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" Presuming that the rule AS = 0 is obeyed. b Source: Herzberg (1950), p. 243.

1, 2, 3,... in the upper electronic state are usually observed.

The rotational selection rule is A / = 0, +1, except for the case of a transition involving fi = 0 for both the upper and lower states. Thus three sets of lines (known as the P, Q, and R branches) corresponding to A /= —1, 0, and +1, respectively, are observed for each band arising from a particular vibrational transition. Figure 3.5 illustrates these transitions schematically. However, if fi = 0 for both upper and lower states ('2 -> 'S transition), the rotational selection rule is A J = ±1, and the Q branch does not appear. For further details, see Herzberg (1945, 1950, 1967).

As a general rule, the most probable, that is, most intense, vibrational transitions within a given electronic transition will be those in which the vibrational probabilities are maximum in both the initial and final states. An important restriction is that only vertical transitions are allowed. This is a consequence of the Franck-Con-don principle, which states that the time for an electronic transition to occur (typically 10"15 s) is so short relative to the time it takes for one vibration 10 s) that the internuclear distance remains essentially constant during the electronic transition.

Figure 3.6 shows the Morse potential energy curves for two hypothetical electronic states of a diatomic molecule, the vibrational energy levels for each, and the shape of the vibrational wave functions (ip) within j'

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