Molecular energies translation

In the above expressions for C(t), the averaging over initial rotational, vibrational, and electronic states is explicitly shown. There is also an average over the translational motion implicit in all of these expressions. Its role has not (yet) been emphasized because the molecular energy levels, whose spacings yield the characteristic frequencies at which light can be absorbed or emitted, do not depend on translational motion. However, the frequency of the electromagnetic field experienced by moving molecules does depend on the velocities of the molecules, so this issue must now be addressed. 

We have thus reduced the problem from finding the ensemble partition function Q to finding the molecular partition function q. In order to make further progress, we assume that the molecular energy e can be expressed as a separable sum of electronic, translational, rotational, and vibrational terms, i.e.,... 

Here we use the label i to denote a molecular energy level, which may denote at once the specific translational (t), rotational (r), vibrational (u), and electronic (e) energy level of the molecule. From Eq. 8.46 and the definition of the molecular partition function q,... 

With each electronic state, we have a series of vibration-rotation levels. See Fig. 4.3. The total molecular energy (excluding translation) for a given state of electronic and nuclear motion is the sum of the equilibrium electronic energy Ue, the vibrational energy vib, and the rotational energy... 

Considering the four types of energy, translational, rotational, vibrational and electronic, it is convenient to classify ten types of molecular energy transfer. In some, the type of energy is preserved, for example the E-E process which produces population inversion in the He/Ne laser8... 

Fig. 4.1.13(a-c) shows partial cross-sections for reactions with the reactant molecules in vibrational quantum states n = 0,1,2 and rotational quantum state J = 0 and products in vibrational states n = 0,1,2, respectively, and any rotational quantum state. Note that the abscissa axis in this plot is the translational energy and not the total energy as in Fig. 4.1.12. The translational energy is found in the latter plot by subtracting the molecular energy En

Temperature is a way of measuring the average molecular energy of materials. The increase of temperature in a system increases the disorganization either in terms of location or in terms of the occupation of their available translational, rotational, and vibra-... 

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