This dissertation, studies two specific topics related to the research of surface science by employing the molecular dynamics (MD) approach, that of a water droplet deposited on a poly (methyl methacrylate) (PMMA) substrate and that of a single tricarboxylic acid derivative, 1, 3, 5-tri(carboxymethoxy) benzene (TCMB, C6H3(OCH2COOH)3 ) adsorbed on gold (100) and (110) surfaces. These can help engineers clarify the characteristics and phenomena of physical adsorption of the molecule, as well as contributing to the application of surface science. This work is divided into two parts. Effect of droplet size on the structural and dynamical behavior of a water droplet spreading on a PMMA amorphous surface: note that most experts prefer to consider a rigid model as the substrate in research of surface wetting because it is more efficient to run the MD simulation such that a long simulation can be accomplished in a short time. The results verify that the rigid model is not suitable to act as the PMMA substrate in simulation because it prevents the diffusion of PMMA molecules, which then affects the penetration behavior of water molecules in the droplet upon impact with the PMMA surface. Several sizes of water droplets are considered in order to understand the size influence of the droplet on the properties of water molecules and on the PMMA surface. The penetrated water molecules and the local roughness increase with a decrease in the size of the droplet, which also leads to a smaller contact angle of the water droplet on the PMMA substrate. When the droplet is composed of more than 1000 water molecules, the contact angle shows agreement with experimental results. As regarding the structure of the water molecule in the droplet on PMMA substrate, the average number of hydrogen-bonded penetrating water molecules is in inverse proportion to the size of the droplet By examining the velocity field, the regular motion of the water droplet is found during the equilibrium process and after the droplet reaches the equilibrium state. The diffusion of the water molecules shows a significant decrease for the penetrated water molecules and an increase as it gradually approaches the vapor/liquid interface. Finally, calculations at different regions are made for the vibration spectrum of the oxygen atom, life time, and the relaxation time of the hydrogen bond. The changes of the hydrogen-bond dynamics of the hydrogen bond are consistent with the change of the distribution of the hydrogen bond angle. Effect of surface structure on the structural and dynamical behavior of a tricarboxylic acid derivative molecule on Au surfaces: the dynamical behavior of the single tricarboxylic acid derivative, 1, 3, 5-tri(carboxymethoxy) benzene (TCMB, C6H3(OCH2COOH)3 ) on Au (100) and (110) surfaces by molecular dynamics simulation approach is studied to provide better understanding of surface diffusion. Four possible conformations of the adsorbed TCMB molecule on the Au surface are found, with differences arising from different numbers of CH2 groups adsorbed on the Au substrate. Both the number of CH2 groups in the TCMB molecule that interact with Au surface and the different geometric relationship between the TCMB molecule and the Au surface strongly affect the translational motion, rotational motion, interaction energy and the Lock-and-Key behaviors of the TCMB molecule. A poor complementarity between the TCMB molecule shape and atomic structure of the surface results in significant migration of the molecule and is therefore an unstable adsorption. These results will be useful for the design of a molecular monolayer.