Density Functional Theory and the Dirac-Coulomb Hamiltonian

Density Functional Theory and the Dirac-Coulomb Hamiltonian 

As described previously, in practical computational schemes of relativistic quantum chemistry the Dirac-Coulomb Hamiltonian is frequently preferred. The use of this Hamiltonian, which retains only the Coulomb interaction between the electrons, omitting the Breit term and higher-order corrections, is justified by the argument that these terms are small and the effect on most properties of chemical interest is insignificant. The validity of this argument appears to be supported by actual applications. Saue and Helgaker (2002) have shown that when this Hamiltonian is used in the 

To show this, we note that in the absence of external magnetic fields, the external potential reduces to the scalar term 

the only way the current density j can contribute to the energy would be through the electron-electron interaction. From (5.49) the operator for this interaction is 

Disregarding for the moment the gauge term, we consider the contribution to the functional U from the two other terms. This may be written as 

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