Upper bound for the charge transferred during a molecular electronic transition: insights from matrix analysis.

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.