Editing Electron density (section)

=== Nuclear cusp condition ===
The electronic density displays cusps at each nucleus in a molecule as a result of the unbounded electron-nucleus Coulomb potential. This behaviour is quantified by the Kato cusp condition formulated in terms of the spherically averaged density, <math>\bar{\rho}</math>, about any given nucleus as<ref>{{cite journal|last=Kato|first=Tosio |year=1957|title=On the eigenfunctions of many-particle systems in quantum mechanics|journal=Communications on Pure and Applied Mathematics|volume=10|issue=2|pages=151–177|doi=10.1002/cpa.3160100201}}</ref>

:<math>\left.\frac{\partial}{\partial r_{\alpha}}\bar{\rho}(r_{\alpha})\right|_{r_{\alpha}=0} = -2Z_{\alpha}\bar{\rho}(0).</math>

That is, the radial derivative of the spherically averaged density, evaluated at any nucleus, is equal to twice the density at that nucleus multiplied by the negative of the [[atomic number]] (<math>Z</math>).