Harmonium as a laboratory for mathematical chemistry

Abstract

Thanks to an algebraic duality property of reduced states, the Schmidt best approximation theorems have important corollaries in the rigorous theory of two-electron moleculae. In turn, the "harmonium mode" or "Moshinsky atom" constitutes a non-trivial laboratory bench for energy functionals proposed over the years (1964--today), purporting to recover the full ground state of the system from knowledge of the reduced 1-body matrix. That model is usually regarded as solvable, but some important aspects of it, in particular the exact energy and full state functionals ---unraveling the "phase dilemma" for the system--- had not been calculated heretofore. The solution is made plain here by working with Wigner quasiprobabilities on phase space. It allows in principle for a thorough discussion of the (de)merits of several approximate functionals popular in the theoretical chemical physics literature. We focus on Gill's "Wigner intracule" method for the correlation energy.

updated version

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Cited by in corpus (7)

• The lowest excited configuration of harmonium
• Testing one-body density functionals on a solvable model
• Quantifying errors of the electron-proton/muon correlation functionals through the Kohn-Sham inversion of a two-component model system
• Exact wave functions for concentric two-electron systems
• Physical Wigner functions
• Exotic Harmonium Model: Exploring Correlation Effects of Attractive Coulomb Interaction
• Spatial correlations and entanglement in a hybrid system of N fermion pairs with harmonic interaction