We have performed a detailed study of molecular dissociation in liquid hydrogen using both Born-Oppenheimer molecular dynamics with Density Functional Theory and Coupled Electron-Ion Monte Carlo simulations. We observe a range of densities where (dP/d{rho}){sub T} = 0 that coincides with sharp discontinuities in the electronic conductivity, which is clear evidence of the plasma phase transition for temperatures 600K {le} T {le} 1500K. Both levels of theory exhibit the transition, although Quantum Monte Carlo predicts higher transition pressures. Based on the temperature dependence of the discontinuity in the electronic conductivity, we estimate the critical point of the transition at temperatures slightly below 2000 K. We examine the influence of proton zero point motion by using Path Integral Molecular Dynamics with Density Functional Theory; the main effect is to shift the transition to lower pressures. Furthermore, we calculate the melting curve of molecular hydrogen up to pressures of 200 GPa, finding a reentrant melting line in good agreement with previous calculations. The melting line crosses the metalization line at 700 K and 220 GPa using density functional energetics and at 550 K and 290 GPa using Quantum Monte Carlo energetics
