The exchange-correlation (XC) hole of the hydrogen molecule with fractional nuclear charge

The exchange-correlation (XC) hole is fundamental for developing density functional approximations and understanding their behaviors in real material calculations. Although it is well defined, there are few XC holes calculated exactly for benchmarking density functionals, largely because of its dependence on the coupling constant [1] that scales the electron-electron Coulomb repulsion. Here, we calculate the coupling-constant-averaged XC hole of the hydrogen molecule at the CCSD level which is basis-set exact for 2 electron systems. We will extend the hydrogen molecule to have fractional nuclear charge which allows the left-right symmetry breaking and enables the strong correlation and charge transfer competition [2]. The effects of bond distance and the nuclei charge disproportionation on the XC hole will be examined.