  We introduce a new approach for the correlation energy of one- and two-valley
two-dimensional electron gas (2DEG) systems. Our approach is based on a random
phase approximation at high densities and a classical approach at low
densities, with interpolation between the two limits. This approach gives
excellent agreement with available Quantum Monte Carlo (QMC) calculations. We
employ the two-valley 2DEG model to describe the electron correlations in
monolayer transition metal dichalcogenides (TMDs). The zero-temperature
transition from a Fermi liquid to a quantum Wigner crystal phase in monolayer
TMDs is obtained using density-functional theory within the local-density
approximation. Consistent with QMC, we find that electrons crystallize at
$r_s=30.5$ in one-valley 2DEG. For two-valleys, we predict Wigner
crystallization at $r_s= 29.5$, indicating that valley degeneracy has little
effect on the critical $r_s$, in contrast to an earlier claim.
