# 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):**17MODEV14**/ Model development**A. Ghysels**/Mass transport at the molecular scale is of essential importance in physical, chemical and biological processes. In medicine, for instance, nutrients, oxygen or drugs need to diffuse inside the cells passing several lipid membrane barriers. 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 barrier are fairly 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 diffusion may take much longer to be observed. This is for instance the case of water permeation through hydrophobic biological membranes and diffusion of bulky molecules from cage to cage in porous materials. In practice, one ends up with a rather long movie of a bulky molecule that is wobbling in a cage, but that never hops 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 destroys the true dynamics: the slow dynamics were transformed into faster dynamics. The wrinkles in time give a nice fast movie, but it destroys the true slow dynamics.

At present, there is no strategy for flattening out these wrinkles in time. This thesis will investigate a methodology 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. Specifically, the conditions where the approach is valid or not will be tested. 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. In particular, the student can focus on the diffusion of bulky molecules in periodic materials, or on permeation of medicine through biological membranes. These two research areas are 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 analyzing simulations with new scripts and in Monte Carlo.

**Mobility:**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).**Motivation Appl. Phys.:**The engineering aspect is the development of a practical computational tool that can analyze biased simulations with inverse Monte Carlo. The physics aspect is the profound study of the Smoluchowsky equations and how it matches to atomistic simulations.