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Electronic correlation refers to the interaction between electrons in a quantum system whose electronic structure is being considered. The term correlation stems from mathematical statistics and means that two distribution functions, f(x) and g(y), are not independent of each other. Properties The electron is a subatomic particle. ...
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Electron configuration is the arrangement of electrons in an atom, molecule or other body. ...
In probability theory and statistics, correlation, also called correlation coefficient, is a numeric measure of the strength of linear relationship between two random variables. ...
Introduction
Electron correlation energy in terms of various levels of theory of solutions for the Schrödinger equation. Within the Hartree-Fock method of quantum chemistry, the antisymmetric wave function is approximated by a single Slater determinant. Exact wave functions, however, cannot generally be expressed as single determinants. The single-determinant approximation does not take into account the correlation between electrons with opposite spin, leading to a total electronic energy different from the exact solution of the non-relativistic Schrödinger equation within the Born-Oppenheimer approximation. Therefore the Hartree-Fock limit is always above this exact energy. The difference is called the correlation energy, a term coined by Löwdin. In computational physics, the Hartree-Fock calculation scheme is a self-consistent iterative procedure to calculate the so-called best possible single determinant solution to the time-independent Schrödinger equation of a many-electron system in a Coulombic potential of fixed nuclei. ...
Quantum chemistry is the application of quantum mechanics to problems in chemistry. ...
In the most restricted usage in quantum mechanics, the wavefunction associated with a particle such as an electron, is a complex-valued square integrable function ψ defined over a portion of space normalized in such a way that In Max Borns probabilistic interpretation of the wavefunction, the amplitude squared...
A Slater determinant (named after the physicist John C. Slater) is an expression in quantum mechanics for the wavefunction of a many-fermion system, which by construction satisfies the Pauli principle. ...
In physics, the Schrödinger equation, proposed by the Austrian physicist Erwin Schrödinger in 1925, describes the time-dependence of quantum mechanical systems. ...
The Born-Oppenheimer approximation, also known as the adiabatic approximation, is a technique used in quantum chemistry and condensed matter physics in order to de-couple the motion of nuclei and electrons. ...
A certain amount of electron correlation is already considered within the HF approximation, found in the electron exchange term describing the correlation between electrons with parallel spin. This basic correlation prevents two parallel-spin electrons from being found at the same point in space and if often called Fermi correlation. Coulomb correlation, on the other hand, descrbies the correlation between the spatial position of electrons with opposite spin due to their Coulomb repulsion. There is also a correlation related to the overall symmetry or total spin of the considered system.
Mathematical viewpoint For two independent electrons a and b, - ,
where ρ(ra,rb) represents the joint electronic density, or the probability of finding electron a at ra and electron b at rb. Within this notation, ρ(ra,rb)dradrb represents the probability of finding the two electron in the respective volume elements dra and drb.
If these two electrons are correlated, then the probability of finding electron a at a certain position in space depends on the position of electron b, and vice versa. In other words, the product of their independent density functions does not adequately describe the real situation. At small distances, the uncorrelated pair density is too large, and too small at large distances - the electrons tend to "avoid each other".
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