\label{fig:HessSparsity} Average sparsity per column (\(S/3N\)) of molecular mechanics and quantum mechanical Hessians in the basis of atomic coordinates for the series of polyacenes.  (An entry in the Hessian is considered nonzero if it is greater than 10 \((\mathrm{cm}^{-1})^2\), which is roughly six orders of magnitude smaller than the largest entry.)  In the molecular mechanics Hessians, the average sparsity per column is roughly constant with the size of the molecule, because each atom has a roughly constant number of neighbors regardless of the size of the entire molecule.