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\section{Computational methods}  To solve the \(\ell_1\) optimization problem of eq.~\ref{eq:bpdn} 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 base 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).  To solve the \(\ell_1\) optimization problem of eq.~\ref{eq:bpdn} 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 base  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 mechanical Hessian calculations were performed withQChem~\cite{Shao_2006} version XXX at  the DFT theory level QChem 4.2~\cite{Shao_2006} software package,  using density functional theory with  the XXX B3LYP exchange-correlation  functional discretized using and  the XXX 6-31G*  basis set. Molecular All molecular  mechanics Hessian  calculations were performed using freely-available open-source Tinker~code Tinker 6.2 software package  using the {\color{red}XX} MM3  force field. field~\cite{}.