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Sets of free energy differences are useful for finding the equilibria ofchemical reactions, while absolute free energies have little physical meaning.However finding the relative free energy between two macrostates by subtractionof their absolute free energies is a valuable strategy in certain importantcases. We present calculations of absolute free energies of biomolecules, usinga combination of the well-known Einstein Molecule method (for treating thesolute) with a conceptually related method of recent genesis for computing freeenergies of liquids (to treat the solvent and counterions). The approach isbased on thermodynamic integration from a detailed atomistic model to one whichis simplified but analytically solvable, thereby giving the absolute freeenergy as that of the tractable model plus a correction term found numerically.An example calculation giving the free energy with respect to saltconcentration for the B- and Z-isomers of all-atom duplex DNA in explicitsolvent and counterions is presented. The coexistence salt concentration isfound with unprecedented accuracy.

Free Energies by Thermodynamic Integration Relative to an Exact Solution, Used to Find the Handedness-Switching Salt Concentration for DNA