CHAP. 12: BASIC TERMS OF CHEMICAL PHYSICS [CONTENTS] 432
whereaandbare constants characteristic for the series.
The electron spectra of molecules are yet more complex. Owing to the mutual influence
of many electrons and nuclei in the molecule, interaction with photons occurs at many wave-
lengths, and the resulting spectrum does not have the form of lines but that of the absorption
coefficient [see12.1.9] dependence on the wavelength. The maximum values on this curve
usually correspond to the transitions of bonding electrons between different energy states.
12.3.5 Vibrational and rotational spectra
In di- and polyatomic molecules, photons are also absorbed due to the quantization of the
molecules vibrational energy [see12.2.5]. Transitions between individual quantum states can
occur only when the vibrational quantum number changes by one, ∆vi =±1. Due to this
selection rule, each vibrational frequency has thus only one single maximum where the pho-
tons with a frequency corresponding to the characteristic frequency of vibration (12.33) are
absorbed. In addition, the absorption line is active (have measurable intensity) only if the
electric dipole moment changes in the course of vibration; homonuclear diatomic molecules
therefore are inactive. Since in the case of more complex (particularly organic) molecules indi-
vidual vibration frequencies can be assigned to certain functional groups, it is possible to use
the vibrational spectrum to identify the structure of molecules. The vibrational spectra lie in
infrared region.
Note: When applying anharmonic terms in calculating energy, (12.34), the single peak
splits into a band composed of several lines close to each other.Similarly as vibrations, the rotations of molecules are also quantized [see12.2.4]. Since,
however, the differences between the energy quantum levels for rotations are relatively small,
pure rotational spectra lie in the microwave region. Rotations also affect the appearance of
vibrational spectra. In low-resolution spectra the range of frequencies where absorption occurs
expands and anabsorption bandis formed. Spectra with a high resolution split into several
absorption maxima.
The selection rule for a rotational transition is the change if the rotational quantum number
lby one. In addition, the rotating molecule must have nonzero dipole moment. It follows from