The transition probability for electric dipole transitions is a measurable property of a system and is therefore, partitionable into atomic contributions using the physics of a proper open system. The derivation of the dressed property density, whose averaging over an atomic basin yields the atomic contribution to a given oscillator strength, is achieved through the development of perturbation theory for an open system. A dressed density describes the local contribution resulting from the interaction of a single electron at some position r, as determined by the relevant observable, averaged over the motions of all of the remaining particles in the system. In the present work, the transition probability density expressed in terms of the relevant transition density, yields a local measure of the associated oscillator strength resulting from the interaction of the entire molecule with a radiation field. The definition of the atomic contributions to the oscillator strength enables one to determine the extent to which a given electronic or vibrational transition is spatially localized to a given atom or functional group. The concepts introduced in this article are applied to the Rydberg-type transitions observed in the electronic excitation of a nonbonding electron in formaldehyde and ammonia. The atomic partitioning of the molecular density distribution and of the molecular properties by surfaces of zero flux in the gradient vector field of the electron density, the boundary condition defining the physics of a proper open system, is found to apply to the density distributions of the excited, Rydberg states.