  We study negative thermal expansion (NTE) in model lattices with multiple
atoms per cell and first- and second-nearest neighbor interactions using the
(anharmonic) Morse potential. By exploring the phase space of neighbor
distances and thermal expansion rates of the bonds, we determine the conditions
under which NTE emerges. By permitting all bond lengths to expand at different
rates, we find that NTE is possible without appealing to fully rigid units.
Nearly constant, large-amplitude, isotropic NTE is observed up to the melting
temperature in a classical molecular dynamics model of a $\mathrm{ReO}_3$-like
structure when the rigidity of octahedral units is almost completely
eliminated. Only weak NTE, changing over to positive expansion is observed when
the corner-linked octahedra are rigid, with flexible second-neighbor bonds
between neighboring octahedra permitting easy rotation. We observe similar
changes to thermal expansion behavior for the diamond lattice: NTE when
second-neighbor interactions are weak to positive thermal expansion when
second-neighbor interactions are strong. From these observations, we suggest
that the only essential local conditions for NTE are atoms with low
coordination numbers along with very low energies for changing bond angles
relative to bond-stretching energies.
