Estimating Reciprocal Partition Functions to Enable Design Space Sampling

TL;DR

This paper introduces a novel Monte Carlo sampling method using reciprocal partition function estimates to efficiently explore chemical design spaces for fast reaction rates, demonstrated on toy models.

Contribution

It presents a new approach combining transition path sampling with Booth's method to unbiasedly estimate reciprocal partition functions for design optimization.

Findings

Effective sampling of designs with faster reaction rates.

Application to Lennard-Jones and tetrahedral cluster models.

Closer approximation to optimal designs with multiple trajectories.

Abstract

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. We illustrate the methodology on two toy models of increasing complexity: escape of a single particle from a Lennard-Jones potential well of tunable depth and escape from a metastable tetrahedral cluster with tunable pair potentials.