is a transition amplitude expressed in the AO basis, 175 also known as a pseudo-density for the excitation. (The quantity y µν is defined analogously.) The idea is that squared amplitudes x 2 µν and y 2 µν are associated with probabilities for transfer of charge from µ ∈ A to ν ∈ B. However, the formula in Eq. (4.3) accounts neither for the normalization condition in Eq. (2.4), nor for the fact that the AOs are not orthogonal. This may not be an issue when l A→B is used to analyze semi-empirical calculations, where the inherent minimal basis might be assumed to be orthonormal, but the same formula has been put forward for all-electron TD-DFT calculations in arbitrary basis sets. Normalization could be enforced in a straightforward fashion,