Finding Reaction Pathways Efficiently

Studying chemical changes using computational materials science tools usually boils down to two styles of investigations. On one hand, you can research possible reaction mechanisms, detailed reaction pathways, and the analysis of actual reaction barriers and rates. On other hand, you can simulate chemical dynamics based on rates to help understand the complex interplay of different processes in a chemical system. Over the last 5-6 years, the BIOVIA Materials Studio team has invested heavily in both of these areas. This blog post is part of a series of two, covering some of the highlights in the Material Studio 2022 release. Here I describe FlexTS, our next-generation tool for obtaining chemical barriers and process rates.

Introducing Materials Studio FlexTS

FlexTS completely redefines the way we compute reaction pathways and barriers, and any intermediate states for distant minima. Its main strength is an extremely efficient route toward finding transition states (TS), that is, the saddle points between two different chemical states. FlexTS was developed in collaboration with world leading scientists from the University of Cambridge and combines the most efficient methods for each stage of the TS search process [1-3]. FlexTS algorithms are very robust, with excellent convergence properties and world-class calculation speeds.

The challenge that computational chemists typically face when computing transition states is that commonly available methods struggle to converge to the actual transition state, often leading to inaccurate or partial results. At the same time, it is essential to establish that any transition state found actually corresponds to the reactants and products envisioned in the study. Our growing experience with this new tool suggests that this is frequently not the case, which can be surprising to both theory and experiment alike.



Finding Reaction Pathways Efficiently

Materials Studio FlexTS tackles each transition state search as illustrated in the simplified figure on the right. It begins by connecting a hypothetical reactant and product with a trajectory of images and running a Nudged Elastic Band calculation [1]. This popular method works by interpolating reactant and product structures with a number of images connected by virtual springs. Optimizing the geometry of the images-and-springs system guarantees finding a reaction pathway, but it also can be extremely slow to converge in practice – costing time, resources, and ultimately money. FlexTS therefore uses the nudged elastic band only in the first part of the transition state search calculation where it is the most efficient method available (top panel in the figure).

Once it is possible to extract a suitable guess for the transition state, FlexTS switches to a hybrid eigenvector following scheme [2]. This is a very efficient method of finding the saddle point as outlined in the second panel of the figure. For those interested in technical details: the hybrid EF algorithm minimizes the structure along the lowest eigenvalue Hessian mode without ever computing the numerically expensive Hessian matrix.

Once FlexTS finds the saddle point and its corresponding reaction mode, it displaces the chemical system away from the saddle point and run an efficient geometry optimization. This reveals the chemical states corresponding to that particular saddle point. Finally, FlexTS compares the structures obtained by the final step and compares those to reactant and product. If FlexTS finds both the reactant and the product, there is a connected path and the calculation finishes [3]. In other cases, the reactants and products found may be sufficient for a given application. If not, FlexTS is happy to repeat the process until it finds a multistep connected path.

In many cases, the complete transition state analysis is quicker than the calculation of vibrations for a single structure. FlexTS is also very easy to use from a user’s perspective, requiring only a few basic selections to perform successful transition state searches.

Multistep pathways

To illustrate the power of this approach, we can consider the molecular system on the right. It illustrates a simple question in molecular information transfer. If we manage to move one hydrogen atom on one side of one of the polycyclic molecules, is that sufficient for this individual bit of information to propagate through the entire system? Or are there intermediate local minima to overcome, in effect to switch six individual hydrogen bonds?

Materials Studio FlexTS can help to answer this question by computing the Minimum Energy Path between the initial and final states of this process. By running the cycle described above several times, it turns out that there are six individual reaction barriers to cross between the initial and final states. The figure on the right illustrates the pathway found by FlexTS in a single calculation, with individual barriers ranging from 2.4 to 22.6 kcal/mol.



The same type of calculation has been extensively applied to many different applications that address battery materials, heterogeneous catalysis, solid state, and pharmaceutical reactions.

The results from a FlexTS calculation include the direct input for a Reaction Kinetics analysis in Materials Studio. This provides a prediction of the actual reaction rate obtained from the activation energies and the vibrational frequencies of the initial and transition state. This calculation completes half of the journey outlined initially, namely to link atomic structure to the rate of one or more chemical reaction steps.

The second post in this series will examine the different tools available in Materials Studio that utilize the energy barrier and rate information to understand complete chemical processes based on different multiscale approximations.

[1] S.A. Trygubenko, D.J. Wales; J. Chem. Phys. 120 2082 (2004)
[2] Y. Kumeda, L.J. Munro, D.J. Wales; Chem. Phys. Lett. 341 185 (2001)
[3] J.M. Carr, S.A. Trygubenko, D.J. Wales; J. Chem. Phys. 122 234903 (2005)'


Felix Hanke is a Senior Scientific Software Developer in the BIOVIA brand and a fellow of the BIOVIA Science Council. He develops quantum mechanical methods in the Materials Science portfolio and works on multiscale simulation techniques, particularly on batteries.'

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