Discontinuities of the exchange-correlation kernel and charge-transfer   excitations in time-dependent density functional theory
  We identify the key property that the exchange-correlation (XC) kernel of time-dependent density functional theory must have in order to describe long-range charge-transfer excitations. We show that the discontinuity of the XC potential as a function of particle number induces a space -and frequency-dependent discontinuity of the XC kernel which diverges as $r\to\infty$. In a combined donor-acceptor system, the same discontinuity compensates for the vanishing overlap between the acceptor and donor orbitals, thereby yielding a finite correction to the Kohn-Sham eigenvalue differences. This mechanism is illustrated to first order in the Coulomb interaction. 
M. Hellgren and E. K. U. Gross
cond-mat.mes-hall physics.atom-ph physics.chem-ph