Isotope effect on the hyperfine splittings of the deuteriobenzene anions: An example of the dynamic Jahn–Teller effect

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Abstract
The vibronic wavefunctions and energy levels of the benzene, benzene−1−d, benzene−2,6−d2, benzene−1,4−d2, and benzene−1,3,5−d3 anion radicals have been obtained and used to determine the effect of deuterium substitution on the degenerate energy levels and spin densities of the benzene anion. It is shown that a dynamic Jahn−Teller effect treatment is required for these systems to obtain a quantitative interpretation of the consequences of deuterium substitution. The ground vibronic states of benzene− and benzene−1,3,5−d3− are degenerate. In benzene−2,6−d2−, the symmetric state (A1 under C2v) is 22 cm−1 below the antisymmetric state (B1 under C2v). In benzene−1−d− and benzene−1,4−d2−, the antisymmetric states are lower by 9 and 39 cm−1, respectively. The benzene−2,6−d2− and benzene−1,4−d2− hyperfine coupling constants and their temperature dependence calculated using the vibronic wavefunctions and energy splittings are in very good agreement with the experimental values. For benzene−1−d, the experimental splitting is estimated to be 20 cm−1, about twice as large as the calculated value, and agreement between the experimental and calculated hyperfine constants is less satisfactory. The vibronic energy splitting are interpreted in terms of the effect of deuterium substitution on the vibrational potential energies corresponding to the symmetric and antisymmetric electronic states. Calculations of the expectation values of the unpaired electron energy over the neutral molecule and the two anion Born−Oppenheimer state vibrational functions show that changes in the average values of the out−of−plane bending coordinates upon deuteration lead to a splitting of the vibrational potential energies. To a first approximation, the differences among the anions are a function of the unpaired orbital bond orders at the deuterated positions in the two electronic states. If the substituted bond order is large and negative, deuterium substitution increases the vibrational potential energy, but if it is approximately zero, the potential energy is essentially unchanged.