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Calculating the underlying quantum behaviour of dense hydrogen has proven to be difficult due to subtle electronic effects and also the lightness of the proton leading to large quantum motion. The analytical form of the contribution from the nuclear and electronic degrees of freedom (DOF) is integrated out of the Schödinger equation by way of the generated pseudo pair potential in this paper. This is accomplished through the adiabatically linear response approximation of an electron gas-jellium model to the perturbations induced by discrete hydrogen ions in the absence of an external field. This pair potential for the hydrogen ions can then be fitted to generate first-principles data. From these pair potentials, computational time can be drastically reduced for larger systems of dense hydrogen to determine their various properties.

Pseudo pair potential between protons in dense hydrogen from first principles