The interpretation of the above transition density matrix ξ M βα (r e , r h ) (in the real-space basis) is well-defined. The off-diagonal elements give indication of the spatial coherence between the electron and hole coordinates, indicating the probability of finding an extra electron at r e and a hole at r h upon transition from adiabtic state ψ α to ψ β . The diagonal elements of this matrix can be thought of as the net charge induced at r upon the electronic transition. This quantity is zero when the electron and hole do no occupy the same r and can thus be thought of as an electron-hole overlap density.