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