where P is the one-electron density matrix. Expressions for A and B in terms of electron repulsion integrals and the exchange-correlation kernel can be found elsewhere. Lastly, the quantities ε a -ε i in Eq. (2.3a) are differences between virtual (ε a ) and occupied (ε i ) Kohn-Sham energy levels defined by the ground-state eigenvalue problem, Eq. (2.1). The difference ε a -ε i appears along the diagonal of A and constitutes a zeroth-order approximation to an electronic excitation energy, consistent with a zeroth-order picture in which an electronic transition consists in promotion of one electron from a single occupied MO into a single virtual MO, ψ i → ψ a .