  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.
