Calculation of the free energy of solvation of the Li⁺ and Na⁺ ions in water and chloroform

The free energies of solvation of the lithium and sodium cations in water and in chloroform were calculated using Monte Carlo computer simulations. The free energies were obtained using thermodynamic integration either on a nearly linear path or on a polynomial path and the integral was evaluated with a Gaussian quadrature. The precision of the results was confirmed through comparison with additional calculations that obtained the solvation free energy differences by mutating a lithium to a sodium cation. Three sources for the discrepancy between the calculated and experimental solvation free energies were considered: the multibody terms were estimated using a polarization model; the long-range contributions were estimated with the Born correction and with a calculation using larger system size; and the extent of charge transfer was examined by ab initio calculations based on complete solvation shells extracted from the simulation.