Characterizing the kinetics of atomic diffusion using the Activation Relaxation Technique

Industry is increasingly synthesizing new molecules and materials with the aim of discovering new properties. With the ever-increasing quality of the products manufactured, and the precision required to produce them, a new need has emerged: that of controlling chemical reactions at the atomic level. The thermodynamics of chemical reactions is governed entirely by the difference in free enthalpy, noted ΔG, between a stable initial state composed of reactants and a stable final state composed of products. Reaction kinetics, meanwhile, is determined by the enthalpy barrier, G _b , which must be crossed from the initial state to the final state, via an unstable state known as the transition state or saddle point. Thus, knowledge of these energies throughout the chemical reaction is of crucial importance for mastering modern chemistry and materials science applications. However, this represents a major algorithmic challenge, as the potential energy E of the physical system depends on the positions (x, y, z) of all the N _at atoms that make it up. Potential energy is therefore a 3N _at -dimensional function that is generally extremely expensive to calculate for a given set of atomic positions.

The most accurate methodology for modeling the energy of an atomic system is to use ab initio calculations, which take into account the electronic structure of the atoms by solving the system's Hamiltonian. However, determining the energy of an atomic system and exploring this potential energy surface with such precision represents a high computational cost. It is therefore essential to have an algorithm capable of efficiently exploring the potential energy surface from an initial state while minimizing the number of calculations required.

The aim of this article is to present the activation-relaxation technique (named "ARTn" for activation-relaxation technique nouveau), a highly efficient method for blindly discovering the different stable and metastable states on a large-scale potential energy surface, whatever the energy model used, and for precisely characterizing the transition point of molecular reactions. ARTn has already been applied with great success to a wide range of complex systems and can in principle be used for any system, from protein aggregation to surface reactions or diffusion in glassy materials. In the remainder of this article, we will calculate potential energy surfaces at 0 K and entropic effects will be neglected: E = G.