# BondMatcher: H-Bond Stability Analysis in Molecular Systems

arXiv: https://arxiv.org/abs/2504.03205 · HTML: https://mlsanity.com/paper/2504.03205/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 103 references that are in the map.
- First posted on arXiv 4 Apr 2025.

## Builds on (most cited first, 12 of 12)

- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [The Topology ToolKit](https://mlsanity.com/paper/1805.09110/) (2018)
- [Task-based Augmented Contour Trees with Fibonacci Heaps](https://mlsanity.com/paper/1902.04805/) (2019)
- [Ranking Viscous Finger Simulations to an Acquired Ground Truth with Topology-aware Matchings](https://mlsanity.com/paper/1908.07841/) (2019)
- [Discrete Morse Sandwich: Fast Computation of Persistence Diagrams for Scalar Data -- An Algorithm and A Benchmark](https://mlsanity.com/paper/2206.13932/) (2022)
- [Topological Analysis of Ensembles of Hydrodynamic Turbulent Flows -- An Experimental Study](https://mlsanity.com/paper/2207.14080/) (2022)
- [Uncertainty Visualization of 2D Morse Complex Ensembles Using Statistical Summary Maps](https://mlsanity.com/paper/1912.06341/) (2019)
- [Localized Topological Simplification of Scalar Data](https://mlsanity.com/paper/2009.00083/) (2020)
- [Continuous Scatterplot Operators for Bivariate Analysis and Study of Electronic Transitions](https://mlsanity.com/paper/2302.00379/) (2023)
- [Visual Analysis of Electronic Densities and Transitions in Molecules](https://mlsanity.com/paper/2106.01215/) (2021)
- [Time-varying Extremum Graphs](https://mlsanity.com/paper/2406.17652/) (2024)
- [Revisiting Accurate Geometry for Morse-Smale Complexes](https://mlsanity.com/paper/2409.05532/) (2024)

## Built on by (most cited first, 2 of 2)

- [Continuous Edit Distance, Geodesics and Barycenters of Time-varying Persistence Diagrams](https://mlsanity.com/paper/2512.12939/) (2025)
- [DebrisTracer: Reliable Tracking in Hypervelocity Impact Fast Imaging](https://mlsanity.com/paper/2607.15986/) (2026)

## Abstract (arXiv)

This application paper investigates the stability of hydrogen bonds (H-bonds), as characterized by the Quantum Theory of Atoms in Molecules (QTAIM). First, we contribute a database of 4544 electron densities associated to four isomers of water hexamers (the so-called Ring, Book, Cage and Prism), generated by distorting their equilibrium geometry under various structural perturbations, modeling the natural dynamic behavior of molecular systems. Second, we present a new stability measure, called bond occurrence rate, associating each bond path present at equilibrium with its rate of occurrence within the input ensemble. We also provide an algorithm, called BondMatcher, for its automatic computation, based on a tailored, geometry-aware partial isomorphism estimation between the extremum graphs of the considered electron densities. Our new stability measure allows for the automatic identification of densities lacking H-bond paths, enabling further visual inspections. Specifically, the topological analysis enabled by our framework corroborates experimental observations and provides refined geometrical criteria for characterizing the disappearance of H-bond paths. Our electron density database and our C++ implementation are available at this address: https://github.com/thom-dani/BondMatcher.