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