2011/03/31 by Kurusch Ebrahimi-Fard, Jose M. Gracia-Bondia, José M. Gracia-Bondía
Chemistry · Physics and Astronomy · #Advanced Chemical Physics Studies #Advanced Physical and Chemical Molecular Interactions #Algebra over a field #Algebraic number #Duality (order theory) #Energy (signal processing) #Focus (optics) #Mathematical chemistry #Property (philosophy) #Quantum Mechanics and Non-Hermitian Physics #State (computer science) #physics.chem-ph
paper · pdf · doi:10.1007/s10910-011-9822-7
published as Journal of Mathematical Chemistry, Volume 50, Number 3 (2012), 440-454 · updated version
openalex publication_date 2011/04/30 · arxiv created 2011/06/13 · arxiv updated 2012/06/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.