  Motivated by the interest in topological quantum paramagnets in candidate
spin-$1$ magnets, we investigate the diamond lattice compound NiRh$_2$O$_4$
using {\it ab initio} theory and model Hamiltonian approaches. Our density
functional study, taking into account the unquenched orbital degrees of
freedom, shows stabilization of $S=1$ and $L=1$ state. We highlight the
importance of spin-orbit coupling, in addition to Coulomb correlations, in
driving the insulating gap, and uncover frustrating large second-neighbor
exchange mediated by Ni-Rh covalency. A single-site model Hamiltonian
incorporating the large tetragonal distortion is shown to give rise to a
spin-orbit entangled non-magnetic ground state, largely accounting for the
entropy, magnetic susceptibility, and inelastic neutron scattering results.
Incorporating inter-site exchange within a slave-boson theory, we show that
exchange frustration can suppress exciton condensation. We capture the
dispersive gapped magnetic modes, uncover `dark states' invisible to neutrons,
and make predictions for future experiments.

Strongly Correlated Electrons