AlF–AlF collision dynamics: from the interaction landscape to complex lifetimes

We first built the previously missing full-dimensional interaction model for AlF–AlF and then used it to study complex formation, structural rearrangement and dissociation, as well as how these processes change with temperature.

A full-dimensional energy map built from the dynamics

Two AlF molecules form a four-atom system with six internal degrees of freedom. Reliable collision dynamics therefore requires a full-dimensional potential-energy surface covering these coordinates.

A potential-energy surface can be viewed as the energy map of a molecular system: it describes how the energy changes as the atoms move, and therefore which structures can form, how collisions evolve and which pathways are energetically accessible.

Before this work, no full-dimensional potential-energy surface suitable for AlF–AlF dynamics was available.

Conventional approaches often begin by selecting a large set of configurations across the coordinate space, calculating each one with a high-level ab initio method, and then fitting the resulting surface. Molecular dynamics, however, does not visit configuration space uniformly. Many predefined structures may rarely occur in an actual trajectory, while important regions such as short-range collisions can remain undersampled.

Our training data were therefore drawn primarily from molecular-dynamics trajectories. CCSD(T) calculations provided high-accuracy reference energies, Gaussian-process regression was used to fit the surface, and active learning added new ab initio data during the simulation when the model uncertainty became too large.

If a newly visited configuration lay in a region already described with sufficient confidence, the simulation used the model prediction directly. If the uncertainty exceeded a threshold, that configuration was calculated with the electronic-structure method and added to the training set.

For AlF–AlF, this sampling strategy was substantially more efficient than predefined hypercube sampling. In the reported tests, a model trained on 5,000 hypercube configurations had errors more than an order of magnitude larger than models trained on configurations sampled by molecular dynamics.

In a later replica-exchange simulation containing more than 26.9 million MD steps, only 2,038 new configurations required additional CCSD(T) calculations, corresponding to about 0.008% of the trajectory. These new reference points were concentrated mainly in the short-range interaction region, where the model required the most additional information.

One bound complex dominates the landscape

The resulting potential-energy surface revealed an AlF–AlF interaction landscape that differs from previously studied CaF and bi-alkali dimers.

Only one stable AlF–AlF minimum was found on the surface, with D_2h symmetry. Its binding energy is approximately 0.69 eV relative to two separated AlF molecules, and the geometry optimized on the machine-learned surface closely reproduces the direct CCSD(T) result.

Geometry optimizations from different starting configurations converge to the same minimum. The surface also allows barrierless exchange of equivalent fluorine atoms between the two AlF molecules.

By contrast, formation of Al₂ + F₂ lies approximately 11.56 eV above two separated AlF molecules and is therefore strongly disfavoured under the conditions considered.

The low-energy collision picture is therefore dominated by formation of the AlF–AlF complex, internal rearrangement and redissociation, rather than access to a new stable chemical product.

This provides a clear microscopic basis for the next step: determining how the complex forms and how long it survives during thermal collisions.

Temperature reshapes the complex dynamics

The second study used this potential-energy surface for molecular-dynamics and replica-exchange simulations over 200–1000 K.

The lifetime of the AlF–AlF complex depends strongly on temperature.

At 200 K, the extracted lifetime is about 7.8 ns.
At 342 K, it falls to about 1.3 ps.
At 1000 K, it is about 0.032 ps, or a few tens of femtoseconds.

Across the simulated range, the lifetime decreases by more than five orders of magnitude.

The trajectories also reveal how the complex forms.

At lower temperature, two AlF molecules approaching in an antiparallel orientation can enter the lowest-energy complex directly. Other initial orientations can rotate into the same stable structure without encountering a substantial barrier.

To analyse the longer trajectories systematically, the sampled structures were grouped into 19 structural clusters. Markov-state modelling and transition-path theory were then used to reconstruct transitions between these states.

At 200 K, complex formation proceeds through relatively simple pathways. At 409 K and 585 K, the trajectories visit more short-lived and higher-energy configurations, and the pathway network becomes more dispersed.

Although temperature strongly changes the complex lifetime and the configurations visited by the trajectories, no channel leading to other stable chemical products was observed anywhere in the 200–1000 K simulations.

Implications for trapped AlF

A major issue in ultracold molecular experiments is the formation of long-lived collision complexes, often discussed in the context of “sticky collisions”. In several bi-alkali systems, such complexes are associated with enhanced molecular loss.

AlF–AlF shows a different interaction picture. The collisions studied here form a non-reactive intermediate complex, and its lifetime decreases rapidly with temperature. The underlying potential-energy landscape is also simpler than those reported for some bi-alkali and CaF systems.

These results support further assessment of AlF collision stability in cold-molecule experiments, while an important distinction remains: the present molecular-dynamics simulations cover 200–1000 K and do not directly simulate the ultracold collision regime.

The two studies therefore provide the full-dimensional interaction surface, complex structure, formation pathways and thermal collision lifetimes needed as a microscopic basis for future work on truly ultracold collisions and trap-loss behaviour.