  Phonon dynamics, charge response and the phonon density of states are
calculated for the high-temperature superconductors HgBa$_{2}$CuO$_{4}$ and
Bi$_{2}$Sr$_{2}$CuO$_{6}$ within a microscopic model for the electronic density
response. The results are compared with previous calculations for
La$_{2}$CuO$_{4}$ and Nd$_{2}$CuO$_{4}$. Our main focus is on the
phononanomalies which are connected with the high-frequency oxygen
bond-stretching modes (OBSM) found before in our calculations for $p$-doped
La$_{2}$CuO$_{4}$ and $n$-doped Nd$_{2}$CuO$_{4}$. We investigate the question
if the characteristic softening of the OBSM and the related strong coupling to
the electrons is also present in HgBa$_{2}$CuO$_{4}$ and
Bi$_{2}$Sr$_{2}$CuO$_{6}$. In particular the importance of the contribution of
the more delocalized Cu$4s$ state besides the localized Cu3d state on the
softening is investigated and the different anticrossing behaviour due to the
presence of several phonon modes with the same symmetry as the OBSM is studied
making the identification of the anomalies quite complicate. Furthermore, the
influence of electronic polarization processes at ions out of the CuO plane in
the ionic layers on the phonon dynamics is calculated. In this context the
qualitative type of charge response, i.e. the presence or not of possible
metallic charge fluctuations at the Hg or Bi ion, respectively, linked via the
apex oxygen to the CuO plane, proves to be very sensitive for certain phonon
modes. All the calculations are compared to the experimental results available
so far. The latter, however, are rather incomplete for the Hg and the Bi
compound.
