  The discovery of the first high critical temperature (Tc) transition metal
diboride superconductor, MgB2 structure alpha-MoB2 under pressure with Tc up to
32 K at 100 GPa, provides new input into some unexplained aspects of
electron-phonon coupling in intermetallic compounds. We establish that MoB2 is
a phonon-mediated superconductor but has little in common with MgB2 (Tc=40 K at
zero pressure). MoB2 is a strongly metallic, three dimensional, multi-Fermi
surface material, becoming of additional interest because it displays a
frequency separation of Mo and B vibrations that mirrors that of metal
superhydrides with Tc approaching room temperature. This separation, which is
unusual in intermetallic compounds, allows an analysis separately for Mo and B
providing, amongst the other parameters essential for understanding phonon
coupling, the matrix elements for scattering by the individual atoms. Strong
coupling (lambda(Mo)=1.48) is provided by Mo (total lambda=1.67). A factor of
15 weaker coupling to each B atom is compensated by that coupling being to mean
high frequency modes around 85-90 meV (maximum of 140 meV), versus 18-20 meV
for Mo. As a result, B enhances Tc by 43% over the Mo-only value, to 33 K,
corresponding to the experimental value. These results provide a guideline for
designing higher Tc materials from a cooperation of strong coupling from heavy
atoms with weakly coupled light atoms. The new high Tc paradigm discovered here
highlights the need for studying and engineering larger ionic scattering matrix
elements.
