  We show that the origin of the antiferromagnetic coupling in spin-1
triangulene chains, which were recently synthesized and measured by Mishra et
al. Nature 598, 287-292 (2021) originates from a superexchange mechanism. This
process, mediated by inter-triangulene states, opens the possibility to control
parameters in the effective bilinear-biquadratic spin model. We start from the
derivation of an effective tight-binding model for triangulene chains using a
combination of tight-binding and Hartree-Fock methods fitted to hybrid density
functional theory results. Next, correlation effects are investigated within
the configuration interaction method. Our low-energy many-body spectrum for
$N_{\rm Tr}=2$ and $N_{\rm Tr}=4$ triangulene chains agree well with the
bilinear-biquadratic spin-1 chain antiferromagnetic model when indirect
coupling processes, and superexchange coupling between triangulene spins are
taken into account.
