\label{fig:NColumnsVsNRings} Number of columns which must be sampled as a function of the number of rings in the polyacene to achieve a relative Frobenius norm error less than $10^{-3}$ in the recovered quantum mechanical Hessian.  Legend entries indicate the (sparse) recovery basis, and columns are always sampled in the DCT basis with respect to the recovery basis.  (Relative error is measured by averaging over ten different trials which sample different sets of random columns.)