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arXiv · 1103.2023

Harmonium as a laboratory for mathematical chemistry

Kurusch Ebrahimi-Fard·Jose M. Gracia-Bondia
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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.

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Kurusch Ebrahimi-Fard, Jose M. Gracia-Bondia. 2011-06-13. Harmonium as a laboratory for mathematical chemistry. https://doi.org/10.1007/s10910-011-9822-7

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