  Recent experimental advances in the cooling and manipulation of bialkali
dimer molecules have enabled the production of gases of ultracold molecules
that are not chemically reactive. It has been presumed in the literature that
in the absence of an electric field the low-energy scattering of such
nonreactive molecules (NRMs) will be similar to atoms, in which a single
$s$-wave scattering length governs the collisional physics. However, in Ref.
[1], it was argued that the short-range collisional physics of NRMs is much
more complex than for atoms, and that this leads to a many-body description in
terms of a multi-channel Hubbard model. In this work, we show that this
multi-channel Hubbard model description of NRMs in an optical lattice is robust
against the approximations employed in Ref. [1] to estimate its parameters. We
do so via an exact, albeit formal, derivation of a multi-channel resonance
model for two NRMs from an ab initio description of the molecules in terms of
their constituent atoms. We discuss the regularization of this two-body
multi-channel resonance model in the presence of a harmonic trap, and how its
solutions form the basis for the many-body model of Ref. [1]. We also
generalize the derivation of the effective lattice model to include multiple
internal states (e.g., rotational or hyperfine). We end with an outlook to
future research.
