The dispersion interaction is a weak (mostly attractive) force between molecules due to correlated zero-point motion of electrons in the different molecules. The first quantum mechanical description is due to London, who derived that the leading term in the dispersion interaction between two hydrogenic atoms is attractive and proportional to R-6, where R is the internuclear distance. In the more general case, the second-order dispersion interaction between two molecules, A and B, can be computed with a generalized Casimir-Polder expression:

where alpha A and alpha B are the frequency dependent response functions of the two molecules.

Dispersion interactions are of critical importance in various molecular simulations, also of extended systems (thousands of atoms). Hence, many approximate models were recently proposed to efficiently estimate the dispersion interactions as a sum of contributions from each atom pair in a molecular system. Such models assume that every pairwise term is isotropic, i.e. equally strong for all relative orientations of two molecules.

Goal

The goal of this thesis is to get an initial understanding of the orientation dependence of the dispersion interactions between pairs of small molecules (water, ammonia, dinitrogen, dihydrogen, benzene, ...). Initially, a small molecule and the neon atom will be combined such that all anisotropic effects can be attributed to the molecule.

In this thesis, dispersion interactions will be modeled with the adiabatic connection fluctuation dissipation (ACFD) theorem. This is an elegant quantum-mechanical theory that is widely used to model electron correlation effects in terms in terms of the frequency-dependent electronic linear response. It was shown that approximate linear response models already yield reasonable estimates of the correlation energy, especially the dispersion interaction. For example, the random-phase approximation (RPA) of the electronic linear response is currently extensively studied for this purpose. One may even derive an RPA equivalent of the Casimiar-Polder expression.

Using the ACFD and RPA framework, the dispersion anisotropy can be attributed to the anisotropy of the frequency dependent linear response of the two molecules involved. This anisotropy will be analyzed further with an atoms-in-molecules decomposition of the frequency dependent response. The results will be directly relevant for the continuing development of computationally efficient models for dispersion interactions that are also applicable to larger molecules.

Mobility
This thesis fits well in a new collaboration with Alexandre Tkatchenko (Luxembourg), who is an expert on many-body dispersion corrections for DFT calculations. A short visit to his group would be valuable to analyse the results of this thesis.

Motivation Appl. Phys.
The computation of dispersion interactions require a fundamental understanding of the quantum-mechanical electronic structure of molecules. The results of this thesis are directly relevant for applied computational research in materials science and chemistry.