Atomic Radial Correlation Energy Density Components
Abstract
The components of the radial correlation energy density are calculated and analyzed for the atoms from He to Ar. The components include the nucleus-electron potential correlation energy density, the kinetic correlation energy density and the electron-electron potential correlation energy density. The necessary correlated one and two-electron density matrices are obtained from the Extrapolated-Full-Configuration-Interaction (exFCI) wave function where the reference wave function is restricted Hartree-Fock (RHF) or restricted open-shell Hartree-Fock (ROHF) depending on whether the atom is closed or open-shell. The accuracy associated with integrating the HF and exFCI energy density components, and the correlation energy density components, is evaluated on the SG-1 and SG-2 atomic grids. The SG-1 grid provides atomic energies that are accurate to about 1 kJ mol$^{-1}$, with the exception of the kinetic energy. The SG-2 grid is required for the analysis of atomic kinetic energies and more subtle energetic effects. There is also a significant amount of integration error cancellation in the correlation energy densities. The radial correlation energy densities display notable shell structure, and there is a substantial difference between the $\alpha$ and $\beta$-electron correlation energy densities for the open-shell atoms.