Comparison of theoretical models for metallic hydrogen

Calculations of the Gibbs free energy of metallic hydrogen were made by the four most common methods and shown to be in good agreement with each other. In addition it is shown that the free-electron correlation energy commonly used in calculations on metallic hydrogen is approximately four times larger than the spread over the Gibbs free energy as calculated by the four methods. Because the free-electron correlation energy expression may be in error by a factor of 2 or 3, it represents the largest source of uncertainty currently facing an ab initio treatment of the metallic hydrogen phase.