  Rare-earth materials hold promise to realize exotic magnetic states owing to
synergy between electron correlations and spin-orbit coupling. Recently,
quasi-two-dimensional honeycomb magnets $A_2$PrO$_3$ ($A$ = alkali metals) were
predicted to be good candidates for Kitaev quantum spin liquids, as the
Kitaev-type bond-dependent anisotropic interactions dominate over
bond-independent isotropic Heisenberg ones. However, experimental observations
are negative, questioning the energy hierarchy in Pr$^{4+}$ ions assumed in the
conjecture on the basis of the conventional Russell-Saunders coupling scheme.
We here revisit the exchange interactions in these Pr compounds, by explicitly
taking into account the ionic states beyond the assumption. We show that, while
increasing the octahedral crystal field splitting, which was assumed to be
negligibly small, relative to the spin-orbit coupling, the Kitaev-type
interactions are suppressed to be subdominant compared to prevailing Heisenberg
ones. Our finding compromises the contradiction as arising from the peculiar
ionic state of the high valence Pr$^{4+}$.
