title: Benchmark calculations on the lowest-energy singlet, triplet, and quintet states of the four-electron harmonium atom.
abstract: For a wide range of confinement strengths ω, explicitly-correlated calculations afford approximate energies E(ω) of the ground and low-lying excited states of the four-electron harmonium atom that are within few μhartree of the exact values, the errors in the respective energy components being only slightly higher. This level of accuracy constitutes an improvement of several orders of magnitude over the previously published data, establishing a set of benchmarks for stringent calibration and testing of approximate electronic structure methods. Its usefulness is further enhanced by the construction of differentiable approximants that allow for accurate computation of E(ω) and its components for arbitrary values of ω. The diversity of the electronic states in question, which involve both single- and multideterminantal first-order wavefunctions, and the availability of the relevant natural spinorbitals and their occupation numbers make the present results particularly useful in research on approximate density-matrix functionals. The four-electron harmonium atom is found to possess the (3)P+ triplet ground state at strong confinements and the (5)S- quintet ground state at the weak ones, the energy crossing occurring at ω ≈ 0.0240919.
authors.affiliation: Institute of Physics, University of Szczecin, Wielkopolska 15, 70-451 Szczecin, Poland.
authors.forename: Jerzy
authors.initials: J
authors.lastname: Cioslowski
authors.affiliation: Theoretical Chemistry Group, Institute of Physical and Theoretical Chemistry, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland.
authors.forename: Krzysztof
authors.initials: K
authors.lastname: Strasburger
authors.affiliation: Institut de Química Computacional i Catàlisi (IQCC) i Departament de Química, Campus de Montilivi s/n, 17071 Girona, Spain.
authors.forename: Eduard
authors.initials: E
authors.lastname: Matito