Pair-correlation function study of the proton-electron system: A method to calculate the contact hyperfine couplings within two-component density functional theory

The quantum effect of light atoms such as hydrogen in materials is usually considered as lattice vibration from an ab initio perspective. Some recent studies have also tried to quantize the hydrogen from the outset within two-component density functional theory and parametrize the two-body correlation energy by vibrational states calculation, then calculate the wave function of the proton directly. Since there is no experimental verification of the calculated wave function, we further develop a pair-correlation function of the proton-electron system by quantum Monte Carlo, thus it is possible to estimate the hyperfine couplings of the proton from the calculated wave function directly. The pair-correlation function form is tested in some basic systems with different functionals and shows its good potential in the study of the contact interactions incorporating the quantum effect of light nuclei such as hydrogen.