On-site Coulomb repulsion
= On-site Coulomb repulsion
{title2=$U>0$}
The energy cost $U=\iint |a(\mathbf r_1)|^2|a(\mathbf r_2)|^2e^2/[4\pi\epsilon_0|\mathbf r_1-\mathbf r_2|]\,\mathrm d^3r_1\,\mathrm d^3r_2$ for <double occupancy> of a localized orbital. It is positive for an ordinary nonzero orbital. A model retaining only this integral also neglects intersite and mixed Coulomb terms; orbital <orthogonality> alone does not make those terms vanish.