The Coulomb, exchange, and correlation components of the electron-electron repulsion in harmonium atoms

Highly accurate Coulomb, exchange, and correlation components of the electron-electron repulsion energies of the three-electron harmonium atoms in the (2)P- and (4)P+ states are obtained for 19 values of the confinement strength ω ranging from 10(-3) to 10(3). The computed data are consistent with their ω → 0 and ω → ∞ asymptotics that are given by closed-form algebraic expressions. Robust approximants that accurately reproduce the actual values of the energy components while strictly conforming to these limits are constructed, opening an avenue to stringent tests capable of predicting the performance of electronic structure methods for systems with varying extents of the dynamical and nondynamical electron correlation. The values of the correlation components, paired with the computed 1-matrices are expected to be particularly useful in the context of benchmarking of approximate density matrix functionals.