Bridging Quantum Drude Oscillators and Electronic-Structure Theory for van der Waals Dispersion Interactions

Van der Waals (vdW) dispersion forces are fundamental to the structure and behavior of biomolecular, solid-state, and polymeric systems. These interactions, arising from Coulomb-correlated quantum fluctuations in charge density, in principle, demand sophisticated quantum chemistry methods, such as coupled cluster and quantum Monte Carlo. However, the high computational cost of these approaches limits their practical application to large and complex systems. Approximate methods, like classical force fields or semi-local density functional theory (DFT), fall short of capturing the intricacies of vdW dispersion forces. This thesis addresses these limitations by advancing the theoretical description of vdW dispersion interactions through the quantum Drude oscillators (QDOs) framework -- a versatile, coarse-grained model for electronic response.

To this end, we first develop a universal, analytical vdW potential based on the QDO model, applicable across the periodic table. With minimal parametrization, this potential is designed for noble gases and generalized to atomic and molecular dimers, achieving high accuracy compared to experimental data and high-level ab initio calculations. Relying on just two atomic parameters -- dipole polarizability and dipolar dispersion coefficient, our vdW-QDO potential is twice as accurate as the widely used Lennard-Jones potential. This marks a significant advance for biomolecular force fields, where accurate vdW modeling is critical yet remains challenging.

While vdW interaction energies are known to scale with system size, their broader influence on other properties remains less explored. Using the dipole-coupled QDO framework within the many-body dispersion (MBD) method, we examine how vdW dispersion interactions impact electron density. Our findings reveal that these interactions induce significant charge polarization even in systems as small as 100 atoms -- a phenomenon often overlooked in semi-local DFT, where vdW forces are usually treated as a post hoc correction. To address this, we propose a fully coupled, optimally tuned variant of the MBD model based on vdW-QDO parameters, effectively capturing vdW-induced polarization in diverse systems from small molecules to proteins. Our results indicate potential improvements in density functional approximations by incorporating vdW polarization effects.

While the one-body density contains full information about the ground state of a system in DFT, the universal functional required to extract this information remains elusive. In contrast, the two-body density matrix represents electronic correlations more directly. Building on this idea, this thesis introduces a density-matrix reformulation of the MBD method. This approach facilitates real-space visualization of vdW dispersion interactions, while also linking the dipole-coupled QDO framework of MBD to nonlocal correlation functionals in DFT. The resulting nonlocal MBD correlation kernel is critically assessed against existing nonlocal functionals, offering a deeper insight into the theoretical underpinnings of vdW dispersion interactions.

In conclusion, this thesis highlights the QDO model as a robust framework for advancing vdW dispersion modeling across multiple levels of theory. From developing accurate interatomic potentials to uncovering vdW-induced polarization effects and linking to nonlocal correlation functionals, the QDO framework provides a unified platform to address key challenges in the field. This work enhances the understanding of vdW forces and offers a versatile toolbox for future studies in computational chemistry, biomolecular modeling, and beyond.