Morse oscillators, potential energy surfaces

FIGURE 14.29 The Morse potential is a better fit to the potential energy curve of a real molecule than is the harmonic oscillator potential energy surface, superimposed... 

Fig. 1.11. (cont.) The Si and S2 potential energy surfaces have been calculated by Nonella and Huber (1986) and Suter, Briihlmann, and Huber (1990), respectively, whereas the PES for the So state is approximated by the sum of two uncoupled Morse oscillators. The shaded circles indicate the equilibrium region of the ground electronic state where the dissociative motion in the excited electronic states starts and the heavy arrows illustrate the subsequent dissociation paths. Detailed discussions of the absorption spectra and the vibrational state distributions of NO follow in Chapters 7 and 9. 

The unavailability of an RKR-like inversion (hence the impossiblity of obtaining the potential energy surface, V(Q), and exact vibrational eigenfunctions directly from experimental data) makes it convenient to use products of simple harmonic or Morse-oscillator basis functions as vibrational basis states... 

It will be necessary to test the general applicability of equation (14) before it receives wide use. However, it should be quite accurate for large excitations as encountered in unimolecular reactions. For one and two separable Morse oscillators equation (14) has been found to be valid at low as well as high energies.By using equation (14) to derive quantal anharmonic densities of states for many different potential energy surfaces it may be possible to find a general semiempirical expression for quantal anharmonic densities of states. 

The principles of photoluminescence applied to solid oxide surfaces can be most easily understood by assuming some simplifications. For example, we can start by considering the Morse potential energy curves (Fig. 1) related to an ion pair such as M-+0-, taken as a harmonic oscillator to represent an oxide, typically an alkaline earth oxide. The absorption of light close to the fundamental absorption edge of this oxide leads to the excitation of an electron in the oxide ion followed by a charge-transfer process to create an exciton (an electron-hole pair), which is essentially... 

As already stated, the Morse potential is our first example of a potential surface that describes a particular motion. The bond vibrates within the constraints imposed by this potential. One may ask, "At any given moment, what is the probability of having a particular bond length " This is similar to questions related to the probability of finding electrons at particular coordinates in space, which we will show in Chapter 14 is related to the square of the wave-function that describes the electron motion. The exact same procedure is used for bond vibrations. We square the wavefunction that describes the wave-like nature of the bond vibration. Let s explore this using the potential surface for a harmonic oscillator (such as with a normal spring), instead of an anharmonic oscillator (Morse potential). For the low energy vibrational states, the harmonic oscillator nicely mimics the anharmonic oscillator. 

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