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Electron density
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== Response density == Another more-general definition of a density is the "linear-response density".<ref>{{cite journal |doi = 10.1063/1.447489 |title = On the evaluation of analytic energy derivatives for correlated wave functions |year = 1984 |last1 = Handy |first1 = Nicholas C. |last2 = Schaefer |first2 = Henry F. |journal = The Journal of Chemical Physics |volume = 81 |pages = 5031β5033|bibcode = 1984JChPh..81.5031H |issue = 11 }}</ref><ref>{{cite journal | doi = 10.1021/j100181a030 | title = Analysis of the effect of electron correlation on charge density distributions | year = 1992 | last1 = Wiberg | first1 = Kenneth B. | last2 = Hadad | first2 = Christopher M. | last3 = Lepage | first3 = Teresa J. | last4 = Breneman | first4 = Curt M. | last5 = Frisch | first5 = Michael J. | journal = The Journal of Physical Chemistry | volume = 96 | pages = 671β679 | issue = 2}}</ref> 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.<ref>{{cite journal | last1 = Gordon | first1 = Mark S. | last2 = Schmidt | first2 = Michael W. | last3 = Chaban | first3 = Galina M. | last4 = Glaesemann | first4 = Kurt R. | last5 = Stevens | first5 = Walter J. | last6 = Gonzalez |first6 = Carlos | year = 1999 | title = A natural orbital diagnostic for multiconfigurational character in correlated wave functions | journal = J. Chem. Phys. | volume = 110 | issue = 9 | pages = 4199β4207 | doi = 10.1063/1.478301|bibcode = 1999JChPh.110.4199G | s2cid = 480255 | url = https://dr.lib.iastate.edu/bitstreams/510e7723-c755-4d31-9f4e-bea3ca000e5e/download}}</ref>
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