Vibrationrotation bands

At shorter wavelengths, individual photons carry more energy and may thus excite transitions between vibrational states. The transition rule for molecules changing their vibrational state through an electric dipole transition is simply Av = ±1 (Hanel et al., 2003). Now since the vibrational and rotational degrees of freedom of a molecule are (more or less) independent, at wavelengths where vibrational transitions are excited, they may also be associated with rotational level changes giving rise to combined rotation-vibration spectra. The form of these vibration-rotation bands

Figure 6.2. Measured line strengths at 296 K in the rotation band of CO (line strengths measured in units of cm-1(molcm~2)-1).

depends on the symmetry of the molecule as follows:

(i) Diatomic molecules. Diatomic molecules have a single vibrational mode and thus a single set of vibration-rotation bands centered at frequencies nv1 where n is an integer and v1 is the fundamental frequency given (from Equation 6.11) by

Just as for rotational transitions, only heteronuclear diatomic molecules may engage in electric dipole transitions and during each vibrational transition, the rotational energy level may also change, for which the selection rule is A/ = ±1. Hence, each vibration rotation band actually consists of two branches, the "P-branch" at frequencies below the central vibrational frequency for which A/ =—1 and the "R-branch" at frequencies above the central vibrational frequency for which A/ =+1. The shape of the R-branch is identical to the pure rotational band since the population and degeneracy of rotational states are not affected by the vibrational state. The shape of the P-branch is the mirror image of the R-branch.

(ii) Linear polyatomic molecules and spherical tops. For these molecules, the main vibration-rotation bands are actually composed of three bands which again

Figure 6.3. Measured line strengths at 296 K in the v2 vibration-rotation band of C02 (line strengths measured in units of cm-1(molcm-2)-1).

660 680 Wavenumbers (cm-1)

Figure 6.3. Measured line strengths at 296 K in the v2 vibration-rotation band of C02 (line strengths measured in units of cm-1(molcm-2)-1).

incorporate possible simultaneous changes in rotational energy levels. Just as for heteronuclear diatomic molecules, rotational energy changes governed by A/ =±1 give rise to the P-branches and R-branches. However, for linear polyatomic and spherical top molecules, an additional "Q-branch" arises since transitions with A/ = 0 are also allowed. For an ideal molecule all the possible transitions in the Q-branch would perfectly overlap, but since the rotational transitions are not perfectly equally spaced, a tight collection of transitions are seen at the central vibrational frequency. A good example of a classic P, Q, R vibration-rotation band is the 15 ^m v2 band of C02 shown in Figure 6.3.

(iii) Symmetric rotors. The situation for symmetric rotors is a little more complicated since additional structure arises from possible variations in the K angular momentum quantum number. Two types of bands arise. Transitions with AK = 0 have a very similar appearance to the classic P, Q, R structure of linear and symmetric top molecules just described and are called parallel bands. However, a second type of band arises from transitions for which AK = ±1, known as perpendicular bands. These have the appearance of a number of P, Q, R branches superimposed on each other with a small frequency shift between each central Q-branch giving rise to a regularly spaced series of Q-branches and associated P-branches and R-branches. The vibration-rotation band of ethane at 800 cm-1 [NB: wavenumbers are often used to describe frequency in visible/

infrared spectroscopy and are defined as the reciprocal of wavelength, usually expressed in centimeters] is a good example of a perpendicular band which is clearly seen in the thermal emission spectra of the giant planets. (iv) Asymmetric rotors. The vibration-rotation bands of asymmetric rotors are even more complex and appear similar to either the parallel or perpendicular bands of symmetric rotors depending on the values of the three principal moments of inertia. Water molecules are asymmetric rotors and the spectrum of each band is so complex that they have the appearance of a random jumble of line positions and strengths.

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