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arXiv · 2608.02536

Committors and Reaction Rates from Trial Functions That Violate the Boundary Conditions

Magnus Petersen·Simon Lichtinger·Roberto Covino
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Abstract

The committor is the optimal reaction coordinate for a rare transition: it pinpoints the transition state and fixes the rate, and it governs events from protein folding to crystal nucleation. It minimises a Dirichlet energy, whose value at the minimum is the reactive flux, over functions that vanish on the reactant state and equal one on the product state. In high dimensions such a trial space is very hard to build. Here we rewrite the variational principle so that the boundary conditions are replaced by a normalisation of one boundary observable, the fidelity. Any trial function is then admissible, including functions that cannot satisfy the boundary values at all. On this basis we estimate the high-dimensional committor and rates from one-dimensional profiles along projected coordinates, taking as input only pre-existing equilibrium or reweighted configurations, a diffusion constant estimate, and the two state definitions. The optimum has a closed form that is cheap to evaluate. We obtain committors for AIB9 and villin HP-35 in full torsion space, and folding and unfolding rates for chignolin from umbrella sampling alone.

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Magnus Petersen, Simon Lichtinger, Roberto Covino. 2026-08-03. Committors and Reaction Rates from Trial Functions That Violate the Boundary Conditions. https://arxiv.org/abs/2608.02536

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