In an article published in the journal PNAS (https://www.pnas.org/content/118/5/e2022303118 ) by Matteo Baggioli, from School of Physics and Astronomy, SJTU and Alessio Zaccone of University of Milano, the law which governs the distribution of vibrational energy states of liquids, which has remained elusive and unsolved for over 100 years, has been derived mathematically for the first time combining the concept of instantaneous normal modes and the so-called Zeldovich regularization for unstable quantum states.