High demand for economically viable separation processes such as adsorptive separation for mixtures of hydrocarbons drives the need for understanding the interaction of hydrocarbons with titanosilicate adsorbents, to replace the energy-intensive cryogenic hydrocarbon separation. Density functional theory (DFT) was used to optimize the geometries and calculate the enthalpies for the interactions between paraffins (C2H6, C3H8), olefins (C2H4, C3H6), and acetylenes (C2H2, C3H4) with a cluster model of the Engelhard titanosilicate having sodium extra-framework cations (Na-ETS-10). The DFT calculations were performed with the M06-L exchange correlation functional and were corrected for the basis set superposition error with the counterpoise method. The calculated enthalpies for the interaction of hydrocarbons with Na-ETS-10 decrease with the decrease in the number of carbon atoms, in the order acetylenes > olefins > paraffins, and compare well with experimental data available in the literature. The enthalpies calculated at the M06-L/6-31++G** level of theory for the two extreme cases, i.e., strongest and weakest interactions, are −62.8 kJ mol−1 (C3H4) and −26.9 kJ mol−1 (C2H6). Additionally, the calculated vibrational frequencies are in good agreement with the characteristic vibrational modes of ETS-10 and of the interactions of hydrocarbons with Na+ in the 12-membered channel in ETS-10.