Excited state double proton transfer of a 1:1 7-azaindole:H2O complex and the breakdown of the rule of the geometric mean: Variational transition state theory studies including multidimensional tunneling

The rule of the geometric mean in rates and kinetic isotope effects has long been used as a criterion for identifying the reaction mechanism, e.g., stepwise vs. concerted, for double proton transfer reactions. Potential energy surfaces of double proton transfers for excited state tautomerization in a 1:1 7-azaindole:H2O complex were generated at the MRPT2//CASSCF(10,9)/6-31G(d,p) level. Variational transition state theory, including multidimensional tunneling approximation, was used to calculate rates and kinetic isotope effects. No intermediates were present along the reaction coordinate. Two protons in the excited state tautomerization were transferred concertedly, albeit asynchronously. Positions of the variational transition states depend very much on the isotopic substitution. The asynchronicity of two protons in flight breaks the underlying assumption of the rule of the geometric mean so that the relation, kHH/kHD ≈ kHD/kDD, is no longer valid in the excited state double proton transfer. Breakdown of the geometric mean rule does not necessarily entail that the reaction mechanism is stepwise; therefore this rule should be used very carefully as a criterion for identification of the mechanism.