  We present a study of the local structure of high pressure hydrogen around
the liquid-liquid transition line based on results from the Coupled
Electron-Ion Monte Carlo method. We report results for the Equation of State,
for the radial distribution function between protons g(r) and results from a
cluster analysis to detect the possible formation of stable molecular ions
beyond the transition line, as well as above the critical temperature. We
discuss various estimates for the molecular fraction in both phases and show
that, although the presence of $H_3^+$ ions is suggested by the form of the
g(r) they are not stable against thermal fluctuations.
