Accelerated Entropic Path Sampling with a Bidirectional Generative Adversarial Network

The role of entropy in mediating
the dynamic outcomes of chemical
reactions remains largely unknown. To evaluate the change of entropy
along post-transition state paths, we have previously developed entropic
path sampling that computes configurational entropy from an ensemble
of reaction trajectories. However, one major caveat of this approach
lies in its high computational demand: about 2000 trajectories are
needed to converge the computation of an entropic profile. Here, by
leveraging a deep generative model, we developed an accelerated entropic
path sampling approach that evaluates entropic profiles using merely
a few hundred reaction dynamic trajectories. The new method, called
bidirectional generative adversarial network–entropic path
sampling, can enhance the estimation of probability density functions
of molecular configurations by generating pseudo-molecular configurations
that are statistically indistinguishable from the true data. The method
was established using cyclopentadiene dimerization, in which we reproduced
the reference entropic profiles (derived from 2480 trajectories) using
merely 124 trajectories. The method was further benchmarked using
three reactions with symmetric post-transition-state bifurcation,
including endo-butadiene dimerization, 5-fluoro-1,3-cyclopentadiene
dimerization, and 5-methyl-1,3-cyclopentadiene dimerization. The results
indicate the existence of a “hidden entropic intermediate”,
which is a dynamic species that binds to a local entropic maximum
where no free energy minimum is formed.