Background and problem

Nanoporous materials have attracted much attention in the past decades due to their impressive potential for applications in the field of natural gas storage, detection and separation of gases, or even as effective drug delivery systems. An example of such nanoporous materials is given by the so-called metal-organic frameworks (MOFs), which are hybrid materials consisting of inorganic bricks connected to each other through organic linkers. Due to their porous nature and favorable interactions with guest species, they have been proven to exhibit extra-ordinary adsorption properties. Several modeling techniques exist to investigate these adsorption properties. On the one hand, one could consider direct molecular simulation by performing Monte Carlo in the grand canonical ensemble (GCMC). While these simulations are very accurate, they tend to be computationally expensive, especially when coupled with an ab initio model such as electronic density functional theory (DFT) for describing the intermolecular interactions, which limits their applicability. On the other hand, one can also use classical density functional theory (cDFT), which is the classical analogue of electronic DFT. However, while electronic DFT is used to compute the electronic wavefunction, as well as its corresponding energy, of an interacting molecular system of fixed number of electrons N at a temperature of 0 K, cDFT is used to compute the particle density n(r), as well as its corresponding grand potential Ω, for an interacting set of gas molecules in a given external potential at given chemical potential µ and finite temperature T:

In the context of gas adsorption in nanoporous materials, the interaction between gas molecules is expressed by an interdistance-dependent interaction potential w(r), while the external potential v(r) expresses the position-dependent interaction energy of an adsorbed gas molecule with the host framework. While cDFT calculations are much faster than GCMC, there accuracy can be equivalent to GCMC under the condition that the so-called excess free energy, i.e. the hard sphere and mean field interaction contributions in the example illustrated in the equation above, is well chosen. As such, the accuracy of the cDFT calculations will be determined by the accuracy of both the interaction potential and external potential. While the interaction potential can be accurately described by an effective potential tuned to match experimental behavior of the pure gas/liquid, one does not have easy access to such experimental input required for tuning the external potential. Therefore, in this thesis, we aim to use ab initio calculations to improve the description of the external potential and lift cDFT calculations for gas adsorption in nanoporous materials to experimental accuracy.

Goal

The most straightforward way to achieve higher accuracy of cDFT calculations would be to use a full ab initio description of the external potential. Unfortunately, as this external potential is required on a fine 3D grid covering the entire unit cell of the nanoporous framework, this would lead to an unfeasible large number of ab initio calculations. Therefore, in this master’s dissertation we aim at combining the speed of classical force fields (FF) with the accuracy of ab initio (AI) methods through the development of a hybrid FF/AI model for the external potential in cDFT simulations of gas adsorption in nanoporous materials. Herein, a distinction is made between high-accuracy and low-accuracy grid points inside the host framework based on importance sampling. More specifically, grid points for which a high particle density is anticipated, will be computed with the more accurate yet slower ab initio method, while grid points for which a low particle density is anticipated, will be computed with the less accurate though faster force field method. However, such an approach can only prove to be more efficient when the number of high-accuracy grid points is considerably smaller than the number of low-accuracy grid points. Therefore, the decision between high and low accuracy will be made using an fast initial cDFT simulation at the force field level. An implementation for doing such cDFT calculations is already available at the CMM and will be used as a starting point for this master thesis.

This master’s dissertation will involve advanced thermodynamic and statistical physics modeling as well as numerical implementation in an available Python package. Furthermore, the student will perform both force field and ab initio simulations using existing software packages to obtain adsorption energies for the low and high accuracy points respectively. Depending on the interest of the student, (s)he can also perform GCMC calculations with the FF and/or hybrid potentials to serve as additional validation. Finally, the CMM has ongoing projects with experimental partners giving access to the necessary experimental data required for a critical validation of the simulation results.