  Linear response methods are applied to identify the increase in
electron-phonon coupling in elemental yttrium that is responsible for its high
superconducting critical temperature Tc, which reaches nearly 20 K at 115 GPa.
While the evolution of the band structure and density of states is smooth and
seemingly modest, there is strong increase in the 4d content of the occupied
conduction states under pressure. We find that the transverse mode near the L
point of the fcc Brillouin zone, already soft at ambient pressure, becomes
unstable (in harmonic approximation) at a relative volume V/Vo=0.60 (P ~ 42
GPa). The coupling to transverse branches is relatively strong at all high
symmetry zone boundary points X, K, and L. Coupling to the longitudinal
branches is not as strong, but extends over more regions of the Brillouin zone
and involves higher frequencies. Evaluation of the electron-phonon spectral
function $\alpha^2F(\omega)$ shows a very strong increase with pressure of
coupling in the 2-7 meV range, with a steady increase also in the 7-20 meV
range. These results demonstrates strong electron-phonon coupling in this
system that can account for the observed range of Tc.
