Calculation of solubility from solvation free energy

Hello. Can anyone kindly guide me on how to calculate solubility from solvation energy of non ionic compound calculated using DMOL3 COSMO solvation model? I  came across the following equations in Literature.
 =                                       (1)

                            (2)

             (3)

All other parameters are know except Ps, Vm and Q representing solute vapour pressure, solute molar volume and octanol-water partition co-efficient respectively.  
 

The use of Ps = RT/Vm  e^(∆Gs/RT) to calculate p for eq. (1) requires Vm which are unknown for the systems under consideration. Also, eq. (2) requires Vm too. Efforts to eliminate both Ps and Vm by combining appropriate equations above proved abortive as the resulting equation still contains either Ps or Vm. Another attempt leads to an equation in which the intended solubilty term (S or Ss) has been eliminated.
The use of eq. (3) requires the octanol - water partition co-efficient which I have no idea of determining using DMOL3 COSMO solvation model. Any contribution for this forum will be highly appreciated. Thanking you in anticipation of your contributions.


where V_m is the molar volume, R the gas constant, and T the temperature