# Analyse:Ym/Fragment 017 01

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[In order to gain a generalised] form of the Kohn-Sham equations, it is necessary at least to introduce two component Pauli wavefunctions, that reproduce the electron and magnetization density.

[...]

Applying the variational principle again yields the Kohn-Sham equations, which now have the form of Schrödinger-Pauli equations.

[...]

The additional effective magnetic field consists of two terms. One of them is due to the variation of the exchange correlation energy with respect to the magnetization density. The second term is the external B-field, if present.

[...]

In many applications, like for example ferromagnetic and antiferromagnetic solids, the magnetization is orientated along one particular direction. For these collinear cases the problem can be simplified further. The z-axis can be chosen along the direction of the magnetic field. Therefore, the Hamiltonian of equation (2.19) becomes diagonal in the two spin components of the wavefunction, i.e. the spin-up and -down problems become completely decoupled and can be solved independently. The energy and all other physical observables become functionals of the electron density and the magnitude of the magnetization density m(r) =

In order to gain a generalised form of the Kohn-Sham equations, it is necessary at least to introduce two component Pauli wavefunctions, that reproduce the electron and magnetization density.

[...]

Applying the variational principle again yields the Kohn-Sham equations, which now have the form of Schrödinger-Pauli equations.

[...]

The additional effective magnetic field consists of two terms. One of them is due to the variation of the exchange correlation energy with respect to the magnetization

[page 13]

density. The second term is the external B-field, if present.

[...]

In many applications, like for example ferromagnetic and antiferromagnetic solids, the magnetization is orientated along one particular direction. For these collinear cases the problem can be simplified further. The z-axis can be chosen along the direction of the magnetic field. Therefore, the Hamiltonian of equation 2.18 becomes diagonal in the two spin components of the wavefunction, i.e. the spin-up and -down problems become completely decoupled and can be solved independently. The energy and all other physical observables become functionals of the electron density and the magnitude of the magnetization density m(r) =

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