Protonation energies and the Laplacian of the electron density: A critical examination

The success and limitations of the Laplacian of the electron density in predicting protonation energies is systematically discussed for a selection of molecules, including aldehydes, amines, amides and diglycine. We address four questions related to (a) the preference between competing protonation sites, (b) correlations between the Laplacian and the protonation energy in substituted homologous series and (c) upon conformational change and (d) the Laplacian's uniqueness in using information stored in the unprotonated molecule. This study forms a solid basis to investigate the use of the Laplacian in the rationalisation of mass spectrometric fragmentation patterns of peptides.