  Accurate potential energy surfaces (PESs) have been determined for the
$^3$A$'$ and $^3$A$''$ states of N$_2$O using electronic structure calculations
at the multireference configuration interaction level with Davidson correction
(MRCI+Q) and the augmented Dunning-type correlation consistent polarize triple
zeta (aug-cc-pVTZ) basis set. More than 20000 MRCI+Q/aug-cc-pVTZ energies are
represented using a reproducing kernel Hilbert space (RKHS) interpolation
scheme. The RKHS PESs successfully describe all reactant channels with high
accuracy. The analytical PESs are characterized by computing the minima and
transition states on it. Quasiclassical dynamics simulations are then used to
determine thermal and vibrational relaxation rates for the N+NO and O+N$_2$
collisions. The agreement between results obtained from the simulations and
from available experiments is favourable for both types of observables, which
provides a test for the accuracy of the PESs. The PESs can be used to calculate
more detailed state-to-state observables relevant for applications to
hypersonic reentry.
