Graduation Year

2026

Document Type

Dissertation

Degree

Ph.D.

Degree Name

Doctor of Philosophy (Ph.D.)

Degree Granting Department

Physics

Major Professor

Lilia Woods, Ph.D.

Committee Member

Kathiresan Selvam, Ph.D.

Committee Member

Inna Ponomareva, Ph.D.

Committee Member

Jacob Gayles, Ph.D.

Committee Member

Sameer Varma, Ph.D.

Keywords

Density Functional Theory, Maximally Localized Wannier Functions, Layered Materials, Van Der Waals Heterostructures, Lattice Multipolar Polarizability

Abstract

This dissertation addresses the long-standing challenge of accurately and efficiently modeling long-range electron correlations, with a particular focus on van der Waals (vdW) interactions. These interactions play an essential role in predicting the structure, stability, and functionality of molecular systems and condensed matter materials. Although Density Functional Theory (DFT) has become a robust cornerstone of computational materials science, traditional formulations of the theory frequently fail to capture dispersive interactions, leading to significant errors in determining interlayer distances, binding energies, and stacking configurations. These limitations become particularly pronounced in layered materials and vdW heterostructures (HSTs), where weak long-range correlations are sensitive to internal materials properties and govern emergent macroscopic behaviors. In realistic systems, complexity is further heightened by the presence of dopants, defects, and twist-angle variations. These factors may be introduced during synthesis or intentionally designed to tune electrical, optical, and magnetic properties. Such perturbations alter local charge distributions and interlayer coupling, thereby reshaping effective vdW interactions and ultimately determining the observed material properties.

A variety of vdW computational schemes have been developed to remedy these deficiencies. Interatomic pairwise methods offer high computational efficiency but neglect many-body effects and anisotropy; meanwhile, nonlocal density functionals suffer from limited transferability due to their approximate treatment of electron correlations. The Random Phase Approximation (RPA) provides a highly accurate description of correlation effects; however, its computational cost remains prohibitive, precluding its widespread application to routine tasks. The Many-Body Dispersion (MBD) method marks a significant advancement, effectively capturing collective electronic response effects in periodic systems. Nevertheless, in principle, this method remains limited to the scope of dipole–dipole interactions. Consequently, no existing method currently satisfies all three criteria simultaneously: high accuracy, optimal computational efficiency, and broad applicability. Approaches based on Maximally Localized Wannier Functions (MLWFs) may offer a promising avenue, leveraging their inherent ability to establish a link between electronic structure and spatial localization. However, current MLWFs-based vdW schemes remain predominantly pairwise-additive in nature and therefore insufficient to fully capture many-body dispersion and anisotropy effects.

To address these limitations, this dissertation introduces a novel framework termed \texttt{vdW-WanMBD}, wherein the MBD method is reformulated upon a foundation of MLWFs. This construction establishes a direct and physically transparent link between vdW interactions and the underlying electronic structure, thereby enabling a systematic analysis of polarizability, anisotropy, and stacking-dependent effects in layered materials and vdW HSTs. This theoretical framework is further extended beyond the dipole approximation to incorporate higher-order multipolar responses, including contributions from quadrupole and octupole moments. This extension leads to a generalized formulation termed \texttt{vdW-WanMBD-multipole}, wherein generalized expressions for multipole–multipole polarizability in extended periodic systems are established. To the best of our knowledge, this constitutes the first unified many-body dispersion framework that explicitly incorporates multipole interactions, thereby providing a more comprehensive and intrinsically anisotropic description of vdW forces. An efficient implementation of the \texttt{vdW-WanMBD} framework has been developed within the \textsf{WANNIER90} ecosystem, supported by a Python-based workflow toolkit designed to facilitate automation and post-processing analysis. This method has been benchmarked through structural optimization studies on representative datasets, including molecular crystals and layered materials. The results demonstrate that combining DFT with \texttt{vdW-WanMBD} significantly enhances structural prediction capabilities compared to currently widely used interatomic pairwise correction schemes, particularly for material systems where high-quality reference geometry data are available.

Overall, the proposed framework provides a physically well-founded description of vdW interactions that is systematically extensible and computationally efficient. By integrating many-body effects, electronic structure information, and multipolar anisotropy into a unified formulation based on MLWFs, the \texttt{vdW-WanMBD} and \texttt{vdW-WanMBD-multipole} methods overcomes key limitations of existing approaches. Although further validation and large-scale benchmarking remain necessary, this method opens up a promising avenue for developing accurate and highly transferable vdW interaction models for complex materials; particularly in systems where weak, long-range correlations play a dominant role.

This dissertation is organized into five chapters. Chapter 1 introduces the theoretical foundations and research motivation, with a focus on layered and two-dimensional (2D) materials, vdW HSTs, and the role of dispersion forces in determining their properties. This chapter also provides an overview of DFT, common vdW correction schemes, and MLWFs-based approaches, while highlighting current limitations in capturing anisotropic and many-body effects.

Chapter 2 investigates how structural and electronic perturbations influence vdW interactions in low-dimensional materials. The focus lies on factors such as doping, vacancies, and twist-angle variations in vdW HSTs. These factors are demonstrated to significantly alter interlayer coupling and system stability through changes in local electronic structure and polarizability.

Chapter 3 presents the development of the \texttt{vdW-WanMBD} method, establishing a MLWFs-based reformulation within the MBD framework, while simultaneously demonstrating the advantages of this approach in establishing a direct link between dispersion forces and electronic structure.

Chapter 4 extends this framework to incorporate multipolar interactions. This chapter establishes generalized expressions for multipole-multipole polarizability and introduces the \texttt{vdW-WanMBD-E87} formulation. Subsequently, the chapter details the development of the \texttt{vdW-WanMBD-multipole} method that integrates many-body effects associated with higher-order multipolar responses, thereby providing a more comprehensive description of anisotropic dispersion interactions.

Finally, Chapter 5 summarizes the key research findings and outlines directions for future researc including the refinement of the methodology, the execution of extensive benchmark assessments, and the application of these methods to the study of complex material systems, where vdW interactions play a central role in the emergence of novel properties.

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