  The electronic structure of layered Sr$_{3}$Ru$_{2}$O$_{7}$ in its
orthorhombic structure is investigated using density functional calculations.
The band structure near the Fermi energy, consists of Ru $% t_{2g}$ states
hybridized with O $p$ orbitals. The $yz$ and $xz$ bands, which are largely
responsible for the nesting related antiferromagnetic spin fluctuations in
Sr$_{2}$RuO$_{4}$ split pairwise into even and odd combinations due to the
interlayer coupling reducing the strength of the nesting. The $xy$ bands show
much less interplanar coupling as expected, and also less $c$-axis dispersion,
so that the barrel like sections are largely intact compared to the single
layer material. The zone folding due to orthorhombicity yields small
cylindrical lens shaped Fermi surfaces centered at the midpoints of the former
tetragonal $\Gamma -X$ lines. Fixed spin moment calculations indicate that
tetragonal Sr$_{3}$Ru$_{2}$O$_{7}$ is borderline ferromagnetic but that
orthorhombicity favors magnetism via a substantial magnetoelastic coupling.
These results are related to experimental observations particularly in regard
to magnetic properties.
