All Paths All at Once: A Quantum Monte Carlo and Neural Committor Approach to Reaction Pathway Search

Chien-Chai Chang

physics.chem-phOct 29, 2026

All Paths All at Once: A Quantum Monte Carlo and Neural Committor Approach to Reaction Pathway Search

Authors: Chien-Chai Chang

Organizations: Department of Engineering and System Science, National Tsing Hua University (NTHU), Hsinchu City, 300044, Taiwan

Abstract

Locating competing reaction pathways is difficult when potential-energy gradients are unavailable. Here we present tReax_expedition, an energy-only approach combining coupled Monte Carlo exploration, stochastic quench labelling and restrained continuation. Exploration identifies connected states, while continuation resolves candidate channels and records sampled chain maxima. Single-search benchmarks on three two-dimensional potentials recovered an intermediate and competing routes without transition-state guesses. For eight of nine gas-phase reactions on GFN2-xTB, sampled chain maxima differed from independently refined saddle energies by less than 0.76 kJ/mol. Alanine dipeptide instead revealed incomplete conformational relaxation, showing that route connectivity can persist despite structural and energetic errors. Neural committor learning and local straddling-pair sampling connect the resulting paths to transition-region sampling, although molecular shooting diagnostics indicate limited committor calibration. These results show how energy-only exploration and continuation recover candidate pathways, while distinguishing route connectivity from geometric localization, barrier resolution and finite-temperature transition statistics.

Figures & tables

Figure 1: Recovery of an intermediate and competing reaction channels. a , Proton transfer coupled to a harmonic bath. b , Müller–Brown potential. c , Two-path potential. Grey curves trace retained continuation nodes over potential-energy contours; blue circles denote quench-label crossings, orange diamonds the highest-energy chain nodes (labelled Chain top node) and black crosses the reference saddles. Dashed lines are the $q=1/2$ contours of numerical diffusion references, not learned committors. Coordinates are in Å. Supplementary Table 10 quantifies the saddle-referenced deviations. One search was performed per model.

Figure 2: Gas-phase reaction profiles reconstructed from energy-only continuation. a–i , Primary continuation chains for HCN isomerization, formaldehyde dissociation, HCOH isomerization, acetylene rearrangement, methoxy isomerization, acetaldehyde tautomerization, HF addition to ethylene, radical ring opening and

\mathrm{S_{N}2}

substitution, respectively. Grey points show node energies relative to the lowest recorded state-

A

minimum, plotted against

\xi

in Å, the summed breaking-bond lengths minus the summed forming-bond lengths (Supplementary Section 5.6 ). Blue circles mark quench-label crossings, orange diamonds the highest-energy chain nodes and dashed lines the independently refined saddle energies. All energies were evaluated with GFN2-xTB. Lines connect evaluated nodes and do not denote force-verified minimum-energy paths.

E_{\rm up}

also includes link and quench-trajectory energies and can differ from the orange node maximum (Table 1 ). One search was performed per reaction.

Figure 3: Residual conformational error in alanine dipeptide. a , Four chains projected onto the backbone dihedrals

(\phi,\psi)

. Blue circles mark quench-label crossings, orange diamonds the highest-energy chain nodes, the black cross the refined ff99SB saddle and the open square the unrelaxed transition-state guess. b , Crossing RMSDs to the refined saddle, calculated for all atoms, heavy atoms and the atoms defining

\phi/\psi

. c , Signed deviations

\delta E=V(\mathbf{R}^{\ddagger}_{0})-E_{\rm reference}

relative to the refined saddle (blue) and the unrelaxed guess (grey), on a symmetric-logarithmic scale. The chain labels ch0–ch3 are shared by b,c; ch0 has the lowest

E_{\rm up}

. All four chains came from one search.

