Path integral molecular dynamics (PIMD) was used to incorporate nuclear quantum effects into the calculation of static properties. 64 ring-polymer beads were used, which is sufficient to converge the properties of interest even at low temperatures. For dynamical properties, thermostatted ring polymer molecular dynamics (TRPMD) , which has been shown to predict accurate vibrational dynamics of liquid water , and partially adiabatic centroid molecular dynamics (PACMD) . A timestep of 0.25 fs was used for TRPMD calculations, and 0.05 fs for PACMD. For PACMD simulations, the Parrinello-Rahman mass matrix was adjusted to shift all normal mode frequencies to to ω NM = 14000 cm -1 . The temperature in PIMD calculations was controlled using the global path integral Langevin equation (PILE-G) thermostat attached to all the non-centroid normal modes, with a time constant of 1000 fs. Both methods predict similar diffusion constants but either may have deficiencies when computing vibrational spectra especially in stretching regions. To obtain excellent quantitative agreement with experimental vibrational spectra, it is necessary to combine both highprecision electronic structure theory and quantum dynamics. Both of these questions are still open and under development. In particular, neither TRPMD or PACMD is recognized as the "gold standard" for uncompromising precision for most systems and properties. In fact, the transition frequency for Morse Oscillator as parametrized to model an O-H bond can be solved analytically. Compared to the analytical solution, the TRPMD simulation tends to overestimate the O-H vibrational frequency, while PACMD systematically improves the description of the stretching region of the O-H bond. Therefore, additional vibrational density of states based on PACMD have been performed.