  A novel variational method is proposed for calculating the percolation
threshold, the real-space structure, and the thermodynamical compressibility of
a disordered two-dimensional electron liquid. Its high accuracy is verified
against prior numerical results and newly derived exact asymptotics. The
inverse compressibility is shown to have a strongly asymmetric minimum at a
density that is approximately the triple of the percolation threshold. This
implies that the experimentally observed metal-insulator transition takes place
well before the percolation point is reached.
