It is of interest to predict the thermodynamic properties and phase behavior of a substance from quantum-chemical calculations of intermolecular interaction energies followed by molecular simulations. However, while quantum-chemical methods can be quite accurate, they do not provide an exact solution to Schrodinger's equation (excluding full CI) and additional errors arise when fitting energies to analytic potential functions. The purpose of this communication is to provide an understanding and quantification of the sensitivity of the calculated properties to changes (or uncertainties) in different parts of the potential function. For this purpose, Gibbs ensemble Monte Carlo simulations were used to determine the effects on phase behavior of small perturbations to various regions of the model Lennard-Jones 12-6 potential. The results indicate that repulsive energies play a limited role in determining the phase behavior and critical properties, while the attractive energies strongly affect the critical temperature, critical pressure, saturation densities, and vapor pressure. The critical density is most strongly affected by the location at which the potential is zero. However, when the phase behavior and second virial coefficient are scaled by the critical properties calculated for each potential, the results obey a corresponding states relation. These results are used to understand and predict variations in the calculated phase behavior for intermolecular potentials obtained using various strategies to fit ab initio-calculated interaction energies. The knowledge obtained is used to provide accurate predictions for neon based on quantum-chemical energies and a recommended fitting strategy. We also show that three-body nonadditivity effects are largely unimportant for neon.