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 Vignale and Rasolt, 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, 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.
Read more about this topic: Density Functional Theory
Famous quotes containing the words include, magnetic and/or fields:
“In one sense it is evident that the art of kingship does include the art of lawmaking. But the political ideal is not full authority for laws but rather full authority for a man who understands the art of kingship and has kingly ability.”
—Plato (428348 B.C.)
“We are in great haste to construct a magnetic telegraph from Maine to Texas; but Maine and Texas, it may be, have nothing important to communicate.”
—Henry David Thoreau (18171862)
“I respect not his labors, his farm where everything has its price, who would carry the landscape, who would carry his God, to market, if he could get anything for him; who goes to market for his god as it is; on whose farm nothing grows free, whose fields bear no crops, whose meadows no flowers, whose trees no fruit, but dollars; who loves not the beauty of his fruits, whose fruits are not ripe for him till they are turned to dollars. Give me the poverty that enjoys true wealth.”
—Henry David Thoreau (18171862)