  In this contribution we start by proving and generalizing a conjecture that
has been established few decades ago, relating the value of the integral of the
detachment/attachment density in two pictures - one accounting for
transition-induced basis relaxation and one which does not account for such a
relaxation. To this end, we combine an extension to Cauchy's interlacing
theorem and a brother theorem that we bring in the paper. Using this result
together with a corollary to Lidskii-Wielandt theorem allows us to derive an
upper bound for the electronic charge that is effectively displaced during the
molecular electronic transition from one quantum state to another. This
quantity can be regarded as the neat charge that has been transferred during
the transition. Our derivations show that this boundary value can be determined
from a simple singular value decomposition and two trace operations.
