  In the layered transition metal oxide LiNbO$_2$ the Nb$^{3+}$ ($4d^2$) ion is
trigonal-prismatically coordinated with O ions, with the resulting crystal
field leading to a single band system for low energy properties. A
tight-binding representation shows that intraplanar second neighbor hopping
$t_2 = 100$ meV dominates the first neighbor interaction ($t_1 = 64$ meV). The
first and third neighbor couplings are strongly modified by oxygen
displacements of the symmetric Raman-active vibrational mode, and
electron-phonon coupling to this motion may provide the coupling mechanism for
superconductivity in Li-deficient samples (where $T_c = 5$ K). We calculate all
zone-center phonon modes, identify infrared (IR) and Raman active modes, and
report LO-TO splitting of the IR modes. The Born effective charges for the
metal ions are found to have considerable anisotropy reflecting the degree to
which the ions participate in interlayer coupling and covalent bonding. Insight
into the microscopic origin of the valence band density, composed of Nb
$d_{z^2}$ states with some mixing of O $2p$ states, is obtained from examining
Wannier functions for these bands.
