Direct ab initio dynamics calculations for rates and the kinetic isotope effects of multiproton transfer in ClONO2+HCl→HNO3+Cl2 reactions with water clusters: Breakdown of the rule of the geometric mean

We performed high-level quantum mechanical calculations and direct ab initio reaction dynamics calculations for multiple proton transfers in ClONO2+HCl -> HNO3+Cl-2 with water clusters containing one to two water molecules, which can be used as a model of the reactions occurring on ice surface in stratospheric clouds. The energy barriers of these reactions depend on the number of water molecules involved. Two and three protons in these reactions with one and two water molecules, respectively, were transferred concertedly and asynchronously. The potential energy barrier at the MP2/6-311++(3df,3pd)//MP2/6-31G(d,p) level was 4.8 kcal/mol for the triple proton transfer involving two water molecules with a rate constant of 1.6x10(3) s(-1) at 197 K. The potential energy curve near the saddle points was very flat and the tunneling effect on the proton transfer was negligible. The primary HH/DH kinetic isotope effect for the double proton transfer involving one water molecule was lower than unity due to the enhanced force constant at the transition state. The rule of the geometric mean for the concerted proton transfer does not hold in these reactions because the zero-point energy changes of each proton in flight at the transition state are not the same in the highly asynchronous processes.