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Wavenumbers (cm-1)

FIGURE 3.4 Vibration-rotation spectrum of 0.18 Torr HC1 at room temperature using a path length of 19.2 m. Resolution is 0.25 cm-1. The rotational transitions are shown as (initial 7, final J) (from B. J. Finlayson-Pitts and S. N. Johnson, unpublished data).

molecular quantum numbers, A, 5, and fi. A is the component of the total electronic orbital angular momentum L along the internuclear axis and can be determined from the electronic spectrum of the molecule (see Herzberg, 1950). Allowed values of A of 0, 1, 2, and 3 correspond to electronic states designated as n, A, and O, respectively.

The spin quantum number 5 represents the net spin of the electrons. It has an integral value or zero for even numbers of electrons and half-integral value for odd numbers. The multiplicity of a molecular state is defined as (25 + 1) and is written as a superscript to the left of the symbol corresponding to A. Values of 5 of 0, 1/2, and 1, corresponding to multiplicities of 1, 2, and 3, are referred to as singlet, doublet, and triplet states, respectively. While most stable molecules have ground singlet states, one important exception is 02, where the ground state is a triplet. As discussed in Chapter 4, this has important implications for its spectroscopy and photochemistry.

For many molecules the quantum number fi is defined and is given by the vector sum of A and n = |a 4- si, where X is the vector component of 5 in the direction of the internuclear axis. £ can have the values +5, 5 - 1,..., - 5 and can be positive, negative, or zero.

Two other symbols are used in designating electronic states according to their symmetry. For homonu-clear diatomic molecules, states are designated "g" or "u" as a subscript to the right of the A symbol, depending on whether or not the wavefunction describing the molecular state changes sign when reflected through the center of symmetry of the molecule. If it does change sign, it is designated "u" (for ungerade = uneven); if it does not, it is designated "g" (for gerade = even).

Finally, the symbols + and —, written as superscripts to the A symbol, refer to two types of sigma states, X+ and If the wavefunction is unaltered by reflection through a plane passing through the two nuclei, the state is positive ( + ); if it changes sign, it is negative (-).

The selection rules for electronic transitions are not as clear-cut as in the case of vibration and rotation. In the case of molecules consisting of relatively light nuclei, which is the case for many molecules of tropo-spheric interest, the selection rules

apply. Thus transitions between states of unlike multiplicity (e.g., singlet -» triplet) are "forbidden" but in some cases may occur with a relatively small probability, most notably with the oxygen molecule, which has a triplet ground state. In terms of the symmetry of the wavefunctions, u <-> g transitions are allowed but u u and g <-> g are forbidden. In addition, states cannot combine with states; that is, 2 + £+ and transitions are allowed but 2 + are forbid den. Table 3.1 summarizes these selection rules for molecules with light nuclei.

Upon absorption of light of an appropriate wavelength, a diatomic molecule can undergo an electronic transition, along with simultaneous vibrational and rotational transitions. In this case, there is no restriction on At'. That is, the selection rule Av = +1 valid for purely vibrational and vibrational-rotational transitions no longer applies; thus numerous vibrational transitions can occur. If the molecule is at room temperature, it will normally be in its lower state, v" = 0; hence transitions corresponding to v" = 0 to v' = 0,

TABLE 3.1 Allowed" Electronic Transitions of Diatomic Molecules Having Light Nucleib

Homonuclear diatomic (equal nuclear charge)

Heteronuclear diatomic (unequal nuclear charge)

ne ns ne

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