Response Density
Another more-general definition of a density is the "linear-response density". This is the density that when contracted with any spin-free, one-electron operator yields the associated property defined as the derivative of the energy. For example, a dipole moment is the derivative of the energy with respect to an external magnetic field and is not the expectation value of the operator over the wavefunction. For some theories they are the same when the wavefunction is converged. The occupation numbers are not limited to the range of zero to two, and therefore sometimes even the response density can be negative in certain regions of space.
Read more about this topic: Electronic Density
Famous quotes containing the word response:
“Because humans are not alone in exhibiting such behavior—bees stockpile royal jelly, birds feather their nests, mice shred paper—it’s possible that a pregnant woman who scrubs her house from floor to ceiling [just before her baby is born] is responding to a biological imperative . . . . Of course there are those who believe that . . . the burst of energy that propels a pregnant woman to clean her house is a perfectly natural response to their mother’s impending visit.”
—Mary Arrigo (20th century)