  We present a new set of solar metallicity atmosphere and evolutionary models
for very cool brown dwarfs and self-luminous giant exoplanets, which we term
ATMO 2020. Atmosphere models are generated with our state-of-the-art 1D
radiative-convective equilibrium code ATMO, and are used as surface boundary
conditions to calculate the interior structure and evolution of
$0.001-0.075\,\mathrm{M_{\odot}}$ objects. Our models include several key
improvements to the input physics used in previous models available in the
literature. Most notably, the use of a new H-He equation of state including ab
initio quantum molecular dynamics calculations has raised the mass by
$\sim1-2\%$ at the stellar-substellar boundary and has altered the cooling
tracks around the hydrogen and deuterium burning minimum masses. A second key
improvement concerns updated molecular opacities in our atmosphere model ATMO,
which now contains significantly more line transitions required to accurately
capture the opacity in these hot atmospheres. This leads to warmer atmospheric
temperature structures, further changing the cooling curves and predicted
emission spectra of substellar objects. We present significant improvement for
the treatment of the collisionally broadened potassium resonance doublet, and
highlight the importance of these lines in shaping the red-optical and
near-infrared spectrum of brown dwarfs. We generate three different grids of
model simulations, one using equilibrium chemistry and two using
non-equilibrium chemistry due to vertical mixing, all three computed
self-consistently with the pressure-temperature structure of the atmosphere. We
show the impact of vertical mixing on emission spectra and in colour-magnitude
diagrams, highlighting how the $3.5-5.5\,\mathrm{\mu m}$ flux window can be
used to calibrate vertical mixing in cool T-Y spectral type objects.
