\label{fig:Anthracene} Results of applying our compressed sensing procedure to the vibrational modes and frequencies of anthracene.  (Top) Even by sampling only 25\% of the quantum mechanical Hessian, the vibrational frequencies obtained via compressed sensing converge to those of the true quantum mechanical Hessian. (Middle) Error in vibrational frequencies for different extents of undersampling. When only 30\% of the columns are sampled, the maximum error in frequency is within 3 cm\(^{-1}\), and with 35\% sampling, the recovery is essentially exact.  (Bottom) Error in vibrational normal modes for different extents of undersampling on a logarithmic scale; the error is calculated as one minus the overlap (dot product) between the exact quantum mechanical normal mode and the normal mode obtained from the matrix reconstructed via compressed sensing. Once 30\% of the columns are sampled, the normal modes are recovered to within 1\% accuracy.