Direct path integral estimators for isotope fractionation ratios

TL;DR

This paper introduces new estimators for isotope fractionation ratios that simplify calculations by avoiding thermodynamic integration, demonstrated through applications to gas-phase ions and hydrocarbons.

Contribution

The authors derive direct path integral estimators for isotope ratios by reformulating the problem as a particle exchange in the ring polymer partition function, reducing computational complexity.

Findings

Estimators accurately compute isotope ratios in gas-phase systems.

Application to Zundel cation and hydrocarbons shows improved efficiency.

Avoids the need for thermodynamic integration in isotope calculations.

Abstract

Fractionation of isotopes among distinct molecules or phases is a quantum effect which is often exploited to obtain insights on reaction mechanisms, biochemical, geochemical and atmospheric phenomena. Accurate evaluation of isotope ratios in atomistic simulations is challenging, because one needs to perform a thermodynamic integration with respect to the isotope mass, along with time-consuming path integral calculations. By re-formulating the problem as a particle exchange in the ring polymer partition function, we derive new estimators giving direct access to the differential partitioning of isotopes, which can simplify the calculations by avoiding thermodynamic integration. We demonstrate the efficiency of these estimators by applying them to investigate the isotope fractionation ratios in the gas-phase Zundel cation, and in a few simple hydrocarbons.