  Our recent re-analysis of the solar photospheric spectra with non-local
thermodynamic equilibrium (non-LTE) models resulted in higher metal abundances
compared to previous works. When applying the new chemical abundances to
Standard Solar Model calculations, the new composition resolves the
long-standing discrepancies with independent constraints on the solar structure
from helioseismology. Critical to the determination of chemical abundances is
the accuracy of the atomic data, specially the $f$-values, used in the
radiative transfer models. Here we describe in detail the calculations of
$f$-values for neutral oxygen and nitrogen used in our non-LTE models. Our
calculations of $f$-values are based on a multi-method, multi-code approach and
are the most detailed and extensive of its kind for the spectral lines of
interest. We also report in this paper the details of extensive R-matrix
calculation of photo-ionization cross sections for oxygen. Our calculation
resulted in reliable $f$-values with well constrained uncertainties. We compare
our results with previous theoretical and experimental determinations {of
atomic data. We also quantify the influence of adopted photo-ionisation
cross-sections on the spectroscopic estimate of the solar O abundance, using
the data from different sources. We confirm that our 3D non-LTE value is robust
and unaffected by the choice of photo-ionisation data, contrary to the recent
claim made by Nahar.
