In the first study, the optimized geometries, molecular properties, and stabilities of new noble gas molecules, XXeOH and XKrOH (X = F, Cl, Br, and I), were studied using CCSD, MP2, CAM-B3LYP, and WB97XD methods and two Aug-CC-PVTZ and 6-311++G** basis sets. In addition, for NBO atomic charges, hybridizations and the bonding properties of XXeOH molecules were studied by AIM calculations (to calculate electron densities, bond elipticities, and Laplacian of electron densities) and second-order intramolecular perturbation energies using NBO calculations. The results showed that IXeOH, showing two OH - and IXe + parts, while in other molecules, they could be presented as XeOH + and X - . Two decomposition routes were proposed for these molecules that showed high exothermic reactions. However, despite their low thermodynamic stabilities, their decomposition rate constants were small and all molecules (except BrXeOH) had high kinetic stabilities, indicating the possibility for identification and characterization of these molecules. Moreover, the ease of formations and relative stabilities of XXeOH molecules were compared using heats of formations, Gi free energies of formations and isodesmic reactions. These calculations showed that the stability of XXeOH molecules was decreased from F to I. In XKrOH molecules, IKrOH and BrKrOH molecules showed two X - and KrOH + parts, while in FKrOH and ClKrOH, they could be presented as XKr + and OH - . A decomposition route was proposed and result showed high exothermic reactions. However, their decomposition rate constants were small and all molecules had high kinetic stabilities. Comparing relative stabilities using heats of formations and isodesmic reactions showed the FKrOH is the most stable and IKrOH is the least stable structure. The reactivity parameters, obtained from population analyses showed that the reactivities increased and stabilities decreased from FKrOH to IKrOH. In the second study, the interactions between graphene (G), S-doped graphene (SG) and 2S-doped graphene (2SG) with eight small molecules including molecular halogens, CH 3 OH, CH 3 SH, H 2 O and H 2 S were studied using density functional theory calculations. The adsorption energies showed that the SG was the best adsorbent, fluorine was the best adsorbate and halogens were adsorbed on graphenes better than the other molecules. Most adsorption processes in the gas phase were exothermic with small positive ?G ads . Moreover, the solvent effect on the adsorption process was examined and all ?H ads and ?G ads values for adsorption processes tended to more negative values in all solvents. Therefore, the most adsorption processes in the solvents are thermodynamically favorable. The second order perturbation energies obtained from NBO calculations confirmed that the interactions between halogens and our molecules had more strength than that of other molecules. The Laplacian of ? values obtained from the AIM calculations indicated that the type of interaction in all our complexes was closed shell interaction. The MO results and DOS plots also revealed sulfur doping could increase the conductivity of graphene and this conductivity was enhanced more when they interacted with graphenes.