Wen, Xuelan2022-02-152022-02-152020-12https://hdl.handle.net/11299/226392University of Minnesota Ph.D. dissertation. December 2020. Major: Chemistry. Advisor: Jason Goodpaster. 1 computer file (PDF); xv, 119 pages.Kohn-Sham density functional theory (KS-DFT, hereafter referred to by DFT) has been widely used to study the electronic structure of molecules and solids due to its affordable computational cost and satisfactory accuracy when functional is carefully chosen. However, DFT can be deficient in treating systems with multireference characters, such as broken bonds, conjugated bonds, and transition metals. In solids states, it is also well-known that pure DFT severely underestimates the band gaps for materials. On the other hand, correlated wavefunction (WF) methods are systematically improvable and provide consistent accuracy for various systems, but at the cost of a steep increase in computational scaling.Projection-based quantum embedding methodologies provide a framework for performing DFT-in-DFT and WF-in-DFT calculations. A total system is divided into two or more subsystems, and each subsystem is solved with the others’ embedding potential. The WF-in-DFT embedding calculations enable us to treat large complex systems at the WF level of accuracy and the DFT level of computational cost. This thesis discusses the development and application of projection-based quantum embedding to study the excited states in molecules and solids. Except for the theoretical works on quantum embedding, this thesis also includes several computational works collaborated with experimentalists from different chemistry fields. Computational modelings help us understand the reaction mechanisms and experimental observable.enband gapsexcited statesquantum embeddingsolvatochromic shiftvertical excitation energyWF-in-DFTThesis or Dissertation