  Vortex molecules can form in a two component superfluid when a Rabi field
drives transitions between the two components. We study the ground state of an
infinite system of vortex molecules in 2D, using a numerical scheme which makes
no use of the lowest Landau level approximation. We find the ground state
lattice geometry for different values of inter-component interactions and
strength of the Rabi field. In the limit of large field when molecules are
tightly bound, we develop a complimentary analytical description. The energy
governing the alignment of molecules on a triangular lattice is found to
correspond to that of an infinite system of 2D quadrupoles, which may be
written in terms of an elliptic function $\mathcal{Q}(z_{ij};\omega_1 ,
\omega_2 )$. This allows for a numerical evaluation of the energy which enables
us to find the ground state configuration of the molecules.
