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The "exact" energy is the energy with full correlation and complete basis set. Electron correlation is sometimes divided into dynamical and non-dynamical (static) correlation. Dynamical correlation is the correlation of the movement of electrons and is described under electron correlation dynamics [3] and also with the configuration interaction ...
The first is a sum of kinetic-energy operators for each electron, the internuclear repulsion energy, and a sum of nuclear–electronic Coulombic attraction terms. The second are Coulombic repulsion terms between electrons in a mean-field theory description; a net repulsion energy for each electron in the system, which is calculated by treating ...
In Kohn-Sham DFT this system is composed by non-interacting electrons, for which the kinetic energy can be calculated exactly and the interaction term has to be approximated. In SCE DFT, instead, the starting point is totally the opposite one: the auxiliary system has infinite electronic correlation and zero kinetic energy.
where ρ is the electronic density and є xc is the exchange-correlation energy per particle of a homogeneous electron gas of charge density ρ. The exchange-correlation energy is decomposed into exchange and correlation terms linearly, = + , so that separate expressions for E x and E c are sought. The exchange term takes on a simple analytic ...
As explained above, the deviations are due to the effects of orbital relaxation as well as differences in electron correlation energy between the molecular and the various ionized states. For N 2 in contrast, the order of orbital energies is not identical to the order of ionization energies.
The perovskite structure of BSCCO, a high-temperature superconductor and a strongly correlated material.. Strongly correlated materials are a wide class of compounds that include insulators and electronic materials, and show unusual (often technologically useful) electronic and magnetic properties, such as metal-insulator transitions, heavy fermion behavior, half-metallicity, and spin-charge ...
(3), is the two-site two-electron Coulomb integral (It may be interpreted as the repulsive potential for electron-one at a particular point () in an electric field created by electron-two distributed over the space with the probability density ()), [a] is the overlap integral, and is the exchange integral, which is similar to the two-site ...
Expressed using the Hubbard model, the Hamiltonian is made up of two terms. The first term describes the kinetic energy of the system, parameterized by the hopping integral, . The second term is the on-site interaction of strength that represents the electron repulsion.