Calculations of the molecular interactions in 1,3-dibromo-2,4,6-trimethyl-benzene: which methyl groups are quasi-free rotors in the crystal?

Dibromomesitylene (DBMH) is one of the few molecules in which a methyl group is a quasi-free rotor in the crystal state. Density functional theory calculations – using the Born–Oppenheimer approximation (BOa) – indicate that in isolated DBMH, Me4 and Me6 are highly hindered in a 3-fold potential V3 > 55 meV while Me2 symmetrically located between two Br atoms has a small 6-fold rotation hindering potential: V6 ∼ 8 meV. Inelastic neutron scattering studies have shown that this is also true in the crystal, the Me2 tunneling gap being 390 μeV at 4.2 K and V6 ∼ 18 meV. In the monoclinic DBMH crystal, molecules are packed in an anti-ferroelectric manner along the oblique a axis, favoring strong van der Waals interactions, while in the corrugated bc planes each molecule has a quasi hexagonal environment and weaker interactions. This results in the nearby environment of Me2 only being composed of hydrogen atoms. This explains why the Me2 rotation barrier remains small in the crystal and mainly 6-fold. Using the same potentials in the Schrödinger equation for a –CD3 rotor has allowed predicting a tunneling gap of 69 μeV for deuterated Me2 in very good agreement with inelastic neutron scattering measurements. Therefore, because of a rare and unexpected local symmetry in the crystal, the Me2 rotation barrier remains small and 6-fold and hydrogen nuclei are highly delocalized and not relevant to the Born–Oppenheimer approximation. This and the neglect of spin states explain the failure of density functional theory calculations for finding the rotation energy levels of Me2.