  The properties of hydrogen at high pressure have wide implications in
astrophysics and high-pressure physics. Its phase change in the liquid is
variously described as a metallization, H2-dissociation, density discontinuity
or plasma phase transition. It has been tacitly assumed that these phenomena
coincide at a first-order liquid-liquid transition (LLT). In this work, the
relevant pressure-temperature conditions are thoroughly explored with
first-principles molecular dynamics. We show there is a large dependency on
exchange-correlation functional and significant finite size effects. We use
hysteresis in a number of measurable quantities to demonstrate a first-order
transition up to a critical point, above which molecular and atomic liquids are
indistinguishable. At higher temperature beyond the critical point,
H2-dissociation becomes a smooth cross-over in the supercritical region that
can be modelled by a pseudo-transition, where the H2-2H transformation is
localized and does not cause a density discontinuity at metallization.
Thermodynamic anomalies and counter-intuitive transport behavior of protons are
also discovered even far beyond the critical point, making this dissociative
transition highly relevant to the interior dynamics of Jovian planets. Below
the critical point, simulation also reveals a dynamic H2-2H chemical
equilibrium with rapid interconversion, showing that H2 and H are miscible. The
predicted critical temperature lies well below the ionization temperature. Our
calculations unequivocally demonstrate that there are three distinct regimes in
the liquid-liquid transition of warm dense hydrogen.
