  The ground state energy of the 2-D Wigner crystal is determined as a function
of the thickness of the electron layer and the crystal structure. The method of
evaluating the exchange-correlation energy is tested using known results for
the infinitely-thin 2D system. Two methods, one based on the local-density
approximation(LDA), and another based on the constant-density approximation
(CDA) are established by comparing with quantum Monte-Carlo (QMC) results. The
LDA and CDA estimates for the Wigner transition of the perfect 2D fluid are at
$r_s=38$ and 32 respectively, compared with $r_s=35\pm5$ from QMC. For thick-2D
layers as found in Hetero-junction-insulated-gate field-effect transistors, the
LDA and CDA predictions of the Wigner transition are at $r_s=20.5$ and 15.5
respectively. Impurity effects are not considered here.
