  After theoretical determination of the internal structural coordinates in
Li$_2$Pd$_3$B, we calculate and analyze its electronic structure and obtain the
frequencies of the two $A_g$ phonons (40.6 meV for nearly pure Li mode, 13.0
meV for the strongly mixed Pd-Li mode). Pd can be ascribed a $4d^{10}$
configuration, but strong 4d character remains up to the Fermi level. Small
regions of flat bands occur at -70 meV at both the $\Gamma$ and X points.
Comparison of the Fermi level density of states to the linear specific heat
coefficient gives a dynamic mass enhancement of $\lambda$ = 0.75. Rough Fermi
surface averages of the deformation potentials $D$ of individual Pd and Li
displacements are obtained. While <$D_{Li}$> is small, <$D_{Pd}> ~ 1.15 eV/\AA
is sizable, and a plausible case exists for its superconductivity at 8 K being
driven primarily by coupling to Pd vibrations. The larger d bandwidth in
Li$_2$Pt$_3$B leads to important differences in the bands near the Fermi
surface. The effect on the band structure of spin-orbit coupling plus lack of
inversion is striking, and is much larger in the Pt compound.
