Properties of atoms in molecules: Transition probabilities

The transition probability for electric dipole transitions is a measurable property of a system and is therefore, partitionable into atomic contributi ons using the physics of a proper open system. The derivation of the dresse d property density, whose averaging over an atomic basin yields the atomic contribution to a given oscillator strength, is achieved through the develo pment of perturbation theory for an open system. A dressed density describe s the local contribution resulting from the interaction of a single electro n at some position r, as determined by the relevant observable, averaged ov er the motions of all of the remaining particles in the system. In the pres ent work, the transition probability density expressed in terms of the rele vant transition density, yields a local measure of the associated oscillato r strength resulting from the interaction of the entire molecule with a rad iation 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 functiona l group. The concepts introduced in this article are applied to the Rydberg -type transitions observed in the electronic excitation of a nonbonding ele ctron in formaldehyde and ammonia. The atomic partitioning of the molecular density distribution and of the molecular properties by surfaces of zero f lux in the gradient vector field of the electron density, the boundary cond ition defining the physics of a proper open system, is found to apply to th e density distributions of the excited, Rydberg states. (C) 2000 American I nstitute of Physics. [S0021-9606(00)31123-0].