  Candidate materials for Kitaev spin liquid phase have been intensively
studied recently because of their potential applications in fault-tolerant
quantum computing. Although most of the studies on Kitaev spin liquid have been
done in 4$d$ and 5$d$ based transition metal compounds, recently there has been
a growing research interest in Co-based quasi-two-dimensional honeycomb
magnets, such as BaCo$_2$(AsO$_4$)$_2$ because of formation of
spin-orbit-entangled $J_{\rm eff}$ = 1/2 pseudospin moments at Co$^{2+}$ sites
and potential realizations of Kitaev-like magnetism therein. Here, we obtain
high-accuracy crystal and electronic structure of BaCo$_2$(AsO$_4$)$_2$ by
employing a combined density functional and dynamical mean-field theory
calculations, which correctly capture the Mott-insulating nature of the target
system. We show that Co$^{2+}$ ions form a high spin configuration, $S=3/2$,
with an active $L_{\rm eff}=1$ orbital degree of freedom, in the absence of
spin-orbit coupling. The size of trigonal distortion within CoO$_6$ octahedra
is found to be not strong enough to completely quench the orbital degree of
freedom, so that the presence of spin-orbit coupling can give rise to the
formation of spin-orbit-entangled moments and the Kitaev exchange interaction.
Our finding supports recent studies on potential Kitaev magnetism in this
compound and other Co-based layered honeycomb systems.
