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Jacob Sanders deleted file Molecular Vibrations 3.tex
over 9 years ago
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While the recovery of molecular mechanics Hessians provides a clear illustration of the scaling of our compressed sensing procedure, molecular mechanics Hessians are already quite cheap to compute in the first place. Since the interactions between pairs of atoms are approximated via a set of empirically-derived pair potentials, the energy derivatives in the Hessian may be directly computed as analytical derivatives of these pair potentials. Hence, from a computational standpoint, the real challenge is to apply our compressed sensing procedure to the computational of quantum mechanical Hessians, and it is to this problem which we now turn.
As Fig.~\ref{fig:HessSparsity} shows, for moderately-sized molecules, the sparsity \(S\) of a quantum mechanical Hessian does not scale linearly with the number of atoms \(N\) in the molecule, although for large molecules this is once again expected to be the case~\cite{}.
