Vibrational energy transitions

Molecules possess discrete levels of rotational and vibrational energy. Transitions between vibrational levels occur by absorption of photons with frequencies v in the infrared range (wavelength 1-1000 p,m, wavenumbers 10,000-10 cm , energy differences 1240-1.24 meV). The C-0 stretch vibration, for example, is at 2143 cm . For small deviations of the atoms in a vibrating diatomic molecule from their equilibrium positions, the potential energy V(r) can be approximated by that of the harmonic oscillator ... 

FIGURE 7.11 An energy level diagram for a molecule or complex ion expanded to show an electronic energy transition and a vibrational energy transition. The electronic transition involves visible or ultraviolet light while the... 

Absorption of IR light results in vibrational energy transitions rather than electronic transitions. The concept of vibrational energy transitions was introduced in Chapter 7. 

Figure 16.13. Energy-level scheme for a diatomic molecule, showing the rotational energy transition (r), the vibrational energy transition (v) in the ground state (No), and electronic energy transition (e) from S0 to the excited state (,S i).

Another technique that can be used to determine the chemical nature of a thin film is infrared spectroscopy. Some materials will absorb certain frequencies in the infrared (wavelengths 2 to 25 microns) because of the excitation of vibrational energy transitions in molecular species. In the same way that electronic transitions in atoms can absorb radiation of specific frequencies, the vibration of a molecule (stretching or bending) will have a resonance value, and it will be excited by any radiation of this frequency. Consider the H20 molecule and its three vibrational modes, as shown in Figure 17. Clearly, each of these vibrational modes has its own resonant frequency, as indicated, and they are all in the infrared range. 

In this case, the system of collision invariants for the most frequent collisions includes along with the momentum and a particle total energy, any value indepiendent of the velocity and rotational level j and depending arbitrarily on the vibrational level i and chemical species c. This values are conserved at the most frequent collisions because, according to the condition (51), vibrational energy transitions and chemical reactions are forbidden in the rapid processes. Based on the above set of the collision invariants, the solution of Eqs. (53) takes the form... 

As for vibrational energy transitions, a number of theoretical and experimental estimates for rate coefficients of these transitions are available in the literature in different temperature intervals. These data can be foimd, for example, in Nagnibeda Kustova (2009) Phys-Chem (2002 2004). The comparison of rate coefficients for vibational energy transitions of N2 molecules obtained using different models is given in Nagnibeda Kustova (2009). 

The rate coefficients for dissociation from different vibrational levels have been studied much less widely than for vibrational energy transitions. Two models are commonly used for calculations the ladder-climbing model assuming dissociation only from the last vibrational level (see, for instance, Armenise et al. (1996 1995) Capitelli et al. (1997) Osiprov (1966)), and that of Treanor and Marrone Marrone Treanor (1963) allowing for dissociation from any vibrational state. 

In the frame of ladder climbing model, the rate of dissociation is specified by the number of molecules occurring on the last vibrational level. Consequently, the dissociation rate is totally specified by the probabilities for the vibrational energy transitions to the last level. In the case when dissociation can occur from any vibrational level, the expression for the rate coefficient for dissociation of a molecule on the vibrational level i can be written in the form Nagnibeda Kustova (2009) ... 

---