  The fundamentals and higher vibrationally excited states for the N$_3^+$ ion
in its electronic ground state have been determined from quantum bound state
calculations on 3-dimensional potential energy surfaces (PESs) at the
CCSD(T)-F12 and MRCI+Q levels of theory. The vibrational fundamentals are at
1130 cm$^{-1}$ ($\nu_1$, symmetric stretch), 807 cm$^{-1}$ ($\nu_3$, asymmetric
stretch), and 406 cm$^{-1}$ ($\nu_2$, bend) on the higher-quality CCSD(T)-F12
surface. For $\nu_1$, the calculations are close to the estimated frequency
from experiment (1170 cm$^{-1}$) and previous calculations\cite{rosmus.n3:1994}
which find it at 1190 cm$^{-1}$. Calculations of the vibrational states on the
MRCI+Q PES are in qualitative agreement with those using the CCSD(T)-F12 PES.
Analysis of the reference CASSCF wave function for the MRCI+Q calculations
provides further insight into the shape of the PES and lends support for the
reliability of Hartree-Fock as the reference wave function for the coupled
cluster calculations. According to this, N$_3^+$ has mainly single reference
character in all low-energy regions of its electronic ground state ($^3$A$''$)
3d PES.
