These methods assign certain initial energies to the nuclei, and thus the resulting classical trajectories can reach more anharmonic areas of the PES. This treatment is successful in many model systems and practical systems, although they can suffer from zero-point energy (ZPE) leakage problems in some systems. A more elegant way of incorporating anharmonicity in MD simulations is through the path-integral formulism. A few major variants are centroid molecular dynamics (CMD) , ring-polymer molecular dynamics (RPMD) , thermostated ring-polymer molecular dynamics (TRPMD) , and quasi-centroid molecular dynamics (QCMD) . They map a quantum nuclear system onto a classical system with chains of beads, and through a good description of the nuclear quantum effects as well as approximations on the autocorrelation functions, they can well describe the anharmonicity and give relatively accurate vibrational spectra. An even more accurate method to describe vibrational spectra is through quantum nuclear dynamics, and a commonly-used method is the multiconfigurational time-dependent Hartree (MCTDH) theory. This theory has been shown to accurately describe the vibrational spectra of systems as large as water clusters with four water molecules, although the underlying computational cost remains a major limiting factor.