The interaction energies of five pairs of interactions: CH3OH-CH3OH, CH3OH-CO2, CO2-CO2, CH3OH-CH3CH2OH, and CH3CH2OH-CH3CH2OH were obtained using MP2, B3LYP, and B3LYP-D3 methods. Activity coefficients of CH3CH2OH-CH3OH and CH3OH-CO2 systems were calculated using the UNIQUAC equation and the phase diagrams of these binary systems were constructed based on the Raoult's law. The B3LYP-D3 methanol/ethanol isothermal phase diagram at 298K is in good agreement with the experimental data and the agreement is slightly better than the MP2 result and much better than the B3LYP result. Thus, the B3LYP-D3 method is promising to obtaining activity coefficients and illustrates the promise of molecular simulation of phase diagram of binary systems. A carbon dioxide/ethanol isothermal phase diagram at 230K was constructed. The current results showed that CO2 and CH3OH are hardly mixed under the simulation conditions.