H/D isotope effect in methyl torsional interaction of acetone as calculated by a multicomponent molecular orbital method

We analyzed the H/D isotope effect in the methyl torsional interactions accompanying two methyl internal rotations for acetone $(CH3COCH3)$ and deuterated acetone (⁠$CD3COCD3$ and $CH3COCD3$⁠) in the ground state by means of the multicomponent molecular orbital (MC_MO) method, which directly accounts for the quantum effects of protons and deuterons. Our estimated rotational constants and moments of inertia for $CH3COCH3$ and $CD3COCD3$ agreed well with the experimental results because of the adequate treatment of protonic and deuteronic quantum effects afforded by the MC_MO method. Because the C–D bond distance in the $CD3$ group was shorter than the C–H distance in $CH3$ owing to the anharmonicity of the potential, the difference in potential energy surfaces of $CH3COCH3$⁠, $CD3COCD3$⁠, and $CH3COCD3$ was strongly related to the differences induced in geometrical parameters by the H/D isotope effect. The potential energy obtained by the MC_MO method was estimated as $290.88cm−1$ for $CH3COCH3$⁠, which is in excellent agreement with the experimental results. For $CH3COCD3$⁠, two potential energies were obtained for $CH3$ and $CD3$ internal rotations. The MC_MO method successfully elucidated the H/D isotope effect for methyl-methyl repulsive interactions by allowing the adequate treatment of protonic and deuteronic wave functions. The potential energies and bond distances associated with methyl internal rotation induced by the H/D isotope effect were also controlled by the distribution of wave functions of protons and deuterons.