| The developing time-dependent density-functional theory (TDDFT) has been attracting more and more attention since its intrinsic advantages, such as explicit physical conception, rigorous basis in theory, convenience in application and general applicability. It is hopeful to become a general method to deal with both linear and non-linear response of multi-electron systems.The studies of excited states of atoms and molecules have opened out many colorful physical pictures. In the past decades, many efficient high level methods, such as configuration interaction method, quantum Monte Carlo simulations and the Green function method, have been developed to deal with the excitation of electrons. While these methods describe electronic excitations properly, they are usually limited to deal with very small systems because of their complication and high computational demands. An alternative efficient approach is to consider the linear response methods based on TDDFT.In this thesis, according to the Petersilka linear response theory which is based on TDLDA, combining with the pseudo-potential model, several excited states of sodium atom are calculated in detail. The resulted sodium spectra consist with the experimental data very well, with a less than 0.6% relative error of the principal series, which show a good evidence for the TDDFT application to the description of the excited system.Recently with the development of laser technology, the subject of interactionbetween strong laser and atoms, molecules has become a new hot topic. When atoms and molecules are radiated by ultra intense laser pulse, a series of new non-linear phenomena which can't be interpreted by perturbation theory appears. The most attractive one is high order harmonic generation (HHG), which can be used as a source of extreme ultraviolet (XUV) and soft X-ray lasers. The importance of studying HHG consists in two aspects. Firstly it can accelerate the development of non-perturbation theory and contribute to the further understanding of strong laser induced new phenomena and the underlying new physical mechanism. Secondly it may provide theory background for the development of simple and cheap short wavelength coherent light generators.The popular theoretic methods to describe the simplified interaction of laser-atoms and molecules are based on time-dependent Schrodinger equations (TDSE). As the number of electrons and the degree of freedom increase, the solutions of the TDSE go beyond current computational ability. However, according to TDDFT, if the electronic density is taken as the principle variable the degree of freedom will remain very small, despite the increase of the number of particles. In this thesis, the HHG of hydrogen molecule radiated by an ultra strong femto-second laser pulse are simulated by the TTDFT method with the general gradient approximation (GGA) of the exchange-correlation energy. The results indicate that the HHG spectrum of H2 has a "Decrease-Plateau-Cutoff' structure, which is similar to the typical atom HHG spectrum; when the polarization of laser is perpendicular or parallel to the molecule axis, there is a kind ofselective phenomena of the order number of HHG, which may be induced by the symmetry of H2 molecule. Compared with the result of one dimension soft Coulomb model, the peak region of the transform ratio both locate between 9th to 19th orders; the cutoff order of TDDFT result is smaller than the classical model. We also find that the difference in the polarization direction may change the cut-off order and spectrum intensity of HHG. Further research about the HHG of H2 and other molecules radiated by lasers with different parameters and how to interpret the physical mechanism underlying the phenomena with the evolution of the electronic density are carrying out.The basic works in this thesis may lead us to explore more interesting and fascinating strong laser induced excitation and nonlinear response of atoms and molecules. |
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