Charge distribution excitation energies

The electric monopole interaction between a nucleus (with mean square radius k) and its environment is a product of the nuclear charge distribution ZeR and the electronic charge density e il/ 0) at the nucleus, SE = const (4.11). However, nuclei of the same mass and charge but different nuclear states isomers) have different charge distributions ZeR eR ), because the nuclear volume and the mean square radius depend on the state of nuclear excitation R R ). Therefore, the energies of a Mossbauer nucleus in the ground state (g) and in the excited state (e) are shifted by different amounts (5 )e and (5 )g relative to those of a bare nucleus. It was recognized very early that this effect, which is schematically shown in Fig. 4.1, is responsible for the occurrence of the Mossbauer isomer shift [7]. 

From the viewpoint of quantum mechanics, the polarization process cannot be continuous, but must involve a quantized transition from one state to another. Also, the transition must involve a change in the shape of the initial spherical charge distribution to an elongated shape (ellipsoidal). Thus an s-type wave function must become a p-type (or higher order) function. This requires an excitation energy call it A. Straightforward perturbation theory, applied to the Schroedinger aquation, then yields a simple expression for the polarizability (Atkins and Friedman, 1997) ... 

There are two general cases of dipole-dipole forces those between molecules in which the distribution of electronic charge is centrosymmetric and those in which it is not. In the first case, there are no permanent electrical dipoles, whereas there is a permanent dipole if the charge distribution is non-centro-symmetric. When permanent dipoles are not present, there are nevertheless fluctuating dipoles as a result of atomic vibrations. These are always present because of zero-point motion. At temperatures greater than 0°K, thermal energy further excites the molecular vibrational modes which create fluctuating electric dipoles. 

Due to differences in charge distribution in the various energy states of a molecule, the electronically excited species can be completely different in its chemical and physical behaviours as compared to the normal ground state molecule. Molecular geometries and internuclear force constants also change. 

Photochemical substitution reactions can proceed through high-energy products such as radical ions, the primary process being a dissociation or an ionization of the excited molecule. Such processes do not have to follow the orientation rules dictated by the charge distribution of the excited molecule, and in many instances the product distribution is still little understood. 

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