Autoconstructing complex reaction networks from finite-temperature dynamics: oxygen activation on a noble-metal cluster

This work uses O₂ activation on a noble-metal cluster as a model system. Starting from finite-temperature first-principles molecular dynamics, it samples the configurations actually visited by the system and their interconversion, then uses those trajectories to build thermodynamic and kinetic reaction networks.

The results show that the configuration with the highest intrinsic O₂ activation ability does not necessarily make the largest contribution to O₂ activation at finite temperature. The distribution of configurations at the relevant temperature, together with their continuing interconversion, changes the actual role of different structures in the reaction network.

A finite-temperature catalyst is not a single structure

Catalytic reactions are often described in terms of elementary processes connecting reactants, intermediates, transition states and products. When the main reaction steps are already reasonably well established, this framework can effectively connect electronic-structure calculations with kinetic modelling.

In structurally dynamic systems, however, the catalyst itself can continuously restructure with temperature. Small metal clusters provide a typical example: at finite temperature they can access multiple stable and metastable configurations, and after molecular adsorption the relative stability of these configurations can change further.

The local structural environment experienced by the reaction is therefore not fixed. For such systems, the properties of an individual optimized structure remain important, but the finite-temperature distribution of configurations and their interconversion also need to enter the reaction description.

When the reaction network is not yet fully known

Many reaction calculations begin with established or candidate reactants, products, intermediates and elementary processes, followed by searches for the corresponding transition states, barriers and rates.

As a system becomes more complex, the number of possible intermediates and connections can grow rapidly, while the states that are actually relevant under the conditions of interest cannot always be fully specified before the calculation begins.

Compared with conventional reaction modelling centred on known elementary processes and transition states, finite-temperature dynamics can further reveal metastable structures that the system actually visits and how they interconvert, and can identify states and connections that were not fully included in the model beforehand.

Reconstructing a reaction network from finite-temperature trajectories

We start from finite-temperature atomistic dynamics, allowing the system to explore structures and transitions that are actually accessible, and then build the reaction network from this dynamical information.

In this way, the model does not have to rely entirely on a predefined set of intermediates, elementary steps or reaction coordinates. Metastable configurations, short-lived states and new structural transitions that appear during the simulation can also enter the subsequent analysis.

The trajectories preserve both the distribution of configurations at the relevant temperature and the connections between them. This makes it possible to examine which states are more stable, which transitions occur more often and how different reaction pathways run through the network.

For systems whose reaction topology is not yet fully established, or whose structural dynamics changes markedly with conditions, this trajectory-based description provides information that is difficult to obtain directly from static structure analysis.

High activation ability does not mean high contribution

The results at 570 K show clearly why the finite-temperature distribution matters.

When different Ag₄ configurations are examined separately, tetrahedral, acute-angle and square-like structures have relatively high O₂ activation probabilities. Compared on their own, they appear particularly active.

But these configurations have relatively low statistical weight at 570 K.

By contrast, diamond, Y and zigzag configurations have lower O₂ activation probabilities but are more common at finite temperature. Once the configurational distribution is included, they contribute more to the sampled O₂ activation events.

High activity in a static structure therefore does not necessarily correspond to a high contribution within a finite-temperature reaction network.

This is why identifying the “most active configuration” alone cannot fully answer which structures matter most under reaction conditions.

Structural interconversion further changes the reaction network

The different configurations do not form independent static populations. Ag₄ continuously moves between these structures.

Some states with low populations but high O₂ activation probabilities can be repeatedly accessed through transitions from other configurations. Conversely, the role of a more common configuration in the network also depends on how it connects to other states.

Knowing how much each configuration is populated is therefore still not enough. The reaction network also retains the connectivity between states and shows which transitions carry the main reactive flux.

In the 570 K network, clear transitions connect some relatively stable structural regions with configurations that have high O₂ activation probabilities. These connections reveal dynamical relationships that a static ranking of structures cannot show.

Temperature changes more than barrier crossing

Increasing temperature often accelerates barrier crossing, but in a continuously restructuring network it also changes the relative stability and populations of different states.

For one representative transition examined in the study, the rate reaches a maximum at around 500 K; as the temperature is raised further, the rate decreases.

At lower temperatures, heating makes transitions between different configurations easier. As the temperature continues to change, however, the statistical weight of the target state also changes. This population shift can offset the faster barrier crossing produced by higher temperature.

Finite-temperature kinetics therefore reflects not only the crossing of an individual barrier, but also the redistribution of the entire structural network with temperature.

From static structures to dynamic reaction networks

Ag₄–O₂ shows what finite-temperature dynamics can add to reaction modelling.

Comparing the O₂ activation probabilities of different structures identifies one set of highly active configurations. Once finite-temperature structural populations are included, the configurations contributing more to the overall activation change; considering transitions between configurations then shows how these states are connected through the reaction network.

For catalytic systems that undergo substantial structural restructuring, a single optimized structure or a set of independent stationary structures is therefore difficult to use as a complete description of the finite-temperature behaviour.

More broadly, when a system contains many metastable states, structural rearrangements or competing processes, reaction modelling needs to consider not only which structures exist on the potential-energy landscape, but also whether those structures are actually visited under the conditions of interest and how they are connected.

Finite-temperature dynamics brings this information into reaction modelling and opens a broader search space for discovering and analysing complex reaction networks.