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Dynamics of electronically excited states including exciton generation and relaxation, exciton-exciton interaction, and charge/energy transfer and transport, are critical to understanding and optimizing photovoltaic materials. Although considerable progress has been made, accurate experimental characterization of such crucial dynamics remains extremely challenging, especially in low-dimensional materials. In this talk, I will discuss how the advancement of quantum mechanical simulations of the dynamics of electronic excitations can reveal the physical mechanisms hindering or improving solar energy harvest. Specifically, we find that surface dangling-bond defects on silicon quantum dots cause rapid charge recombination and low carrier mobility in the inorganic-organic PV cells. Although small quantum dots are essentially free of defects, their optical gaps are too large. To solve this issue, a full-spectrum-light-absorption scheme is computationally designed, taking advantage of complexity and flexibility of low-dimensional materials consisting of different characteristics and dimensions. In this scheme the multifunctional ligands are used to (1) passivate against oxidation, (2) facilitate interfacial charge transfer, and (3) improve both charge transport and optical absorption. A joint theoretical and experimental study has demonstrated the feasibility of this approach. Finally, I will briefly talk about how this scheme and the well-tested quantum mechanical simulations can be employed to help improve energy-conversion efficiency in perovskite photovoltaics including perovskite-based tandem cells.