We present a series of first-principles calculations for Hg based high T-c cuprates investigating the effect of pressure, doping, and composition on the electronic and crystalline structure. In particular, the total and site-projected hole concentration in the CuO2 planes and the density of states are studied in detail. We discuss effects of inhomogeneity introduced by doping and the limitations on creating holes by either doping, pressure, or the number of CuO2 layers per unit cell. From an analysis and comparison of our results to available experimental data on the pressure dependence of T-c, we conclude that the effective coupling constant to the boson mediating the Cooper pairing is of the order of 1 ruling out the weak coupling approaches. (C) 2007 Elsevier B.V. All rights reserved.