  To explore conditions underlying the superconductivity in electron-doped
TiNCl where T$_c$ = 16 K, we calculate the electronic structure, Wannier
functions and spin and charge susceptibilities using first-principles density
functional theory. TiNCl is the first high-temperature superconductor
discovered in the $\alpha $-structure of the layered transition-metal nitride
family MNCl (M=Ti, Zr, Hf). We construct a tight-binding model based on Wannier
functions derived from the band structure, and consider explicit electronic
interactions in a multi-band Hubbard Hamiltonian, where the interactions are
treated with the random phase approximation (RPA) to calculate spin and charge
susceptibility. The results show that, consistent with TiNCl being a
nonmagnetic material, spin fluctuations do not dominate over charge
fluctuations and both may have comparable impact on the properties of the doped
system.
