Quantum Embedding and Localization Methods for Strongly Correlated Molecules and Materials

Strongly correlated electronic systems underpin a wide range of emerging quantum technologies, including solid-state defects for quantum information processing, molecular magnets, spin qubits, and quantum sensing platforms. Predictive computational design of these materials requires electronic structure methods capable of simultaneously describing strong electron correlation, excited-state phenomena, spin-dependent interactions, and environmental effects. While multireference wave function methods provide the necessary accuracy, their computational cost severely limits their application to realistic molecular and condensed-phase systems. This dissertation addresses this challenge through the development and application of quantum embedding and fragmentation methodologies that extend multireference electronic structure theory to increasingly complex quantum materials.

The first part of this dissertation develops embedding-based approaches for describing optical properties of strongly correlated defects in extended solids. Complete Active Space Density Matrix Embedding Theory (CAS-DMET) and NEVPT2-DMET are applied to oxygen vacancy defects in magnesium oxide, where a systematic double-extrapolation protocol is introduced to approach both the non-embedding and thermodynamic limits. This framework enables quantitatively reliable calculations of absorption and emission energies while significantly reducing the computational cost of conventional multireference treatments of periodic systems.

The second part extends embedding methodologies to the description of spin-dependent electronic structure. Density Matrix Embedding Pair-Density Functional Theory (DME-PDFT) is developed to recover dynamic electron correlation beyond the embedded active space, providing an efficient route for studying transition metal complexes and other strongly correlated molecular systems. Building upon these developments, CAS-DMET is further extended to investigate spin-phonon relaxation in molecular magnets and molecular crystals, demonstrating that quantum embedding can accurately describe spin dynamics and decoherence processes while substantially reducing computational cost.

Beyond classical electronic structure calculations, this dissertation explores fragmentation strategies for hybrid quantum-classical algorithms through the development of efficient methodologies within the Localized Active Space Unitary Selective Coupled Cluster (LAS-USCC) framework. These developments improve the scalability of quantum chemistry algorithms for large active spaces and establish connections between embedding concepts and emerging quantum computing approaches.

Finally, electronic structure calculations based on time-dependent density functional theory are employed to investigate fluorescent protein chromophores as potential biocompatible quantum sensors. These studies demonstrate how first-principles calculations can provide insight into spin-dependent properties in biologically relevant systems and expand the scope of computational approaches for quantum materials beyond traditional inorganic and molecular platforms.

Collectively, the work presented in this dissertation establishes embedding and fragmentation as versatile frameworks for accurately describing the optical and spin properties of strongly correlated quantum systems across multiple length scales. By combining multireference electronic structure methods with physically motivated subsystem decompositions,
these approaches bridge the gap between chemical accuracy and computational scalability, providing practical computational tools for the study and design of quantum materials relevant to quantum information science, molecular spintronics, and quantum sensing.