# Improved force-field approximations of symmetry-adapted perturbation theory

# Improved force-field approximations of symmetry-adapted perturbation theory

Promotor(en):**18MODEV09**/ Model and software development**T. Verstraelen**/Molecular dynamics simulations are used in many scientific domains to understand a system of interest at the atomic scale, e.g. "how does a drug molecule interact with an enzyme?" or "how is a gas adsorbed in a nanoporous material?" Such simulations typically use force-field models to assure that the computational cost of the simulations remains feasible. These force fields are simple mathematical expressions for the forces acting on atoms, which are needed to perform molecular dynamics simulations. The simplest example is the Lennard-Jones model, which is suitable for noble gases. More complex systems exhibit different types of interatomic forces for which separate terms are introduced in a force field. Historically, such complex models were developed without relying on quantum-mechanical electronic structure theories. Instead, a large number (hundreds) of parameters in empirical models were adjusted with statistical methods to reproduce experimental or theoretical data sets. This traditional approach is limited because one must estimate more parameters for every new molecule or material of interest, which is a laborious and often ambiguous task. With the increasing interest in atomistic simulations, it is clearly desirable to reduce the empiricism and the number of adjustable parameters, as to obtain more accurate force fields which are at the same time easier to apply to any new atomistic model of interest.

We recently published a significant step in this direction, by proposing a force field for intermolecular interactions with only three adjustable parameters, the Monomer Electron Density Force Field (MEDFF). [1] The central idea is to express all intermolecular interactions in terms of electron densities, which can be easily computed with Density Functional Theory. This model already gives very promising results for dispersion-dominated interactions, e.g. a quantitative reproduction of second virial coefficients. It is now also successfully used to model gas adsorption in nanoporous materials. However, there is still room for improvement, e.g. MEDFF still makes considerable errors for interactions between polar molecules, e.g. when they form a hydrogen bond. At a fundamental level, this can be attributed to approximations in MEDFF with a weak connection to the quantum-mechanical description of electronic systems. The goal of this thesis is to replace these weak elements by more physically sound models and to validate them using standard data sets to benchmark models for intermolecular interactions.

**Objectives**MEDFF decomposes intermolecular interactions in the same categories as symmetry-adapted perturbation theory (SAPT). This is a form of perturbation theory, where one starts from the electronic wavefunctions of two separate molecules. The interaction energy between these two is expanded in a series by switching on the Coulomb interaction between them and by enforcing the antisymmetry of the electronic wavefunction of the complex. The energy terms appearing in this expansion, can be grouped into four main categories: electrostatics, exchange repulsion, induction and dispersion. In MEDFF, each category has a corresponding model in terms of the electron densities of the two molecules. Furthermore, the molecular electron densities are simplified as a sum of atom-centered spherical functions. A first step in this thesis is to test how MEDFF would improve without relying on spherical atomic densities. This is a relatively simple problem, which allows the student to become familiar with all the computational tools for this thesis. The remainder of the thesis will focus more on the theoretical foundations of the energy models in MEDFF. Exchange repulsion is currently assumed to be proportional to the overlap integral of the two electron densities. While this model is extensively used in the literature, a clear derivation (from SAPT) is still missing. Such a derivation could lead to potentially improved models and elucidate new terms in the overlap model. Another avenue for improvements is to decompose the linear response of the electronic wavefunction into atomic polarizabilities. This is currently done by rescaling polarizabilities of isolated atoms. A more rigorous procedure could make use of the Modern Theory of Polarization, which expresses the polarization density as the time integral of the current density while adiabatically switching on a perturbation. The student is free to focus more on either the theoretical derivations in this topic or the numerical implementation and validation of newly proposed models.

**Mobility**This research topic requires no mobility.

**Motivation Appl. Phys.**The physics aspect of this thesis is the development of a classical approximation of a quantum-mechanical description of the electronic structure of matter. The engineering aspect is the implementation of the methodology in advanced simulation software for HPCs.

- Study programmeMaster of Science in Physics and Astronomy [CMFYST]ClustersFor Engineering Physics students, this thesis is closely related to the cluster(s) MODELING, FUNDAMENTALS, NANOKeywordsmolecular simulations, Computational physics, intermolecular interactions, Force fields, NanoscaleReferences
[1] S. Vandenbrande, M. Waroquier, V. Van Speybroeck & T. Verstraelen (2017) The Monomer Electron Density Force Field (MEDFF): A Physically Inspired Model for Noncovalent Interactions. Journal of Chemical Theory and Computation, 13(1), 161–179. https://doi.org/10.1021/acs.jctc.6b00969