Accurate acquirement of vibrational spectra of high-pressure molecular hydrogen have been a great challenge. Here, we propose an effective approach to address the inherent uncertainty and low signal-to-noise ratio of forces in Quantum Monte Carlo (QMC) calculations and implement phonon spectra calculations for complex crystals such as the C2/c-24 phase. We used the compressive sensing method of LASSO for fitting the interatomic force constants (IFCs) to reduce the proportion of larger error data in QMC. And the IFCs give a potential energy surface that is consistent with the one calculated by the QMC method, demonstrating the reliability of this method. We reported the phonon spectra of the C2/c-24 phase at different pressures, and thus the Raman and infrared frequencies, which give much better results matching the experiments compared with the single electron calculation results.

QMC,High pressure hydrogen,vibrational spectra,PES