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The Slater determinant is named for John C. Slater, who introduced the determinant in 1929 as a means of ensuring the antisymmetry of a many-electron wave function, [2] although the wave function in the determinant form first appeared independently in Heisenberg's [3] and Dirac's [4] [5] articles three years earlier.
Slater determinants are constructed from sets of orthonormal spin orbitals, so that | =, making the identity matrix and simplifying the above matrix equation. The solution of the CI procedure are some eigenvalues E j {\displaystyle \mathbf {E} ^{j}} and their corresponding eigenvectors c I j {\displaystyle \mathbf {c} _{I}^{j}} .
An example provided in Slater's original paper is for the iron atom which has nuclear charge 26 and electronic configuration 1s 2 2s 2 2p 6 3s 2 3p 6 3d 6 4s 2.The screening constant, and subsequently the shielded (or effective) nuclear charge for each electron is deduced as: [1]
A helium atom is an atom of the chemical element helium. Helium is composed of two electrons bound by the electromagnetic force to a nucleus containing two protons along with two neutrons, depending on the isotope , held together by the strong force .
Exact wave functions, however, cannot generally be expressed as single determinants. The single-determinant approximation does not take into account Coulomb correlation, leading to a total electronic energy different from the exact solution of the non-relativistic Schrödinger equation within the Born–Oppenheimer approximation.
Some quantum chemistry software uses sets of Slater-type functions (STF) analogous to Slater type orbitals, but with variable exponents chosen to minimize the total molecular energy (rather than by Slater's rules as above). The fact that products of two STOs on distinct atoms are more difficult to express than those of Gaussian functions (which ...
By contrast, an isolated Ni atom (electron configuration = 3d 8 4s 2) in a cubic crystal field will have two unpaired electrons of the same spin (hence, =) and would thus be expected to have in the localized electron model a total spin magnetic moment of = (but the measured spin-only magnetic moment along one axis, the physical observable, will ...
It is a special case of the configuration interaction method in which all Slater determinants (or configuration state functions, CSFs) of the proper symmetry are included in the variational procedure (i.e., all Slater determinants obtained by exciting all possible electrons to all possible virtual orbitals, orbitals which are unoccupied in the electronic ground state configuration).