  The development of novel sub-nanometer clusters (SNCs) catalysts with
superior catalytic performance depends on the precise control of clusters'
atomistic sizes, shapes, and accurate deposition onto surfaces. Recent
advancements in manufacturing and characterization techniques have paved the
way for the production and atomic resolution characterization of
transition-metal SNCs catalysts, positioning them as a promising new class of
materials for this application. Nevertheless, the intrinsic complexity of the
adsorption process complicates the ability to achieve an atomistic
understanding of the most relevant structure-reactivity relationships hampering
the rational design of novel catalytic materials. In most cases, existing
computational approaches rely on just a few structures to conclude clusters'
reactivity thereby neglecting the complexity of the existing energy landscapes
thus leading to insufficient sampling and, most likely, unreliable predictions.
Moreover, modelling of the actual experimental procedure that is responsible
for the deposition of SNCs on surfaces is often not done even though in some
cases this procedure may enhance the significance of certain (e.g., metastable)
adsorption geometries. This study proposes a novel approach that utilizes
particle swarm optimization (PSO) method, in conjunction with ab-initio
calculations, to predict the most relevant SNCs structures on a surface in beam
experiments, and consequently their reactivity. To illustrate the main steps of
our approach, we consider the deposition of Molybdenum SNC of 6 Mo atoms on a
free-standing graphene surface, as well as their catalytic properties
concerning the CO molecule dissociation reaction. This study demonstrates the
feasibility of the PSO technique for studying catalyst transition-metal SNCs
and establishes a reliable procedure for performing theoretical rational design
predictions.
