  We use an accurate implementation of density functional theory (DFT) to
calculate the zero-temperature generalized phase diagram of the 4$d$ series of
transition metals from Y to Pd as a function of pressure $P$ and atomic number
$Z$. The implementation used is full-potential linearized augmented plane waves
(FP-LAPW), and we employ the exchange-correlation functional recently developed
by Wu and Cohen. For each element, we obtain the ground-state energy for
several crystal structures over a range of volumes, the energy being converged
with respect to all technical parameters to within $\sim 1$ meV/atom. The
calculated transition pressures for all the elements and all transitions we
have found are compared with experiment wherever possible, and we discuss the
origin of the significant discrepancies. Agreement with experiment for the
zero-temperature equation of state is generally excellent. The generalized
phase diagram of the 4$d$ series shows that the major boundaries slope towards
lower $Z$ with increasing $P$ for the early elements, as expected from the
pressure induced transfer of electrons from $sp$ states to $d$ states, but are
almost independent of $P$ for the later elements. Our results for Mo indicate a
transition from bcc to fcc, rather than the bcc-hcp transition expected from
$sp$-$d$ transfer.
