  We report on an instanton-based analysis of the gluon Green functions in the
Landau gauge for low momenta; in particular we use lattice results for
$\alpha_s$ in the symmetric momentum subtraction scheme (${\rm MOM}$) for
large-volume lattice simulations. We have exploited quenched gauge field
configurations, $N_f=0$, with both Wilson and tree-level Symanzik improved
actions, and unquenched ones with $N_f=2+1$ and $N_f=2+1+1$ dynamical flavors
(domain wall and twisted-mass fermions, respectively).
  We show that the dominance of instanton correlations on the low-momenta gluon
Green functions can be applied to the determination of phenomenological
parameters of the instanton liquid and, eventually, to a determination of the
lattice spacing.
  We furthermore apply the Gradient Flow to remove short-distance fluctuations.
The Gradient Flow gets rid of the QCD scale, $\Lambda_{\rm QCD}$, and reveals
that the instanton prediction extents to large momenta. For those gauge field
configurations free of quantum fluctuations, the direct study of topological
charge density shows the appearance of large-scale lumps that can be identified
as instantons, giving access to a direct study of the instanton density and
size distribution that is compatible with those extracted from the analysis of
the Green functions.
