Using the concepts of scaled particle theory, an analytical theory is developed to investigate the Limiting behavior of solvation free energies at the particle creation limit. The new theory directly incorporates the weakly attractive, dispersion interaction terms into the analytical calculations. For neutral molecular systems, the effects of longer ranged electrostatic interactions are also incorporated, albeit in an ad hoc way, and the validity of the utilized assumptions are then demonstrated with numerical examples. It is shown that it is possible to blend the numerical and analytical methods to increase the reliability of quantitative results, and, at the same time, to achieve savings on computational expenditure for certain types of calculations. Different methods of performing the thermodynamic integration in solvation free energy calculations are also compared. Studied examples clearly show the importance of proper treatment of the divergence at the particle creation limit in obtaining quantitatively reliable results for the solvation free energies.