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An example is the neutral helium atom (He), which has two bound electrons, both of which can occupy the lowest-energy states by acquiring opposite spin; as spin is part of the quantum state of the electron, the two electrons are in different quantum states and do not violate the Pauli principle.
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 is often called Pauli correlation.
For an electron in an electron gas, the exchange symmetry creates an "exchange hole" in its vicinity, which other electrons with the same spin tend to avoid due to the Pauli exclusion principle. This decreases the energy associated with the Coulomb interactions between the electrons with same spin. [ 3 ]
An alternative notation that is commonly used for the Pauli matrices is to write the vector index k in the superscript, and the matrix indices as subscripts, so that the element in row α and column β of the k-th Pauli matrix is σ k αβ.
A year later, George Uhlenbeck and Samuel Goudsmit identified Pauli's new degree of freedom as electron spin, in which Pauli for a very long time wrongly refused to believe. [19] In 1926, shortly after Heisenberg published the matrix theory of modern quantum mechanics, Pauli used it to derive the observed spectrum of the hydrogen atom. This ...
Previously, this type of interaction was considered to be enhanced by relativistic effects.A major contributor is electron correlation of the closed-shell components, [2] which is unusual because closed-shell atoms generally have negligible interaction with one another at the distances observed for the metal atoms.
The Slater determinant arises from the consideration of a wave function for a collection of electrons, each with a wave function known as the spin-orbital (), where denotes the position and spin of a single electron. A Slater determinant containing two electrons with the same spin orbital would correspond to a wave function that is zero everywhere.
Fundamentally, an atomic orbital is a one-electron wave function, even though many electrons are not in one-electron atoms, and so the one-electron view is an approximation. When thinking about orbitals, we are often given an orbital visualization heavily influenced by the Hartree–Fock approximation, which is one way to reduce the ...