We present density functional theory (DFT) calculation results of krypton and xenon atoms interaction on the surface of uranium dioxide single crystal. A pseudo-potential approach in the generalised gradient approximation (GGA) was applied using the ABINIT program package. To compute the unit cell parameters, the 25 atom super-cell was chosen. It has been revealed that close to the surface of a potential well is formed for xenon and krypton atom due to its interaction with the atoms of oxygen and uranium. Depth and shape of the well is the subject of ab initio calculations in adiabatic approximation. The calculations were performed both for the case of oxygenic and metallic surfaces. It has been shown that the potential well for the oxygenic surface is deeper than for the metallic surface. The thermal stability of immobilising the atoms of krypton and xenon in the potential wells were evaluated. The results are shown in graphs.