(777f) An Automated Approach for Developing Graph-Theoretical Cluster Expansions of the Total Energy of Adsorbed Layers

An Automated
Approach for Developing Graph-Theoretical Cluster Expansions of the Total
Energy of Adsorbate Layers

E. Vignola^1,2, S. N. Steinmann², M. Stamatakis,³
P. Sautet^2,4

¹TOTAL Petrochemicals, Route de la Chimie,76700 Gonfreville-l'Orcher, France; ²
Univ Lyon, Ens de Lyon, CNRS, Université
Lyon 1, Laboratoire de Chimie
UMR 5182, F-69342, Lyon, France; ³ Department of Chemical
Engineering, University College of London, Torrington Place, London WC1E7JE,
United Kingdom; ⁴ Department of Chemical and Biomolecular
Engineering, University Of California Los Angeles, CA, USA

The
accurate description of the total energy of adsorbate layers is crucial for the
understanding of chemistry at interfaces. For catalysis applications in
particular, adsorbate-adsorbate lateral interactions have been shown to
significantly affect activation energies of reactions, thereby shaping
experimentally observed trends. [1,2] Modelling the interactions of atomic
adsorbates has traditionally been achieved using effective Ising-type
Hamiltonians [3], whereby a set of spin-like values is attributed to the
layer’s lattice points describing the occupancy of the corresponding catalytic
sites (vacant occupied by a species). Pairwise additive adsorbate-adsorbate
lateral interactions in this model are captured by appropriate coupling
constants.

Such
a Hamiltonian is however limited, as it cannot account for adsorbates that bind
to more than one sites (bi-dentate or even multi-dentate species), and it
cannot capture many-body contributions to the total energy (3-body interactions
– triplets). To overcome these limitations one has to adopt a cluster expansion
Hamiltonian formalism [4], which has recently been implemented in a
graph-theoretical scheme [5,6] to enable the
representation of multi-dentate species. Automating the development of such
cluster expansion Hamiltonians for catalytic systems is challenging. Existing approaches
for such automation [7] can only tackle mono-dentate adsorbates and cannot
account for the various binding modes that molecules exhibit on solid surfaces.

The
current work develops a scheme for automating the development of cluster
expansions applicable to molecular species on catalytic surfaces. The scheme
has been implemented in a FORTRAN 95 program compatible with the
graph-theoretical kinetic Monte Carlo code, Zacros [8].
     

Figure
1. Pattern Recognition and Encoding Scheme

References

[1]  
Stamatakis, M.; Piccinin, S. ACS Catalysis 2016,
6, 2105  

[2]  
Frey, K.; Schmidt, D. J.; Wolverton, C.; Schneider,
W. F.  Catal. Sci. Technol,
2014, 4, 4356

[3]  
Mussardo, G. Statistical Field Theory. An Introduction to Exactly Solved
Models in Statistical Physics, Oxford University Press, New York, 2010.

[4]  
Sanchez, J. M.; Ducastelle, F.; Gratias, D. Phys. A Stat. Mech. its Appl. 1984, 128
(1-2), 334.

[5]  
Stamatakis, M.; Vlachos, D. G. J. Chem. Phys. 2011, 134, 214115

[6]  
Nielsen, J.; d’Avezac, M.; Hetherington, J.;
Stamatakis, M. J. Chem. Phys. 2013, 139 (22), 224706

[7]  
van de Walle, A.; Ceder, G. J. Phase Equib. 2002,
23, 348.

[8]  
Stamatakis M. Zacros: Advanced Lattice-KMC simulation Made Easy, http://www.zacros.org/,
2013.