Editing Density functional theory (section)

==Generalizations to include magnetic fields==

The DFT formalism described above breaks down, to various degrees, in the presence of a vector potential, i.e. a [[magnetic field]]. In such a situation, the one-to-one mapping between the ground-state electron density and wavefunction is lost. Generalizations to include the effects of magnetic fields have led to two different theories: current density functional theory (CDFT) and magnetic field density functional theory (BDFT). In both these theories, the functional used for the exchange and correlation must be generalized to include more than just the electron density. In current density functional theory, developed by [[Giovanni Vignale|Vignale]] and Rasolt,<ref name="vignale" /> the functionals become dependent on both the electron density and the paramagnetic current density. In magnetic field density functional theory, developed by Salsbury, Grayce and Harris,<ref name='GrayceHarris94'>{{cite journal|title=Magnetic-field density-functional theory|journal=Physical Review A|year=1994|first1=Christopher|last1=Grayce |first2=Robert |last2=Harris|volume=50|issue=4|pages=3089–3095| doi=10.1103/PhysRevA.50.3089 |bibcode = 1994PhRvA..50.3089G|pmid=9911249 }}</ref> the functionals depend on the electron density and the magnetic field, and the functional form can depend on the form of the magnetic field. In both of these theories it has been difficult to develop functionals beyond their equivalent to LDA, which are also readily implementable computationally.