Isotope effects in the phase diagram of hydrogen and deuterium*

Hydrogen forms a range of molecular solid crystals, and under extreme pressure, it is predicted to form atomic phases. Recent static and dynamic experiments showing metallization provide evidence for this.

In classical statistical mechanics, atomic mass does not contribute to the thermodynamic free energy: phase diagrams are independent of isotope. In practice, very large isotope effects have been observed in low temperature hydrogen and deuterium. Perhaps more surprisingly, a large isotope effect in the liquid-liquid transtion has also been reported about 1000K. These discrepancies must be due to quantum mechanical effects.

We present calculations of these phase boundary shifts based on path integral molecular dynamics, explaining the isotope effect in terms of elementary quantum mechanics. The liquid-liquid transition effect can be traced to the zero-point vibrational energy which make the covalent bond weaker in hydrogen than in deuterium. The low temperature transitions come from the different mass dependence of quantum rotors and oscillators.

We also describe a new theoretical development incorporating path integrals including exact bosonic exchange in lattice switch monte carlo free energy differences.