Generalized Path Reweighting and History-Dependent Free Energies

Transition interface sampling (TIS) and replica exchange TIS (RETIS) are powerful methods for computing rates of rare events inaccessible to straightforward molecular dynamics (MD) simulations. Path reweighting extends their output, enabling the evaluation of diverse thermodynamic and kinetic quantities, including reaction prediction metrics, activation barriers, committor functions, and free energies. The recently developed Infinity-RETIS algorithm boosts parallel efficiency through asynchronous replica exchanges in the infinite-swap limit, eliminating the wall-time bottlenecks of conventional RETIS. This approach introduces fractional samples and biased sampling distributions, requiring a generalized path reweighting framework, for which we derive expressions demonstrating how it can be used to compute exact dynamic and thermodynamic variables. We then focus on a special class of free energy surfaces defined by history-dependent conditions, whose values are influenced by kinetic factors such as particle mass and friction, unlike standard unconditional free energy surfaces. These conditional free energies can reveal kinetically relevant barriers even with suboptimal reaction coordinates and therefore provide a rigorous and versatile tool for characterizing complex molecular transitions.

💡 Research Summary

Transition Interface Sampling (TIS) and its replica‑exchange variant (RETIS) are powerful tools for estimating rare‑event rates, but conventional RETIS suffers from two practical drawbacks. First, ensembles with different average path lengths generate an imbalance in the number of sampled trajectories; short‑path ensembles produce many more samples than long‑path ensembles. Second, the need to synchronize replica‑exchange moves forces workers handling short paths to wait for those handling long paths, creating a wall‑time bottleneck.

The authors address these issues by introducing the “infinite‑swap” (∞ RETIS) algorithm. In ∞ RETIS each interface is assigned a set of workers that perform shooting moves independently and asynchronously. After every shooting move the algorithm mimics the effect of an infinite number of replica exchanges among all free ensembles. This is achieved by assigning a fractional multiplicity µ ji to each unique trajectory Xj for each ensemble i. µ ji represents the non‑integer number of times the trajectory would appear in ensemble i if an infinite number of swaps were performed. The total fractional count for ensemble i, ηi = ∑j µ ji, replaces the ordinary integer sample count Ni.

To further accelerate sampling, ∞ RETIS often employs a high‑acceptance “wire‑fencing” shooting scheme that deliberately biases the sampling distribution. The unbiased target distribution ρi(X) is replaced by ρi(X) wi(X), where wi(X) is a known weight factor that enhances acceptance. Consequently, any observable O must be re‑weighted by the inverse of this factor. The authors derive a compact generalized re‑weighting formula that simultaneously accounts for fractional multiplicities and bias weights:

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