The thermal diffusive properties of d-block transition metals are presented in this dissertation using semi-emperical methods. The microscopic study of the diffusion on the surfaces of the metals in presence of the adislands is carried out by molecular dynamics simulation (MD) technique. The diffusion mechanism of small 2- dimensional islands on the (111) surfaces of the transition metals, both for the homo- and hetero-diffusion of the adislands on the surfaces are studied, at different temperatures. The important atomic processes at the back of thermal diffusive behavior of the adislands as well as of the surfaces are elaborated. During the of small islets’ diffusion, the hoping events and zigzag concerted motion along with rotation are observed for Ag 1-atom to 3-atom islands while single-atom and multi-atom processes are discovered for Ag 4-atom and 5-atom islands, during the diffusion on Ag(111) surface. The diffusion coefficient, activation energy barrier and diffusion prefactor are determined for small Ag-islands diffusion on Ag(111) surface. A noticeable increase in the value of activation energy barrier is found with the increase in the number of atoms in Silver adislands on Silver (111) surface. A logical linear fit is observed for the diffusion coefficient for studied temperatures (300, 500, and 700 K). There is the same increasing and/or decreasing trends for both the diffusion coefficient and effective energy barrier are observed in both the self-learning Kinetic Monte Carlo (SLKMC) and MD calculations, for the temperature range of 300–700 K. The diffusion mechanism of small clusters of Copper (Cu) comprising of 1-9 atoms on Ag(111) surface is the major part of the study. Simulations carried out at three different temperatures of 300 K, 500 K and 700K, show dominant concerted motion for the Cu-smaller islands (containing 2 to 4 atoms), while shapechanging multiple-atom processes are found responsible for the diffusion of larger islands of Cu on Ag(111) surface. Arrhenius plots of the diffusion coefficients reveal the effective energy barrier less than 260 ± 5 meV for all Cu9/Ag(111). There is good scaling of the effective energy barrier with size, but most notably it remains constant for islands with 4 to 6 atoms of Cu on Ag(111) surface. The increase in the diffusion coefficient is within a factor of 10 at the said temperatures. The observed anharmonic features of the Cuadislands (breakage and pop-up) at Ag(111) surface as well as the surface anharmonicity of the Ag-substrate in the form of fissures, dislocations, vacancy creation and atomic exchange, are also the part of the dissertation. Regarding the observed diffusion mechanism of small clusters of Ag/Ag(111), the results are in a reasonable agreement with ab-initio density-functional theory calculations for Al/Al(111) while the energy barrier values are in the same range as the experimental values for Cu/Ag(111) and the theoretical values using ab-initio density-functional theory supplemented with embedded-atom method for Ag/Ag(111). For the smaller sized Copper islands on (111) surface of Silver, the variation in effective energy barrier with the island size is in good agreement with the experimental findings. These findings provide better input for KMC simulations and can supplement the experiments of the surface science.