Our previous development efforts have incorporated a set of unique features into *Zacros*, for the convenient modelling of complex reaction kinetics encountered in realistic catalytic materials. The package was commercialised by UCL Business and was first released in Oct. 2013, after a long history of development. Information about completed projects is shown here.

M. Stamatakis (PI), Dr Ilectra Christidi (CoI). "** Zacros Towards Petascale Kinetic Monte Carlo Simulations with the Time-Warp Algorithm**". 2021-2022. Sponsored by the Edinburgh Parallel Computing Centre by an Embedded CSE support grant (ARCHER2-eCSE01-13).

The project aimed at further advancing the implementation of the Time-Warp algorithm in *Zacros* towards massively parallel simulations in scalable hardware architectures. Additionally, medium and large-scale benchmarks demonstrated to power of the approach and explored the effect of user-tuneable parameters on performance.

Relevant publications:

- Savva, G. D., Benson, R. L., Christidi, I.-A. and M. Stamatakis (2023). “Exact distributed kinetic Monte Carlo simulations for on-lattice chemical kinetics: lessons learnt from medium- and large-scale benchmarks”.
*Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences*, 381(2250): 20220235**[Invited paper]**. (doi: 10.1098/rsta.2022.0235) - Savva, G. D., Benson, R. L., Christidi, I.-A. and M. Stamatakis (2023). “Large-scale benchmarks of the Time-Warp/Graph-Theoretical Kinetic Monte Carlo approach for distributed on-lattice simulations of catalytic kinetics”.
*Physical Chemistry Chemical Physics*, 25: 5468-5478**[Invited paper]**. (doi: 10.1039/D2CP04424B) - Ravipati, S., Savva, G. D., Christidi, I. A., Guichard, R., Nielsen, J., Réocreux, R. and M. Stamatakis (2022). “Coupling the Time-Warp algorithm with the Graph-Theoretical Kinetic Monte Carlo framework for distributed simulations of heterogeneous catalysts”.
*Computer Physics Communications*, 270: 108148. (doi: 10.1016/j.cpc.2021.108148)

M. Stamatakis (PI). "** Zacros Software Package Development: Code Refactoring, Exact Spatial Parallelism and Algorithms for Emerging Hardware**". 2017-2019. Sponsored by the Edinburgh Parallel Computing Centre by an Embedded CSE support grant (eCSE10-08).

The project implemented the *Time Warp* algorithm, an exact parallel simulation scheme, within *Zacros*. The scheme is based on domain decomposition and exact treatment of boundary conflicts using rollbacks, such that the trajectories simulated follow the original stochastic model (the master equation), rather than an approximate version thereof. This is a major advantage, making it possible to simulate new and unexplored physical phenomena, evolving on very large domains (surfaces), without worrying about artefacts arising from the computational scheme. A modest speedup was observed in our benchmarks (3.5× for 36 MPI processes), and future work will aim towards improving the efficiency of our implementation.

Relevant publication:

M. Stamatakis (PI), J. Hetherington (co-I), B. Silva (co-I). "** Zacros Software Package Development: Pushing the Frontiers of Kinetic Monte Carlo Simulation in Catalysis**". 2014-2015. Sponsored by the Edinburgh Parallel Computing Centre by an Embedded CSE support grant (eCSE01-001).

This project focused on algorithmic implementations to improve the performance and scalability of *Zacros*. The main research objective was the incorporation of spatial decomposition schemes for parallelising the simulation to an arbitrary number of processors, successfully harnessing the power of ARCHER. We thus employed distributed-memory (MPI) parallelism making it possible for Zacros to run simulations of large domains, with each core tackling a different part of the domain. An approximate scheme was implemented that resulted in 23× speedup using 24 computers. Future work will enable us to exploit an ever increasing number of machines.

Relevant publication:

M. Stamatakis. "**Graph Theoretical Kinetic Monte Carlo: Preliminary Investigation of Approaches to Parallelisation**". Jan-Mar 2013. Sponsored by the RITS Department, under the termly call for software development proposals.

The energetic models were extended to tackle arbitrarily complex adsorbate-adsorbate lateral interactions, involving long-range and many-body contributions. Brønsted-Evans-Polanyi relations were implemented for capturing the effect of local coverage on the activation energies of elementary processes. As part of this project, *Zacros*'s continuous integration and testing framework was developed on the RSDT Jenkins server. This allows the testing of new features of the code as they are being developed. Memory allocation on *Zacros* was optimised, thereby speeding up KMC simulations involving short-range lateral interactions. OpenMP shared memory parallelisation was further implemented, providing significant speed up for problems that involve long-range interactions. Speedups of 10x were verified on the Legion@UCL cluster with up to 12 cores.

Relevant publications:

- Nielsen, W., d’Avezac, M., Hetherington, J. and M. Stamatakis (2013). “Parallel kinetic Monte Carlo simulation framework incorporating accurate models of adsorbate lateral interactions”.
*Journal of Chemical Physics*139(22): 224706. (doi: 10.1063/1.4840395) - Case study: "Simulation software advancing the discovery of new catalysts"

M. Stamatakis, D. G. Vlachos. "**Graph Theoretical Kinetic Monte Carlo Method Development**". 2010-2012. Carried out as part of M. Stamatakis's post-doc at D. G. Vlachos's lab at the University of Delaware, USA.

This project laid out the foundations of the Graph-Theoretical KMC method which is implemented in *Zacros*. This method enables the representation and treatment of arbitrarily complex reactions, involving many sites in specific neighbouring arrangements, potentially occupied by multi-dentate species. Energetic interactions were limited to pairwise additive contributions in this original implementation. The first reaction to be modelled with this framework was the water-gas shift on flat and stepped Pt surfaces, followed by a study of CO oxidation on Au_{6} nanoclusters. Both systems involve complicated catalytic structures and reactions in which multi-dentate species participate.

Relevant publication:

- Stamatakis, M. and D. G. Vlachos (2011). “A Graph-Theoretical Kinetic Monte Carlo Framework for on-Lattice Chemical Kinetics”.
*Journal of Chemical Physics*134(21): 214115. (doi: 10.1063/1.3596751)