| Quantum dots (QDs), also known as nanocrystals, are a special class of materials known as noble metal and semiconductors, which are crystals composed of periodic groups of II-VI, III-V, or IV-VI materials. Quantum dots are very small, ranging from 2-10 nanometers in diameter. Recently noble metal and semiconductor quantum dots, such as Au, Ag, TiO2, CdSe, CdS, are extensively investigated. The size of the dot becomes small enough that it approaches the size of the material's Exciton Bohr Radius, then the electron energy levels can no longer be treated as continuous-they must be treated as discrete, meaning that there is a small an finite separation between energy levels. This situation of discrete energy levels is called quantum confinement. Due to its quantum size effects, quantum dots behave lots of unique characters, which are very different from bulk systems. Researchers have studied quantum dots in nonlinear optics, photovoltaic material, magnetic medium, photocatalyst, biological sensor, etc.An organic photovoltaic cell (OPVC) is a photovoltaic cell that uses organic electronics-a branch of electronics that deals with conductive organic polymers or small organic molecules for light absorption and charge transport. The plastic itself has low production costs in high volumes. Combined with the flexibiity of organic molecules, this makes it potentially lucrative for photovoltaic applications. Molecular engineering like changing the length and functional group of polymers can change the energy gap, which allows chemical change in these materials. The optical absorption coefficient of organic molecules is high, so a large amount of light can be absorbed with a small amount of materials. The main disadvantages associated with organic photovoltaic cells are low efficiency, low stability and low strength compared to inorganic photovoltaic cells.In the first part of Chapter 1, we introduced the basic idea of density functional theory, from original Thomas-Fermi model, Hohenberg-Kohn theorem, to Kohn Sham equation. Similarly, we also introduced time dependent functional theory, from Runge-Gross to time dependent Kohn-Sham (TDKS) equation. Based on the above content, we illustrated how to solve TDKS equation by propagating density matrix in time domain. Finally, we introduced fewest switches surface hopping (FSSH) method based on the TDKS formalism, together with line width theory. In the second Chapter, we studied phonon induced plasmon dephasing for silver quantum dots. Silver quantum dots, known as noble metal, is unique due to its localized surface plasmon resonance. The homogeneous linewidth for plasmon resonance is determined by plasmon dephasing and relaxation. In the first part, the electron-phonon coupled plasmon dephasing is investigated. The results indicate that the electron-phonon dephasing mechanism is an important part of the overall dephasing process, and that it creates a note worthy contribution to the plasmon linewidth. The dephasing time shows weak dependence on QD size but changes significantly with temperature. In the second part, we investigated electron-phonon relaxation for silver QDs by FSSH-TDKS method. The relaxation times range from 500 to 1800 fs, relaxation for high energy plasmon states is slower than low energy states, which agree well with experimental results.In the first part of Chapter 3, the ultrafast electron transfer processes in three dye-sensitized TiO2 nanocrystals are studied by using the real-time TDDFT. We predict an electron injection time of a few femtoseconds for the present finite systems, which is slightly longer than the experimental measurements and other theoretical predictions for the ET time on the same dye-sensitized bulk TiO2 systems due to the small clusters used in our simulation. We find that the ET time is appreciably dependent on the QD size when the QD is quite small. However, the size effects on ET time reduce dramatically as the cluster size reaches to a moderate middle size. In the second part, multi-exponential electron transfer processes across ultrasmall dye-TiO2 nanocrystal are studied by ab initio nonadiabatic molecular dynamics. The multi-exponential electron transfer occurs from the finite separation between energy levels of conduction band, which leads to both adiabatic and nonadiabatic electron transfer. Furthermore, slow back electron transfer exists in alizarin-TiO2 system, which increases the possibility of efficiency of solar cell.In the last chapter, a novel class of compounds aimed at improving the efficiency of organic photovoltaic devices is investigated by ab initio electronic structure theory. Two heterojunctions composed of chemically bound donor and acceptor species shows little charge transfer in the ground electronic state. In contrast, photoexcitation results in substantial charge separation between the two species, suggesting that the optically excited states present a separated charge pair rather than a strongly interacting pair of charges forming an exciton. The optical cross-section of this charge separated state is quite high due to a good overlap of the tails of the ground and excited states wave-functions. The absorption spectrum of the systems covers visible spectrum and extends to infrared, suggesting good prospects of light harvesting. The calculations results indicate that the proposed class of semiconducting heteroj unctions may be able to overcome the exciton bottleneck problem in organic photovoltaic materials.
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