Electronic correlation
Within the Hartree–Fock method of quantum chemistry, the antisymmetric wave function is approximated by a single Slater determinant.
Static correlation is important for molecules where the ground state is well described only with more than one (nearly-)degenerate determinant.
IQA correlation energy partitioning has also been shown to be possible with coupled cluster methods.
E.g. one can have some nearly degenerate determinants for the multi-configurational self-consistent field method to account for static correlation and/or some truncated CI method for the biggest part of dynamical correlation and/or on top some perturbational ansatz for small perturbing (unimportant) determinants.
To simplify them, interelectron distances are expanded into a series making for simpler integrals.
In condensed matter physics, electrons are typically described with reference to a periodic lattice of atomic nuclei.
Non-interacting electrons are therefore typically described by Bloch waves, which correspond to the delocalized, symmetry adapted molecular orbitals used in molecules (while Wannier functions correspond to localized molecular orbitals).
A number of important theoretical approximations have been proposed to explain electron correlations in these crystalline systems.
The Fermi liquid model of correlated electrons in metals is able to explain the temperature dependence of resistivity by electron-electron interactions.
It also forms the basis for the BCS theory of superconductivity, which is the result of phonon-mediated electron-electron interactions.
The Hubbard model is based on the tight-binding approximation, and can explain conductor-insulator transitions in Mott insulators such as transition metal oxides by the presence of repulsive Coulombic interactions between electrons.
Its one-dimensional version is considered an archetype of the strong-correlations problem and displays many dramatic manifestations such as quasi-particle fractionalization.
In other words, the product of their independent density functions does not adequately describe the real situation.
