In my thesis, I present the major works that I have finished during my PhD study. In the past 4-5 years, my research is focused on developing and applying the time-dependent density functional theory (TDDFT) or time-dependent Hartree-Fock (TDHF) theory or novel numerical algorithms to investigate the electronic structures, optical spectra and ultrafast electron dynamics of nano-size functional materials. We perform theoretical studies toward understanding the interaction between the materials and the external fields, the principles of linear and nonlinear responses of the materials, the mechanism of the molecular high-order harmonic generation, the nonadiabatic effect of polyatomic molecules in the intense laser field and the coupling effect of electron—nuclei of flexible conjugated polymers, etc. The following three manifolds are concerned: (1) We develop the time-dependent density functional theory and numerical algorithms to describe the interaction between the complex systems and intense laser fields, to investigate the electron dynamics of systems and to describe the coupling of electron-nuclei in complex molecular systems, (2) We study the mechanism of molecular high order harmonic generation theoretically and investigate the interaction between the harmonic spectra and polarization direction of the external field or the geometries of molecules to show the relationship between the geometries and electron structures which can not be observed in experiment. (3) We investigate the properties of some important systems, such as high order harmonic spectra of finite length C/BN nanotubes; the absorption and emission spectra of flexible conjugated polymers; the electron dynamics of polyatomic molecules using theoretical model and software about calculation of quantum chemistry. We consider the effect of sizes and geometries of nano-materials on electronic structures and dynamics and show the relationship between the geometries of functional materials and properties which can not be described in experiment easily.The main results are summarized as follows: 1. We develop fast propagator approaches to solve the time-dependent Kohn-Sham equation in TDDFT to investigate the electron dynamics of complex molecules, to describe the rearrangement of electrons and the ultrafast electron dynamics of molecules.2. By combining TDDFT and correlation equations, we construct a theoretical model and codes which can deal with harmonic and anharmonic oscillators and study the absorption and emission spectra of flexible conjugated polymers and the distribution of exciton.3. The calculations of silicon nano-clusters prove that, the silicon particles with sizes of 1nm and the optical excitations at 3.7, 4.0 and 4.66V observed in experiment may consist of 29 Si atoms surrounded by 24 hydrogen atoms not by 36 hydrogen atoms.4. The investigations about quasi-one-dimensional all carbon-nano-materials such as carbon nanotubes or polymers, show that, the geometries and sizes of the systems play a vital role on their physical properties such as energy bands and linear absorption spectra. And different systems require quite different system sizes to achieve the converged physical properties. Besides, doping also can alter the charge distributions, local electronic structures and linear optical feature.5. From the time-dependent simulations about systems in intense external field, we find when systems interact with strong laser field, C and BN nanotubes can generate high order harmonic very efficiently. So they are the ideal pulsed sources of the very fashionable atttosecond lasers. There are clearly differences of nonlinear optical properties between the finite and infinite size nanotube models. The laser can drive the electrons to move along or normal to the tubes being dependent on the polarization of field.6. The studies about polyfluorenes show that, the vibronic structure in absorption and emission spectra dependent on the chain geometries and temperature very distinctly. And chemical substitudents have appreciable influence on both absorption and emission spectra. Besides, for fluorescence proteins, the optical properties can decides by their chromophore mainly, but protein environment also have influence.