Rotational quantized energy levels

For reactions between atoms, the computation needs to model only the translational energy of impact. For molecular reactions, there are internal energies to be included in the calculation. These internal energies are vibrational and rotational motions, which have quantized energy levels. Even with these corrections included, rate constant calculations tend to lose accuracy as the complexity of the molecular system and reaction mechanism increases. 

In addition to electronic transitions, molecules exhibit two other types ot radiation-induced transitions vibrational transitions and rotational transitions. Vibrational transitions occur because a molecule has a multitude of quantized energy levels (or vibrational states) associated with the bonds that hold the molecule together. 

FIGURE 11.10 The quantized energy levels of 2-D rotation. They increase in energy according to the square of the quantum number m. 

To calculate N (E-Eq), the non-torsional transitional modes have been treated as vibrations as well as rotations [26]. The fomier approach is invalid when the transitional mode s barrier for rotation is low, while the latter is inappropriate when the transitional mode is a vibration. Hamionic frequencies for the transitional modes may be obtained from a semi-empirical model [23] or by perfomiing an appropriate nomial mode analysis as a fiinction of the reaction path for the reaction s potential energy surface [26]. Semiclassical quantization may be used to detemiine anliamionic energy levels for die transitional modes [27]. 

At low energies, the rotational and vibrational motions of molecules can be considered separately. The simplest model for rotational energy levels is the rigid dumbbell with quantized angular momentum. It has a series of rotational levels having energy... 

The importance of the idea that energy is quantized is impossible to overstate. It applies to all types of energies related to atoms and molecules. It forms the basis of the various experimental techniques for studying the structure of atoms and molecules. The energy levels may be electronic, vibrational, or rotational depending on the type of experiment conducted. 

We have now looked at the way photons are absorbed. Photons of UV and visible light cause electrons to promote between orbitals. Infrared photons have less energy, and are incapable of exciting electrons between orbitals, but they do allow excitation between quantized vibrational levels. The absorption of microwaves, which are less energetic still, effects the excitation between quantized rotational levels. 

The result (Equation 4.90) could have been derived more simply. It has been emphasized that the quantum mechanical contribution to the partition function ratio arises from the quantization of vibrational energy levels. For the molecular translations and rotations quantization has been ignored because the spacing of translational and rotational energy levels is so close as to be essentially continuous (As/kT 1). 

Both rotations and vibrations of molecules are quantized. This means that only particular values of rotational angular momentum or vibrational energy are possible. We speak of these permitted values of the energies as the vibrational and rotational energy levels. 

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