Reaction	No. of atoms	$E_{a}$ (eV)	$\Delta E$ (eV)	$E_{a}$ (eV)	$\Delta E$ (eV)	Crossing RMSD (Å)
		Reference		tReax_expedition
$\mathrm{HCN\to HNC}$	3	3.175	0.868	3.175	0.868	0.013
$\mathrm{H_{2}CO\to H_{2}+CO}$	4	3.167	1.862	3.168	1.863	0.003
$\mathrm{HCOH\to H_{2}CO}$	4	1.744	-2.244	1.745	-2.244	0.008
$\mathrm{HCCH\to H_{2}CC}$	4	2.614	2.360	2.614	2.360	0.008
$\mathrm{CH_{3}O^{\bullet}\to{}^{\bullet}CH_{2}OH}$	5	1.723	0.370	1.726	0.370	0.012

Table 1: Same-surface activation energies, reaction energies and candidate-structure comparisons. Both

E_{a}

columns use the recorded state-

A

energy:

E_{\rm saddle}-E_{A}

for the independently refined first-order saddle and

E_{\rm up}-E_{A}

for tReax_expedition. Reference

\Delta E

is the product-minus-reactant energy of independently refined minima; tReax_expedition

\Delta E=E_{B}-E_{A}

uses the final recorded state minima. All energies are in eV, without zero-point or thermal corrections;

\Delta E

is a potential reaction energy, not a finite-temperature enthalpy. Crossing RMSD is the all-atom deviation from the reference saddle after alignment and symmetry handling. Gas-phase reactions use GFN2-xTB; alanine dipeptide uses ff99SB. Values are rounded to three decimals, with one search per system.

Chemical Reaction Prediction

See all 24 papers

Correlation-Free Transition Path Sampling through Shooting Point Generation Guided by Committor Learning
Sep 17, 2026Maximilian Negedly, Sebastian Falkner, Alessandro Coretti +1Conditional Generative Modeling
Faculty of Physics, University of Vienna, 1090 Vienna, Austria · Vienna Doctoral School in Physics, University of Vienna, 1090 Vienna, Austria · Institute of Physics, University of Augsburg, 86159 Augsburg, Germany
Machine learning kinetics from molecular dynamics data
Sep 15, 2026Jonathan Weare, Aaron R. DinnerMarkov Models Molecular Dynamics Simulation
Courant Institute School of Mathematics, Computing, and Data Science, New York University, New York, New York 10012, United States · Department of Chemistry and James Franck Institute, University of Chicago, Chicago, Illinois 60637, United States
Rare Event Analysis via Stochastic Optimal Control
Apr 14, 2026Yuanqi Du, Jiajun He, Dinghuai Zhang +2Rare-Event Estimation Stochastic Optimal Control
Microsoft Research New England · Cornell University · University of Cambridge +1

Sep 17, 2026J/K move · Enter open · S save

Correlation-Free Transition Path Sampling through Shooting Point Generation Guided by Committor Learning

Maximilian Negedly, Sebastian Falkner, Alessandro Coretti, Christoph Dellago

Faculty of Physics, University of Vienna, 1090 Vienna, Austria · Vienna Doctoral School in Physics, University of Vienna, 1090 Vienna, Austria · Institute of Physics, University of Augsburg, 86159 Augsburg, Germany

Conditional Generative Modeling

Open paper AskPDF arXiv

Studying the dynamical behavior of a system often depends on characterizing how it transitions between long-lived states. Because such transitions are rare, observing them usually requires specialized enhanced sampling techniques. Transition Path Sampling (TPS) is a well-established method for generating reactive trajectories, which is simple to implement and does not require the definition of a preconceived reaction coordinate. However, its efficiency is limited by its sequential nature and the resulting correlations between sampled paths. Previous work addressed this limitation by combining TPS with a sampling scheme based on conditioned Boltzmann Generators, a generative machine learning model capable of sampling a given target probability distribution. This approach produces uncorrelated transition paths but relies on an accurate reaction coordinate, which is rarely known in advance. Building on recent advances in committor learning, specifically on the Artificial Intelligence for Molecular Mechanism Discovery (AIMMD) method, in this work we introduce GenAIMMD, an iterative algorithm that actively and self-consistently learns the ideal reaction coordinate (the committor) and trains a conditioned Boltzmann Generator to sample from arbitrary bias windows along it. GenAIMMD thereby provides a correlation-free and fully parallelizable path sampling scheme that does not require prior knowledge of the system's transition mechanism. We apply GenAIMMD to a two-dimensional toy model and a higher-dimensional polymer system. In both cases, GenAIMMD succeeds in training the Boltzmann Generator and learning the committor. Benchmark results show a substantial increase in performance compared to standard TPS.

Abstract

Chemical Reaction Prediction

Explore similar work

Correlation-Free Transition Path Sampling through Shooting Point Generation Guided by Committor Learning

Machine learning kinetics from molecular dynamics data

Rare Event Analysis via Stochastic Optimal Control