Entropic Path Sampling
Entropic path sampling (EPS) was developed by our group as a trajectory-based protocol to quantify how configurational entropy varies along a reaction path, especially after the transition state, by harvesting ensembles of snapshots from quasiclassical direct-dynamics trajectories, slicing them into structural windows (e.g., by forming-bond length), and computing entropy with an internal-coordinate, histogram-based estimator using the mutual-information spanning tree. The resulting −TΔS profile reveals “entropic traps” and allows one to distinguish long-lived dynamic intermediates from rigorously defined entropic intermediates (free-energy minima that arise from entropy rather than potential-energy wells). EPS has been benchmarked on cyclopentadiene dimerization, where it captures subtle (≤3 kcal·mol⁻¹) entropic features that normal-mode (harmonic) analysis misses or reverses in sign, demonstrating the value of trajectory ensembles and anharmonic entropy estimates for post-TS bifurcations and selectivity analysis.
An accelerated variant, BGAN-EPS, uses a bidirectional generative adversarial network to augment configuration distributions so that converged entropic profiles can be recovered from only a few hundred trajectories (e.g., ~124 versus a 2,480-trajectory reference), enabling routine application to complex systems. Beyond speedups, BGAN-EPS also uncovered a “hidden entropic intermediate”, a dynamically trapped species at a local entropic maximum without a corresponding free-energy minimum, highlighting how entropy can mediate outcomes on otherwise downhill surfaces.
The software code:
https://github.com/rshin1209/bgan_eps/
https://github.com/ZJYgrp/Entropic_Path_Sampling
Publications:
https://pubs.acs.org/doi/abs/10.1021/acs.jpcb.3c01202
https://pubs.acs.org/doi/10.1021/acs.jpclett.1c03116
https://pubs.acs.org/doi/10.1021/acs.jctc.4c01138?ref=recommended