An off-lattice kinetic Monte Carlo kernel guided by topological and geometrical analysis to bridge accurate ab-initio calculations and large scale simulations

The kMC method is traditionally used on-lattice, where a property
such as atomic type, is assigned to each point of a fixed lattice.
The evolution is then a series of changes on the
property of lattice points, called events given by a catalog,
that occur with a probability associated with reaction
barriers.

In the more general case, ie object-kMC¹,
the concept of event is not restricted to single atom
transformations. Due to limitations imposed by the
lattice, these approaches often fall short
for complex system evolution, such as ion diffusion in
amorphous/disordered solids, collective transformations, or events with
specific environmental dependency.
In², to accelerate molecular dynamics through OKMC,
off-lattice capabilities have been implemented by using
on-the-fly search of events, enabled by graph theory
and empirical potential.

We propose an alternative approach that uses graph theory
and gometric shape-matching to build a catalog from ab-initio
results, and take into accout the symmetries of events which
allows their execution in any direction, without need of lattice.
Our proposed atom-resolved off-lattice kMC can treat a large
variety of systems. Some examples will be shown emphasizing
the different capabilities.

¹ Domain et al, J Nucl Mat 335, 2004
² El-Mellouhi et al, Phys Rev B 78, 2008