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

Abstract

Path integral molecular dynamics (PIMD) simulations for C 6 H 6 , C 6 D 6 , and C 6 T 6 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. 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 C 6 H 6 and C 6 D 6 . The PIMD simulations also predicted the same projected bond lengths for C 6 T 6 as those of C 6 H(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.

Nuclear quantum and H/D isotope effects on aromaticity: path integral molecular dynamics study

“…For example, several groups and we have reported that NQEs of hydrogen nuclei enhance the hydrogen bond strength and facilitate proton transfer reactions. [19][20][21][22][23][24] Furthermore, we have also demonstrated that considering the NQEs is indispensable for the analysis of the H/D isotope effects. 24 The NQEs of heavier atoms, such as carbon, have not been focused because their nuclei are much heavier than electrons.…”

“…[19][20][21][22][23][24] Furthermore, we have also demonstrated that considering the NQEs is indispensable for the analysis of the H/D isotope effects. 24 The NQEs of heavier atoms, such as carbon, have not been focused because their nuclei are much heavier than electrons. However, several recent studies have pointed out that the NQEs are also important when calculating the electronic structures of carbon atoms.…”

“…Although aromatic rings tend to become flat and are considered rigid, recent theoretical studies have revealed that even the C 6 -ring framework of benzene is not rigid but highly flexible. [11][12][13] Thus, several groups have analyzed the aromaticity of molecule, taking thermal fluctuations into account with molecular dynamics (MD) simulations. Cysewski suggested that structural distortions arising from the normal mode may have an impact on the delocalization of p electrons in benzene, even at room temperature.…”