The free energy difference of the binding of benzoquinones and naphthoquinones at the Q(A) site of the photosynthetic reaction center from Rhodobacter sphaeroides immersed in water and hexane is calculated and compared with experimental values. The water-to-hexane solvent-transfer free energies are also calculated. An improved thermodynamic perturbation technique with double-wide sampling is employed which takes the asymmetry of the distribution of data into account and minimizes the statistical error by using optimal midpoints. Dependencies on different atomic partial charges and different degrees of solvation are discussed.