Among metal oxide semiconductor photocatalytic materials, TiO2 has attracted vast attention and is considered to be the most promising materials in the fields of renewable energy and environmental protection due to its stable properties, high activity, low cost and non-toxicity. To investigate the interaction mechanisms and influence factors of TiO2 material in photocatalytic reactions, scientists have put in great research efforts and great progresses have been achieved. Researches show that there exist many factors influenced the photocatalysis process. Besides the wide band gap (3.2 eV for anatase) which inhibits the efficiency of optical adoption, some other factors such as the crystal structure, constituents of grains, grain surfaces, dopants, carrier trapping agent and external environment would have various degrees of influence on the photocatalytic process. The excellent photocatalytic performance mainly derives from anatase and rutile polymorph, especially the anatase polymorph which has relatively high activity contributes significantly to the photocatalytic performance of TiO2. Generally, the high activity of anatase polymorph is mainly resulted from the higher oxidizing ability and larger capability for adsorbing molecules or hydroxyl groups, smaller grain size and high specific surface area. While as larger grains and lower adsorption capability are the principal origin of lower activity of rutile polymorph, researches indicate that the activity of TiO2 is closely related to the highly active surface of grains. The highly active surfaces of TiO2 have higher capability of oxidation and degradation in interaction with molecules. This has raised awareness of important role of highly active surfaces in the photocatalytic reactions. Both experimental and theoretical works show that (001) surface has the highest activity amongst the facets of anatase polymorph. The interaction between molecules and (001) surface is quite strong. Thus, molecule is relatively easy to dissociate on this surface. Moreover, TiO2-B (100) was found to have a similar high activity. Obviously, increasing the proportion of highly active surface among the facets of grains is very meaningful to enhance the photocatalytic performance of TiO2 grains. The first-principles method becomes an essential complement to experimental investigations and has been widely used in the studies of properties of TiO2 materials. Through investigation of the properties of TiO2 via first-principles method, this provides an insight into the detailed process and mechanisms of TiO2 in the interaction with molecules from the microcosmic perspective thoroughly and profoundly. In this thesis, a systematic investigation is performed on some properties such as geometric parameters, electronic structures, activities and adsorption capability of molecules of TiO2 anatase (101), rutile (110), anatase (001) and TiO2-B (100) surfaces. Moreover, the mechanisms of interactions between surfaces and molecules have also been investigated and explained. Using the DFT method, we investigate formaldehyde (HCHO) adsorption on rutile (110), anatase (101), anatase (001) unreconstructed surface as well as anatase (001)-(1x4) reconstructed surface. The results show that the activities of these surfaces have the order of anatase (101) < rutile (110) < anatase (001). Though the anatase (001) surface has the highest activity, it is unstable and has the trend of reconstruction. Interestingly, we found that the reconstruction of anatase (001) surface has not only kept the high activity but also raised the surface stability. HCHO molecule can be stably adsorbed chemically on all these surfaces. In the most stable adsorption configurations, the molecule forms into a dioxymethylene species (CH2O2) through the bonding with surface 2 fold coordinated O atom (O2C). Dioxymethylene species was found to be the important product of HCHO adsorption and has been usually observed experimentally. The carbonyl of dioxymethylene in the adsorbed HCHO is 14-17% longer than that of the free HCHO molecule indicating that intramolecular interaction between C and O atoms has been weakened and it is easy to be decomposed, which may be an important factor in the degradation of HCHO. Additionally, involving the adsorption on anatase (001) surface, (1x4) reconstructed surface has more capability of adsorption than (1x1) unreconstructed surface due to the higher adsorption energy. The eVer (1x4) reconstructed surface has a surface energy of 0.52 J/m2, which is much lower than that of unreconstructed surface, implying that the reconstruction would improve not only the reactivity but also the stability. Therefore, increase of the proportion of (1x4) reconstructed surface among the grain surfaces would improve the activity and stability performances. These results indicate that a careful preparation of novel anatase TiO2 crystals with large amount of (001) facets may be an important way for further improving the properties of titania-based photocatalyst and gas sensors. The adsorptions of HCHO without and with hydroxyl group co-adsorption on TiO2–B (100) surface are also systematically investigated using the first principle method. The results show that the adsorption of HCHO with chemical adsorption structures in the form of dioxymethylene species (CH2O2) occurs on both unhydroxylated and hydroxylated surfaces. On the hydroxylated surface, effects of two kinds of hydroxyl groups, one is bridging OH (BH) group, another is terminal OH (TH) group, which are products of dissociation of water on TiO2-B (100) surface, are found. The adsorption of HCHO was weakened by the existence of BH, while enhanced by the co-adsorption of TH. Through the electronic structure analysis, we found that as compared to the adsorption on the unhydroxylated surface: (i) HCHO gains more electrons on the hydroxylated surfaces, and (ii) HCHO gains more electrons with TH co-adsorption among the two hydroxylated surfaces. This difference originates from the different effects of hydroxyl groups upon the surface, i.e. BH raises the Fermi l eVel and TH lowers the Fermi l eVel, which induces that the surfaces with different chemical activities. Moreover, the existence of H2O was also found to have promotive effect on the adsorption energies of HCHO on the larger periodicity, indicating low density of H2O molecule on the surface can strengthen the interaction between HCHO and TiO2-B surfaces. These results indicate that H2O molecule and hydroxyl groups, which are the fragments of dissociated H2O, play a completely different role when co-adsorption with HCHO on TiO2-B (100) surface, and a humid environment may have an important effect on the TiO2-B (100) surface in photocatalysis reaction processes. Using the DFT+U method, we further investigated the influence of F-dopants, which substitute the O atoms near the Ti5C atom in the anatase (001) surface, on the surface activities. Three kinds of F-dopants of FI, FII and FIII, which are the F-dopants substituting a surface O2C atom, or a surface O3C atom, or an O3C atom below a surface Ti5C atom, representing F-dopants of different depths, were considered. The results of interaction between F-doped surfaces and molecules show that FI dopant raises the stability of surface, while FIII dopant raises the activity of surface. The surface doped with FII has an activity similar to the pristine one. Additionally, the surface energy was found not to be the only factor which can influence the surface properties. In the F doped surface, another important factor is the excess electron induced by F-dopant and fully located in the 3d orbital of Ti3+. This electron pushes the Fermi l eVel to the bottom of conduction band and makes the slab an n-type semiconductor. As a result, the activity of surface was greatly enhanced. In most cases, the adsorption of molecules on F-doped surfaces is stronger than on the pristine one. The study shows that Ti3+ has some unique effects on not only electronic and magnetic but also structural properties of adsorbed gases. The bridge role of Ti3+ induced by F-dopants in electron transferring and enhancing effects on adsorptions suggests a great potential of these species for future applications of titania-based catalyst.