Estimating Reciprocal Partition Functions to Enable Design Space Sampling

Alex Albaugh, Todd R. Gingrich

Research output: Contribution to journalArticlepeer-review


Reaction rates are a complicated function of molecular interactions, which can be selected from vast chemical design spaces. Seeking the design that optimizes a rate is a particularly challenging problem since the rate calculation for any one design is itself a difficult computation. Toward this end, we demonstrate a strategy based on transition path sampling to generate an ensemble of designs and reactive trajectories with a preference for fast reaction rates. Each step of the Monte Carlo procedure requires a measure of how a design constrains molecular configurations, expressed via the reciprocal of the partition function for the design. Though the reciprocal of the partition function would be prohibitively expensive to compute, we apply Booth’s method for generating unbiased estimates of a reciprocal of an integral to sample designs without bias. A generalization with multiple trajectories introduces a stronger preference for fast rates, pushing the sampled designs closer to the optimal design. The single- and multiple-trajectory implementations are illustrated for the escape of a particle from a Lennard-Jones potential well of tunable depth.

Original languageEnglish (US)
JournalUnknown Journal
StatePublished - Nov 19 2019

ASJC Scopus subject areas

  • General

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