Condon-Morse curve

Figure 7.7 Condon-Morse curve illustrating the cause of the thermal expansion of bonds...

The elastic modulus of a material arises from the relation between an applied force and the resultant change in the average separation distance of the atoms which form the structure of that material. If we consider the Condon-Morse curve for force, F, as a function of atomic separation distance, r, we can write an expression of the form ... 

The multiplicity of excitations possible are shown more clearly in Figure 9.16, in which the Morse curves have been omitted for clarity. Initially, the electron resides in a (quantized) vibrational energy level on the ground-state Morse curve. This is the case for electrons on the far left of Figure 9.16, where the initial vibrational level is v" = 0. When the electron is photo-excited, it is excited vertically (because of the Franck-Condon principle) and enters one of the vibrational levels in the first excited state. The only vibrational level it cannot enter is the one with the same vibrational quantum number, so the electron cannot photo-excite from v" = 0 to v = 0, but must go to v = 1 or, if the energy of the photon is sufficient, to v = 1, v = 2, or an even higher vibrational state. 

Thermal expansion of close packed structures such as NaCl is the direct result of an increase in bond length with increasing temperature. The increase in bond length arises from the asymmetry of the potential energy versus interatomic distance curve of the Condon-Morse potential energy diagram (Figure 7.7). This curve results from the interaction of the repulsive and attraction terms of the interatomic potential, E, which is often expressed as ... 

At ambient temperatures, the ground-state molecule occurs in the lowest vibrational state and the most probable distance between the nuclei lies close to the position of the minimum of the lowest Morse curve. As the distance of the nuclei does not change during excitation, it is evident that the absorption of a photon generates not only electronically, but also vibrationally excited states (to satisfy the condition of sufficient overlap of the vibrational wave functions of the two states— the Franck-Condon principle [6, 7]—see Fig. 2). 

The Frank-Condon principle is based on the fact that the time of an electronic transition (of the order of 10 s) is shorter than that of a vibration (of the order of 10 s). This means that during an electronic transition the nuclei do not change their positions. This phenomenon can be illustrated using the Morse potential energy curves for diatomic molecules (Figure 2.17). The series of horizontal lines... 

Figure 4.9 Morse potential energy curves for chloromethane and its ions. The curves are calculated using the activation energy determined from data in Figure 4.8. The high-temperature data is for unimolecular dissociation via the curve crossing on the approach side of the molecule. Only the VEa is negative and dissociation occurs in the Franck Condon transition. The thermal energy dissociation occurs through the thermal activation of the molecule, as is the case for all DEC(l) molecules.

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