  We analyze in detail the electronic properties of high pressure hydrogen
around the liquid-liquid phase transition based on Coupled Electron-Ion Monte
Carlo calculations. Computing the off-diagonal single particle density matrix
and the momentum distribution we discuss localization properties of the
electrons. The abrupt changes of these distributions indicate a metal to
insulator transition occurring together with the structural transition from the
atomic to molecular fluid. We further discuss the electron-proton and
electron-electron pair correlation functions, which also change abruptly at the
transition.
