# Wrinkles in time: extracting the true intrinsic dynamics of mass transport from biased atomistic simulations

# Wrinkles in time: extracting the true intrinsic dynamics of mass transport from biased atomistic simulations

Promotor(en):**19MODEV03**/ Model and software development**A. Ghysels**/Mass transport at the molecular scale is of essential importance in physical, chemical and biological processes. In materials science, crystallization of alloys requires the organization and mobility of individual metal atoms, or for catalysis in porous materials, reactants need to enter the pores and diffuse through the channels to catalytic hot spots. Modeling this diffusion at the atomistic scale allows to follow individual molecules and observe their diffusion: molecules hop over energy barriers and interact with their surroundings.

Unfortunately, some energy barriers are high, such that diffusion becomes slow compared to the typical time scale that may be modeled with atomistic simulations. Simulations of 100 nanoseconds is already considered fairly long, while it might take much longer to observer the molecules diffusing over the high barriers. In practice, one ends up with a rather long movie where not much happens. A bulky molecule might be trapped in a pore of the material and might wobble in a cage while never hopping to a nearby cage because of a high barrier. An advanced approach is clearly needed to effectively simulate transport in these 'slow' systems.

**Goal**When the true dynamics are too slow, it is tempting to speed up the dynamics artificially. By adding a bias potential, the energy barriers can be lowered, and molecules will hop more easily over barriers. In the resulting movie, the bulky molecule would hop around through the material's cages. However, one immediately realizes that this bias also creates wrinkles in time! The true yet slow dynamics were transformed into faster dynamics. The wrinkles in time give a nice fast movie, but it destroys the true slow dynamics.

This thesis will investigate a methodology to flatten out these wrinkles in time. The aim is to extract the true dynamics from a biased simulation. The proposed approach is based on the Smoluchowsky equation, which describes position-dependent diffusion D(x) on a free energy surface F(x). The position-dependent description should give us the opportunity to bias the free energy surface, i.e. F(x) → F(x) + Vbias(x), while the diffusion D(x) remains unaltered. The decoupling between free energy and dynamics is the underlying assumption why this new approach could give a solution for the wrinkles in time.

In the thesis, a proof of principle simulation will first be performed with a toy model (the drunk random walker), such that the influence of energy barriers F(x), diffusion profile D(x), and the bias can examined, using a learning algorithm based on inverse Monte Carlo simulations. The approach will be based on an inverse Monte Carlo routine. Next, the approach will be applied to diffusion applications that are currently hindered by slow dynamics, such as the diffusion of propene molecules through zeolitic porous crystals, a research area that is actively investigated at the Center for Molecular Modeling. The new methodology will be implemented such that a series of simulations may be investigated efficiently.

The student should be interested on one hand in physics with some feeling for mathematical expressions, and on the other hand in Monte Carlo and in analyzing simulations with new scripts. One of the long term impacts of this thesis work is that one will be able to experiment in silico with the slow permeation of bulky reactant and product molecules in catalytic reactions and separations.

This research topic will be conducted in the framework of a strong international network and if possible the student will be actively involved in work discussions with collaborative partners (e.g. National Institutes of Health, Maryland, USA).

**Aspects**Master of Science in Engineering Physics: The engineering aspect is the development of a practical computational protocol that can analyze biased simulations with inverse Monte Carlo, which will allow diffusion simulations of chemical compounds through nanoporous materials. The physics aspect is the profound study of the Smoluchowsky equations and how it matches to atomistic simulations.