  In this contribution, we report some matrix-algebraic derivations leading to
the definition of an upper bound for the electronic charge that is effectively
displaced during a molecular electronic transition from one electronic quantum
state to another. This quantity can be regarded as the neat charge that has
been transferred during the transition, i.e., when we compare the departure and
arrival states one-electron reduced densities and make the "bilan". For
defining its upper bound, we start by proving a relationship that has been
empirically established few decades ago, relating the value of the integral of
the detachment/attachment density in two pictures (one accounting for
transition-induced orbital rotation and one which does not account for such an
orbital relaxation effect). After proving that the detached/attached charge has
a higher value in the relaxed picture than in the unrelaxed one for a family of
excited-state calculation methods, we establish that the upper bound to the
relaxed detached/attached charge value is equal to the unrelaxed
detached/attached charge value, to which we add the sum of singular values of
the orbital-relaxation matrix.
