| Nonlinear optics is the study of the interaction of intense laser light with matter, and it is a rapidly developed subject since the birth of the laser. As the important embranchment of the field of modern optics, nonlinear optics has more and more attracted people's considerable attention. It has become an important project to find new nonlinear optical materials with strong nonlinear optical properties and quick response velocity due to their attractive application foreground, for instance, in modern laser technology, optical communication, data storage, optical information processing, and other fields. Much emphasis has been put on organic nonlinear optical materials because they have many advantages, such as large nonlinear optical coefficient, wide response wave band, good flexibility, high optical damage threshold, low cost, and easy combination and modification. The thesis studies the linear and nonlinear optical properties of a variety of newly synthesized organic molecules utilizing many theoretical and computational approaches on the base of the ab initio level, represents the relation of the molecular structures and properties, investigates the solvent effects on the molecular geometry structures and optical properties, and discusses the possible photopolymerization mechanism by analyzing the molecular charge-transfer process. The whole works contain two parts: one part is the study of the one-and two-photon absorption (OPA and TPA) properties of a series of one-and multi-branched organic molecules in gas; the other part is about the solvent effects on the molecular structures and nonlinear optical properties. The main contents and results are represented as follows. First, we study the one-and two-photon absorption properties of organic molecules in gas. 1. The one-and two-photon absorption properties of one-dimensionality organic molecules. At the hybrid density functional theory (DFT) level, the one-and two-photon absorption cross sections of a series of organic molecules with D ? π? A, D ? π? D, A ? π? A types are studied by employing few-state model method. It is well known that the maximum two-photon absorption cross sections of the lowest excited states can be exactly described by only considering few electronic states for one-dimensionality organic molecules. The results indicate that the maximum one-and two-photon transitions all take place in the first excited state for one-dimensionality D ? π? A type asymmetry charge-transfer molecules, but it is different for one-dimensionality D ? π? D and A ? π? A types symmetry charge-transfer molecules where the maximum one-and two-photon absorptions are not happening at the same excited state. Then, we analyze the microcosmic mechanism of increasing the molecular TPA cross sections. The TPA cross sections can be enhanced by increasing the dipole moment difference between the lowest excited and the ground states and the transition dipole moments between the states, and by making the directions of transition dipole moment vectors parallel or antiparallel. In addition, by analyzing the TPA properties of a series of organic molecules, it is found that the TPA activities are related to some factors including molecular conjugated length, the strengths of electron-donor (D) and electron-acceptor (A) for pushing and pulling electrons, the molecular plane and symmetry. And it is also be found that the length of the side-chain linked to the molecule has very little influences on the molecular linear and nonlinear optical properties. 2. The two-photon absorption cross section by use of the response theory approach. We also study the TPA cross sections of the one-dimensionality D ? π? A asymmetrical organic molecules by using the response theory approach where the contributions of all intermediate states being taken into account, and attain the analytic values of computation results. The calculated result of TPA cross sections with response theory approach is different from that with density functional theory due to the response theory approach being carried out at the Hartree-Fock level in which the electronic correlated energy is neglected, it shows that the electron correlated energy is important for the accuracy of computing the TPA cross sections. It is also demonstrated that the general trend is similar for the both of theoretical methods by analyzing the TPA activities of a series of organic molecules. Otherwise, the availability of the few-state model method is testified by the response theory approach. 3. The two-photon cross sections of multi-branched organic molecules. Being differ fromone-dimensionality molecules, the few-state model method is not suitable for computing the TPA cross sections of the multi-branched molecules because they have more charge-transfer states, thus, we apply the response theory approach to attribute the TPA properties of multi-branched molecules. By analyzing the TPA actions of a series of one-and multi-branched molecules been composed of the same elementary structural unit, one can see that the energy gap between the molecular excited states decreases as well as the density of states increases along with the enhancement of the molecular dimensionalities, moreover, some low-lying degenerate states of multi-branched molecules supply more available excitation channels, then the multi-branched molecules should have larger TPA cross sections in many excited states in visible region, these factors benefit for the increase of the TPA. Second, the solvent effects on the molecular structures and optical properties are investigated in detail. Now, many experiments measurements of the TPA cross sections of organic molecules take place in solvents. When solute molecules are solvated in the solvents, the solute molecular charge distribution will polarization solvents around it and this gives rise of a reaction field which acts back on the molecules, then, the molecular geometry structure and optical properties will be modified. So the solvent should be considered in order to realizing the good agreement between the numerical simulation and the experimental results. 1. Solvent effects on the molecular two-photon absorption properties. The maximum TPA cross sections of many molecules in solvents are computed by use of the polarized continuum model (PCM), Onsager reaction field model and semiclassical model, respectively. In the semiclassical model, the molecule is treated quantum mechanically and the reaction field induced by the interaction between the solvents and the solute molecule is regarded as a equivalent classical static field. The theoretical studies show that the TPA cross sections of the molecules are enhanced in solutions, this can be explained by the fact that when the solute molecules are solvated in solvents, the excitation energies of the molecules are decreased, the transition dipole moments are increased, especially for one-dimensionality D ? π? A charge-transfer molecules, the dipole moment differences have a relatively large enhancement compared to that in gas. 2. Hydrogen-bonding effects. In previous studies about the solvent effects, only the longrange interaction between the solvents and the molecule was generally taken into account, and the short range interaction namely hydrogen-bonding was rarely considered, although it is well known to have a largely effect on the molecular geometrical structure and optical properties. In this thesis, the hydrogen-bonding effect on the geometrical structures, charge distributions, and solvatochromic shifts of 4-nitro-buta-1, 3-dienylamine molecule are studied in detail. It is shown that the geometrical structure of 4-nitro-buta-1, 3-dienylamine molecule has been greatly changed in solvents, because the πconjugate electrons are very easily induced by the reaction field. When the hydrogen-bonding interaction is considered, the inner-molecular charge-transfer becomes stronger which farther influences the molecular structure. So the hydrogen-bonding effect should not be neglect in order to precisely describing the interaction between the solute molecule and solvents. 3. Solvent effects on the molecular linear and nonlinear polarizabilities. At Hartree-Fock level, the response theory approach is applied to compute the linear polarizability and the first order nonlinear hyperpolarizability of 4-nitro-buta-1, 3-dienylamine molecule in solution. The results display that the linear polarizability and the first order nonlinear hyperpolarizability of the molecule are all enhanced with the increase of the polarity of solvents, however, the nonmonotonic behavior for the enhancement of the polarizabilities with respect to the polarity of solvents is also observed. Moreover, the solvent effect on the first order nonlinear hyperpolarizability is stronger than that upon the linear polarizability of the molecule. The content of this thesis is as follows. The first chapter gives a brief introduction of nonlinear optics and also the developing process of the nonlinear optics and nonlinear optical materials. In the second chapter, some theories of studying the many-particle system are introduced, including the Born-Oppenheimer approximation, the Hartree-Fock approximation, the density functional theory and a few common exchange-correlation functional. The time-dependent perturbation theory where the interaction between the molecule and the electromagnetic field is regard as perturbation on the molecule are introduced in chapter three, the explicit expressions of one, two-photon transition matrix element and the nonlinear polarizabilities are obtained by solving the schr?dinger equation. In the fourth chapter, the different approaches developed recently for calculating molecular nonlinear optical properties are summarized, including sum-over-state, few-state model, finite field, analytic derivative...
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