molecular Dynamics Study

Path integral molecular dynamics (PIMD) simulations for C6H6, C6D6, and C6T6 have been carried out to directly estimate the distribution of projected C–H­(D,T) bond lengths onto the principal axis plane. The average values of raw C–H­(D,T) bond lengths obtained from PIMD simulations are in the order of ⟨R C–H⟩ > ⟨R C–D⟩ > ⟨R C–T⟩ due to the anharmonicity of the potential energy curve. However, the projected C–H­(D,T) bond lengths are almost the same as those reported by Hirano et al. [J. Mol. Struct. 2021, 1243, 130537]. Our PIMD simulations directly and strongly support the explanation by Hirano et al. for the experimental observations that almost the same projected C–H­(D) bond lengths are found for C6H6 and C6D6. The PIMD simulations also predicted the same projected bond lengths for C6T6 as those of C6H­(D)6. In addition to the previous local mode analysis, the present PIMD simulations predicted, for benzene isotopologues, that the vibrationally averaged structure is planar but non-flat.