Predictive Electronic-Structure and Excited-State Simulations of Heterogeneous Materials from First Principles

Heterogeneous materials are ubiquitous in nature and modern technology, playing central roles in phenomena across physics, chemistry, geology, and biology. At solid interfaces, surfaces, defects, and nanoscale architectures, abrupt structural and chemical inhomogeneities can give rise to functional properties that are absent in the corresponding homogeneous bulk phases. Understanding and controlling these properties is therefore essential for the rational design of materials for energy, quantum, and electronic technologies. The theoretical and computational description of heterogeneous materials remains challenging. Although density functional theory (DFT) with semilocal or conventional hybrid functionals is widely used, these exchange-correlation approximations often fail to provide quantitatively reliable electronic structures for heterogeneous materials. More advanced approaches, including many-body perturbation theory methods such as the GW approximation and the Bethe--Salpeter equation, as well as high-level many-body and embedding methods, can provide accurate benchmarks for electronic and excited-state properties. However, their computational cost often becomes prohibitive for the large supercells required to describe interfaces, low-dimensional systems, nanoparticles, and defects. This dissertation focuses on the development and application of first-principles methods for predicting electronic and excited-state properties of heterogeneous materials. In particular, I develop a class of nonempirical hybrid functionals with spatially dependent screened exchange, formulated within the generalized Kohn--Sham framework, to account for spatial variations in structural and chemical environments at the nanoscale. I show that these functionals accurately predict the electronic structure of a variety of heterogeneous systems, including nonmetallic interfaces, two-dimensional materials, defective solids, and nanoparticles. I further refine and assess these functionals for a broad class of materials through a systematic study of metal oxides, demonstrating their ability to describe band gaps, dielectric properties, and magnetic moments with improved accuracy. I then use the proposed hybrid functionals within the framework of linear-response time-dependent density functional theory. This extension enables excited-state simulations in complex dielectric environments and provides a promising route toward predictive calculations of neutral excitations in a broad range of heterogeneous systems, including point defects in three-dimensional and two-dimensional materials, molecular qubits, and charge-transfer molecules. Finally, this dissertation explores a complementary machine-learning strategy to accelerate the computation of dielectric screening in many-body perturbation theory. In GW and Bethe--Salpeter calculations, the construction of the screened Coulomb interaction requires dielectric-response matrices, whose evaluation often represents one of the dominant computational bottlenecks. I develop a framework that predicts these matrices directly from atomic structure, thereby bypassing the costly, direct first-principles calculation of the dielectric matrices. The predicted matrices can be incorporated into existing GW workflows for quasiparticle calculations and Bethe--Salpeter workflows for optical absorption spectra. I show that models trained on smaller systems can transfer to larger systems, including nanoparticles and defect-containing supercells, suggesting a scalable strategy for efficient dielectric screening calculations in complex materials. Together, these developments in physically motivated, nonempirical hybrid functionals, their extension to linear-response time-dependent density functional theory, and machine-learning approaches to dielectric response advance the predictive simulation of heterogeneous materials and provide a foundation for high-throughput screening and design of heterogeneous systems with targeted properties.