  Accurate path integral Monte Carlo or molecular dynamics calculations of
isotope effects have until recently been expensive because of the necessity to
reduce three types of errors present in such calculations: statistical errors
due to sampling, path integral discretization errors, and thermodynamic
integration errors. While the statistical errors can be reduced with virial
estimators and path integral discretization errors with high-order
factorization of the Boltzmann operator, here we propose a method for
accelerating isotope effect calculations by eliminating the integration error.
We show that the integration error can be removed entirely by changing particle
masses stochastically during the calculation and by using a piecewise linear
umbrella biasing potential. Moreover, we demonstrate numerically that this
approach does not increase the statistical error. The resulting acceleration of
isotope effect calculations is demonstrated on a model harmonic system and on
deuterated species of methane.
