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Hydrogen-Bond Networks

This page is a self-contained, textbook-style introduction to hydrogen-bond detection in MolPy. A hydrogen bond is identified geometrically — by a donor–acceptor distance and a donor–H···acceptor angle — and the per-frame bond list it produces is the starting point for counting coordination, mapping networks, and (combined with the persistence analysis) measuring hydrogen-bond lifetimes. The canonical applications are water, alcohols, and protic ionic liquids.

As elsewhere, the geometric search runs in Rust (molrs); the MolPy layer feeds it the donor/acceptor selections and returns a typed result.

Conventions used throughout

  • Distances are in Å, angles in degrees.
  • A donor is a (D, H) pair (the heavy atom and its bonded hydrogen); an acceptor is a single heavy atom.
  • The default criterion is the Luzar–Chandler geometry: donor–acceptor distance ≤ 3.5 Å and D–H···A angle ≥ 150°.

1. A hydrogen bond is a geometric event

There is no quantum-mechanical observable that switches on at a hydrogen bond, so simulations use a geometric criterion: a donor (D, H) and an acceptor A are hydrogen-bonded at a frame when

\[ r_{D\cdots A} \le r_c \qquad\text{and}\qquad \angle(D\text{–}H\cdots A) \ge \theta_c. \]

The distance can be measured donor-to-acceptor or hydrogen-to-acceptor (selectable through the criterion). The cutoffs are not universal constants — they should be read off the first minimum of the relevant \(g(r)\) and the distance–angle CDF, which is exactly the joint distribution whose populated region defines the bond.

2. Detecting hydrogen bonds

Supply the donor (D, H) pairs and the acceptor indices; tune the geometry with an optional HBondCriterion:

import numpy as np
from molpy.compute import HBonds, HBondCriterion

donors = np.array([[o1, h1], [o1, h2]], dtype=np.int64)   # (D, H) pairs
acceptors = np.array([o2, o3, o4], dtype=np.int64)

hb = HBonds(donors, acceptors, HBondCriterion(dist_cutoff=3.5, angle_cutoff=150.0))
result = hb(frames)

result.counts      # number of H-bonds per frame
result.per_frame   # lists of (D, H, A, distance, angle) per frame

The per-frame tuples let you build the bond network (degree distribution, ring statistics) or feed specific donor–acceptor pairs into a lifetime analysis.

3. From a bond list to lifetimes

A single-frame count tells you how many hydrogen bonds exist, not how long they last. To get the lifetime, treat each detected donor–acceptor pair as an association and run the pair-persistence survival analysis on it: the intermittent correlation gives the structural hydrogen-bond lifetime \(\tau_\text{HB}\) of Luzar–Chandler, while the continuous correlation gives the much shorter "first-break" time. Reporting both, with the geometric criterion used, is the standard way to characterize hydrogen-bond dynamics.

4. Pitfalls checklist

  1. Criterion sensitivity → counts and lifetimes depend strongly on \(r_c\) and \(\theta_c\); choose them from the distance–angle CDF and state them explicitly.
  2. Donor list must pair D with its H → each donor entry is (heavy, hydrogen); a heavy atom with two hydrogens contributes two donor rows.
  3. Self-pairs → exclude intramolecular donor/acceptor combinations if you only want intermolecular bonds.
  4. Distance convention → donor–acceptor vs. hydrogen–acceptor cutoffs are not interchangeable; pick one and keep it consistent across systems.
  5. Lifetime ≠ count → a high instantaneous count can coexist with a short lifetime; the two answer different questions.

5. References

  • A. Luzar, D. Chandler, Nature 379, 55 (1996); Phys. Rev. Lett. 76, 928 (1996) — geometric criterion and hydrogen-bond kinetics.
  • D. C. Rapaport, Mol. Phys. 50, 1151 (1983) — continuous vs. intermittent bond correlation functions.
  • M. Brehm, M. Thomas, S. Gehrke, B. Kirchner, J. Chem. Phys. 152, 164105 (2020) — TRAVIS.

See also