Determination of solvation free energy using molecular dynamics with solute Cartesian mapping: An application to the solvation of 18-crown-6

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Abstract
The determination of relative stabilities of conformations of a molecule in solution has received much interest due to its relevance to chemical and biological properties in solution. Free energy perturbation (FEP) methodologies using molecular dynamics simulations have been used for the evaluation of free energy differences between two similar molecular systems. We present here a FEP method for the evaluation of the solvation free energy difference between two conformations. The simulations are carried out by fixing the Cartesian coordinates of a solute molecule. The molecule is switched from one conformer to another through a linear couping of the Cartesian coordinates of the two conformers. The solvation free energy is calculated from the interactions between the solvent and the solute using the standard FEP approach. This method is expected to be particularly useful for molecules with complicated conformational changes involving a large number of dihedral angle rotations. A crown ether, 18-crown-6, a cyclic molecule with 18 rotatable bonds, is used as a test case to demonstrate the method. The solvation free energy differences between four selected conformations of 18-crown-6 have been determined. The results are in agreement with available experiments and consistent with other theoretical calculations.

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