Lattice-switch Monte Carlo and the related diabat methods have emerged as efficient and accurate ways to compute free energy differences
between polymorphs. In this work, we introduce a one-to-one mapping from the reference positions and displacements in one molecular
crystal to the positions and displacements in another. Two features of the mapping facilitate lattice-switch Monte Carlo and related diabat
methods for computing polymorph free energy differences. First, the mapping is unitary so that its Jacobian does not complicate the free
energy calculations. Second, the mapping is easily implemented for molecular crystals of arbitrary complexity. We demonstrate the mapping
by computing free energy differences between polymorphs of benzene and carbamazepine. Free energy calculations for thermodynamic cycles,
each involving three independently computed polymorph free energy differences, all return to the starting free energy with a high degree of
precision. The calculations thus provide a force field independent validation of the method and allow us to estimate the precision of the
individual free energy differences
