  We present new methodological features and physical ingredients included in
the 1D radiative transfer code HELIOS, improving the hemispheric two-stream
formalism. We conduct a thorough intercomparison survey with several
established forward models, including COOLTLUSTY, PHOENIX, and find
satisfactory consistency with their results. Then, we explore the impact of (i)
different groups of opacity sources, (ii) a stellar path length adjustment, and
(iii) a scattering correction on self-consistently calculated atmospheric
temperatures and planetary emission spectra. First, we observe that
temperature-pressure (T-P) profiles are very sensitive to the opacities
included, with metal oxides, hydrides, the alkali atoms (and ionized hydrogen)
playing an important role for the absorption of shortwave radiation (in very
hot surroundings). Moreover, if these species are sufficiently abundant, they
are likely to induce non-monotonic T-P profiles. Second, without the stellar
path length adjustment, the incoming stellar flux is significantly
underestimated for zenith angles above 80{\deg}, which somewhat affects the
upper atmospheric temperatures and the planetary emission. Third, the
scattering correction improves the accuracy of the computation of the reflected
stellar light by ~10%. We use HELIOS to calculate a grid of cloud-free
atmospheres in radiative-convective equilibrium for self-luminous planets for a
range of effective temperatures, surface gravities, metallicities, and C/O
ratios, to be used by planetary evolution studies. Furthermore, we calculate
dayside temperatures and secondary eclipse spectra for a sample of exoplanets
for varying chemistry and heat redistribution. These results may be used to
make predictions on the feasibility of atmospheric characterizations with
future observations.
