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Toward a Balanced Description of Weak and Strong Correlation

Peter M. W. Gill, School of Chemistry, University of Sydney, Sydney, Australia

In a dense uniform electron gas (UEG), the kinetic component of the Hamiltonian dominates the Coulombic one, the orbital picture of electronic structure is a good approximation and the electrons are often described as “weakly correlated†. As the density of the UEG decreases, the Coulombic component eventually dominates the kinetic one, the orbital picture fails, and the electrons are described as “strongly correlated" [1].

The extremes, and the spectrum of behavior between then, are conveniently studied by performing accurate wavefunction and energy calculations of nα spin-up electrons and nβ spin-down electrons on a D-dimensional sphere of radius R. We have done this for nα ∈ 1, 2, 3, . . . and a range of radii 0 ≤ R < ∞ in D = 1 and these results were published some time ago [2, 3]. More recently, we have performed calculations with nα,nβ ∈ 0,1,4,9,16,... and a range of radii 0 ≤ R < ∞ in D = 2 [4].

By combining simple approximate wavefunctions for the weakly and strongly correlated cases, one is led to a “balanced†wavefunction which provides a qualitatively correct treatment of UEGs of all densities. In doing so, one also realizes that the concepts of “weakly†and “strongly†correlated systems are arbitrary : viewed through an appropriate lens, so-called strongly corre- lated systems are weakly correlated, and vice versa.

[1] P.M.W. Gill and P.F. Loos, Theor. Chem. Acc 131, 1069 (2012)
[2] P.F. Loos and P.M.W. Gill, J. Chem. Phys. 138, 164124 (2013)
[3] P.F. Loos, C.J. Ball, and P.M.W. Gill, J. Chem. Phys. 140, 18A524 (2014) [4] S.G. Dale and P.M.W. Gill, in preparation