Estimation of frequency factors for the calculation of kinetic isotope effects from classical and path integral free energy simulations

We use the modified Bigeleisen-Mayer equation to compute kinetic isotope effect values for non-enzymatic phosphoryl transfer reactions from classical and path integral molecular dynamics umbrella sampling. The modified form of the Bigeleisen-Mayer equation consists of a ratio of imaginary mode vibrational frequencies and a contribution arising from the isotopic substitution's effect on the activation free energy, which can be computed from path integral simulation. In the present study, we describe a practical method for estimating the frequency ratio correction directly from umbrella sampling in a manner that does not require normal mode analysis of many geometry optimized structures. Instead, the method relates the frequency ratio to the change in the mass weighted coordinate representation of the minimum free energy path at the transition state induced by isotopic substitution. The method is applied to the calculation of O-16/18 and S-32/34 primary kinetic isotope effect values for six non-enzymatic phosphoryl transfer reactions. We demonstrate that the results are consistent with the analysis of geometry optimized transition state ensembles using the traditional Bigeleisen-Mayer equation. The method thus presents a new practical tool to enable facile calculation of kinetic isotope effect values for complex chemical reactions in the condensed phase.

Automated summary

We used the modified Bigeleisen-Mayer equation to calculate kinetic isotope effect values for non-enzymatic phosphoryl transfer reactions. The modified equation includes the ratio of vibrational frequencies and the effect of isotopic substitution on the activation free energy. We developed a practical method to estimate the frequency ratio correction directly from umbrella sampling, which avoids the need for normal mode analysis. This method provides a new tool for calculating kinetic isotope effects in complex chemical reactions in the condensed phase.