Effect of Electron-electron Cusp Condition on the Exchange-Correlation (XC) Hole Studied with Hooke's atoms

The exchange correlation (XC) hole is critical for understanding density functional theory and the associated XC density functional approximations. The XC hole of a system can be calculated with accurate wavefunction methods. CCSD is a wavefunction method widely used for ordinary atoms and molecules and exact for 2 electron systems at the basis set limit, while it misses the electron-electron cusp condition with finite conventional basis sets. Here, using the Hooke's atom for which the analytic wavefunction solutions are available, we study the effect of cusp condition on the XC hole calculated from CCSD. We show that the cusp effect-driven error in CCSD is negligible with the t-aug-cc-pV5Z basis set, and becomes smaller for more diffusive electron densities. We also studied the coupling constant averaged and system and angle averaged XC hole against the PBE and LDA XC holes.