  Strong correlation effects caused by Hund's coupling have been actively
studied during the past decade. Hund's metal, strongly correlated while far
from the Mott insulating limit, was studied as a representative example.
However, recently, it was revealed that a typical Mott system also exhibits a
sign of Hund physics by investigating the kink structure in the spectral
function of $\mathrm{NiS_{2-x}Se_x}$. Therefore, to understand the Hund physics
in a half-filled multi-orbital system near the metal-insulator transition, we
studied pressure-induced metallic states of $\mathrm{NiS_2}$ by using density
functional theory plus dynamical mean-field theory. Hund physics, responsible
for suppressing local spin fluctuation, gives low-energy effective
correlations, separated from Mott physics, which suppresses charge fluctuation
at higher energy. This effect is prominent when $J$ becomes comparable to the
quasiparticle kinetic energy, showing apparent scaling behavior of the kink
position $E_{kink} \sim J \cdot Z$. We suggest that the Hund effect can also be
observed in the optical conductivity as a non-Drude-like tail with $1/\omega$
frequency dependence and non-monotonic temperature evolution of the integrated
optical spectral weight at a fixed frequency. Our study demonstrates the
important role of Hund's coupling for electronic correlations even in a
half-filled system.
