Energy levels, diagrams rotational

Figure 3b. OH energy-level diagram—rotational structure...

Figure 9.18 shows a typical energy level diagram of a dye molecule including the lowest electronic states Sq, and S2 in the singlet manifold and and T2 in the triplet manifold. Associated with each of these states are vibrational and rotational sub-levels broadened to such an extent in the liquid that they form a continuum. As a result the absorption spectrum, such as that in Figure 9.17, is typical of a liquid phase spectrum showing almost no structure within the band system. 

Figure 10.1 Schematic energy-level diagram for a molecule. Two electronic levels A and B are present, with their vibrational levels (v) and rotational levels (/). The relative separation of electronic and vibrational levels is generally much greater than we have shown here.

Figure 3.6 The energy-level diagram for a rotational spectrum...

The anisotropy of the interaction couples the translational and rotational states of collisional systems. This in turn couples the various dipole components. Instead of computing for each set of expansion parameters X XiSL one general profile for all rotational components associated with that set, one now has a much more complex computational task to compute the induced absorption continua. Moreover, the energy level diagrams as well as the spectra of van der Waals dimers are much more complex when the anisotropy of the interaction is accounted for. 

Fig. 11.2. Energy-level diagram of H20(A) in the lowest vibrational state for total angular momentum quantum number J = 4 E = 0 corresponds to the lowest rotational level 00o. The nomenclature Jk k+ with K+ = J, J — 1,..., 0 and K = 0,1,..., J follows the standard spectroscopic convention (Levine 1975 ch.5 Zare 1988 ch.6).

Fig. 11.9. Rotational state distributions of OH in the 2Il3/2(A ) A-doublet for four initial rotational states of H2O all having the same total angular momentum quantum number J = 4. The normalization between experiment and theory is made for each case separately and is indicated by the arrows. The corresponding energy level diagram is shown in Figure 11.2. Adapted from Hausler, Andresen, and Schinke (1987).

Schematic energy level diagrams for the most widely used probe methods are shown in Fig. 1. In each case, light of a characteristic frequency is scattered, emitted, and/or absorbed by the molecule, so that a measurement of that frequency serves to identify the molecule probed. The intensity of scattered or emitted radiation can be related to the concentration of the molecule responsible. From measurements on different internal quantum states (vibrational and/or rotational) of the system, a population distribution can be obtained. If that degree of freedom is in thermal equilibrium within the flame, a temperature can be deduced if not, the population distribution itself is then of direct interest.

Molecular Systems. Molecules present a considerably more complex picture. Illustrated in Figure 3 is the energy level diagram for OH, the hydroxyl radical. The structure consists of several electronic states, each of which supports a number of vibrational states. Rotational motion is superimposed on each electronic-vibrational state as illustrated in Figure 3b. OH is an attractive molecule for analysis because of its dominant importance in combustion kinetic schemes and because its structure, while more complicated than any atom s, is fairly simple compared to many other molecules. 

Figure 2.9. A schematic energy level diagram for the X Apn2) and A 1 A2(n,7i ) states of thiophosgene showing the vibronic transitions that give rise to the a, b, and c rotational band types.

Figure 8.22. Schematic energy level diagram for the first four rotational levels of N2 in its A 3E+ state, showing the nuclear hyperfine states which are allowed to combine with each N level. Relative vertical spacings are not drawn to scale [43].

Figure 8.36. Energy level diagram showing the nuclear spin Zeeman energies for the 7Li and 79Br nuclei in LiBr. The nuclear g-factor for 7Li (3.256) is larger than that for 79Br (2.106). Each level shown is split into a further triplet by the rotational Zeeman interaction which removes the Mj threefold-degeneracy for J = 1.

Figure 9.33. Energy level diagram showing the transitions involving the four lowest rotational levels of CH in then = 0 level of the 4E state [691 The laser wavelengths used were (a) 333 gill, (b) 167 gm, (c) 111 gm, full details of which are given in table 9.1.

Figure 9.34. Laser magnetic resonance spectrum of CH in its a 4 state recorded in parallel polarisation (AMj = 0) with the 166.6 /un laser line of CH2F2. The rotational transition is N = 2 <—, and the quintet fine structure may be understood by reference to the energy level diagram in figure 9.33. The lines marked with an asterisk arise from an impurity species the doublet splittings of the CH lines are due to proton hyperfine interaction [69].

Figure 10.46. Case (a) rotational energy level diagram forNiO in its X3 state, and the transitions observed by Namiki and Saito [136].

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