The weak-correlation limits of few-electron harmonium atoms

The weak-correlation asymptotics of electronic properties of harmonium atoms comprising up to four electrons are investigated. In particular, closed-form expressions are derived for the first- and second-order contributions to the Hartree-Fock and correlation energies of eight electronic states that include three singlets, one doublet, two triplets, one quartet, and one quintet, six of which are singly determinantal and two are multi-determinantal. This diversity of states offers a much richer set of benchmarking tools for calibration of approximate electron-correlation methods than the previously published data. The availability of the computed energy contributions due to individual spinorbitals and their pairs present in the dominant Slater determinants further enhances the utility of these benchmarks