A partition coefficient calculation method with the SFED model

The Solvation Free Energy Density (SPED) model, a solvation model proposed by No et al. was modified to give better solvation free energies of the molecules having high polarizable groups. The SPED at a point around the molecule was represented by a linear combination of four basis functions, the contribution from the cavitation free energy of a solvent, and a constant. As an application of the SPED model, the linear expansion coefficients of the Hydration Free Energy Density (HFED) and the 1-Octanol Free Energy Density (1-OFED) were determined. Both calculated hydration free energy and 1-octanol solvation free energy of selected 95 organic molecules agreed well with experimental values. The standard errors were 0.47 and 0.39 kcal/mol, respectively. 1-Octanol/water partition coefficients (P) of the molecules were calculated from the difference of the HFE and 1-OFE of the molecules. At the same time, the logP density (LPD) of a molecule was represented by the same basis functional form with the SPED model. The logP of a molecule can be obtained by the integration of the LPD of the molecule. The coefficients of the basis functions were determined by using experimental logP as constraints through an optimization procedure. Both logPs calculated from the free energy difference and from the LPD agreed well with the experimental data. The absolute mean errors were obtained as 0.34 and 0.32, respectively.