  We introduce a model to study the collisions of two ultracold diatomic
molecules in one dimension interacting via pairwise potentials. We present
results for this system, and argue that it offers lessons for real molecular
collisions in three dimensions. We analyze the distribution of the adiabatic
potentials in the hyperspherical coordinate representation as well as the
distribution of the four-body bound states in the adiabatic approximation (i.e.
no coupling between adiabatic channels). It is found that while the adiabatic
potential distribution transitions from chaotic to non-chaotic as the two
molecules are separated, the four-body bound states show no visible chaos in
the distribution of nearest-neighbor energy level spacing. We also study the
effects of molecular properties, such as interaction strength, interaction
range, and atomic mass, on the resonance density and degree of chaos in the
adiabatic potentials. We numerically find that the dependence of the four-body
bound state density on these parameters is captured by simple scaling laws, in
agreement with previous analytic arguments, even though these arguments relied
on uncontrolled approximations. This agreement suggests that similar scaling
laws may also govern real molecular collisions in three dimensions.
