  We establish a variational principle for properly mapping a fractional
quantum Hall (FQH) state to a fractional Chern insulator (FCI). We find that
the mapping has a gauge freedom which could generate a class of FCI ground
state wave functions appropriate for different forms of interactions.
Therefore, the gauge should be fixed by a variational principle that minimizes
the interaction energy of the FCI model. For a soft and isotropic
electron-electron interaction, the principle leads to a gauge coinciding with
that for maximally localized \emph{two-dimensional} projected Wannier functions
of a Landau level.
