  We investigate the electronic structure and the hole content in the
copper-oxygen planes of Hg based high Tc cuprates for one to four CuO2 layers
and hydrostatic pressures up to 15 GPa. We find that with the pressure-induced
additional number of holes of the order of 0.05e the density of states at the
Fermi level changes approximately by a factor of 2. At the same time the saddle
point is moved to the Fermi level accompanied by an enhanced k_z dispersion.
This finding explains the pressure behavior of Tc and leads to the conclusion
that the applicability of the van Hove scenario is restricted. By comparison
with experiment, we estimate the coupling constant to be of the order of 1,
ruling out the weak coupling limit.
