  Phase diagram of the ground states of DNA in a bad solvent is studied for a
semi-flexible polymer model with a generalized local elastic bending potential
characterized by a nonlinearity parameter $x$ and effective self-attraction
promoting compaction. $x=1$ corresponds to the worm-like chain model.
Surprisingly, the phase diagram as well as the transition lines between the
ground states are found to be a function of $x$. The model provides a simple
explanation for the results of prior experimental and computational studies and
makes predictions for the specific geometries of the ground states. The results
underscore the impact of the form of the microscopic bending energy at
macroscopic observable scales.
