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\section{Computational methods}  To solve The main additional computational task required to implement our approach is the solution of  the \(\ell_1\) optimization problem of eq.~\ref{eq:bpdn} given by eq.~\ref{eq:bpdn}. From the many algorithms available for this purpose,  we rely on the spectral projected gradient \(\ell_1\) (SPGL1) algorithm developed by van~den~Berg and Friedlander~\cite{Berg2008} and their freely-available implementation.The matrix for the change of basis operation is given by the Kronecker product of \(P\) with itself, however, we do not build the matrix and perform all the matrix multiplications as implicit operations in terms of P. This last approach has a much smaller numerical cost and memory requirements. Numerically the condition \(PAP^T = B\) is satisfied up to an error of \(10^{-7}\) in the Frobenius norm (vectorial 2-norm).  All quantum The matrix for the change of basis operation is given by the Kronecker product of \(P\) with itself, however, we do not build the matrix and perform all the matrix multiplications as implicit operations in terms of P. This last approach has a much smaller numerical cost and memory requirements. Numerically the condition \(PAP^T = B\) is satisfied up to an error of \(10^{-7}\) in the Frobenius norm (vectorial 2-norm).  Quantum  mechanical Hessian calculations were performed with the QChem 4.2~\cite{Shao_2006} software package, using density functional theory with the B3LYP exchange-correlation functional~\cite{Becke_1993} and the 6-31G* basis set. All molecular mechanics Hessian calculations were performed using freely-available open-source Tinker 6.2~\cite{Tinker} software package using the MM3 force field~\cite{Allinger_1989}.