Chapter 1
Infrared Spectroscopy and Its Application in Atmospheric Research

1.1 Basic Theories

Infrared (IR) spectroscopy analyzes the interaction between infrared light and a molecule. This technique applies to a molecule that can selectively absorb at certain wavelengths in the infrared region and undergo an internal transition in the vibration energy level and rotational energy level. When the photon energy is equal to the energy required for the molecular transition, which corresponds to the radiation frequency matching the dipole frequency, then the molecule will absorb the radiation and undergo an oscillation transition. One of the great advantages of IR is that it can practically analyze samples in various states.

As shown in Figure 1.1, the IR portion of the electromagnetic spectrum is divided into near-, mid-, and far-IR regions. The near-IR region, which is the highest in energy, with absorptions in the range ~14000-4000 cm-1 (corresponding to wavelength in the ), can excite overtone or harmonic vibrations. The mid-IR region, having absorptions at ~4000-400 cm-1 ( wavelength), may be used to study the fundamental vibrations and associated rotational-vibrational structures, whereas the far-IR region that has absorptions at ~400-10 cm-1 ( wavelength) lies adjacent to the microwave region. It is the lowest in energy and is suitable for use in rotational spectroscopy.

Figure 1.1 Electromagnetic spectrum.

When a chemical bond vibrates, the molecule absorbs an IR radiation. This absorption can be measured by the infrared spectrometer and be converted into a spectrum. The infrared ray was first found in 1800 by the British scientist Herschel, and in 1936, the first prism spectrometer, a single beam infrared spectrometer, was made. The double beam infrared spectrometer was later developed in 1946. In the 1960s, the second generation of infrared spectrometer using grating as dispersive element came out. In the 1970s, as the Fourier transform infrared spectrometer (FTIR) emerged, the IR spectroscopy scanning speed greatly improved. Following developments led, in the late 1970s, to laser infrared spectrometers, confocal microscopic infrared spectrometers, and so on.

The infrared spectrum, also known as molecular vibration rotation spectrum, belongs to the molecular absorption spectrum and is simply the graph plotted with the absorbed infrared light against the infrared wavelength or frequency. When a sample is irradiated with the infrared light with continuous frequency, the molecule absorbs the radiation of some frequencies. The molecular vibration or the rotation leads to a change in dipole moment, resulting in the vibration-rotation energy level to transit from the ground state to the excited state. The wavenumber or the wavelength curve is recorded by the transmission rate percentage . The infrared absorption spectrum is generally expressed by a wave curve or a T-wavenumber curve. In the infrared spectrum, the ordinate is the transmittance percentage, the abscissa is the wavelength range , or the wavenumber (cm-1).

All functional groups in a molecule have their own specific absorption peaks with different infrared characteristics. In different compounds, the absorption vibration of the same functional group always appears in a narrow range of wavenumbers, not on a fixed wavenumber as the specific number of waves is related to the environment in which the group is located in the molecule. The factors that cause the frequency displacement of the group are multifaceted, among which the external factors are mainly the physical state and chemical environment in which the molecule is located, such as temperature and solvent effects. For the internal factors leading to group frequency displacement, there are electric effects of substituents such as induction effect, conjugate effect, intermediate effect, dipole field effect, etc. The mechanical effects include mass effect, tension-induced bond angle effect, and vibration coupling effect, among which hydrogen bond effect and coordination effect also lead to group frequency shift. When these effects occur between molecules, they are referred to as external factors. When they are within molecules, they are referred to as internal factors.

The vibration transition probability is measured by the intensity of the infrared band, and it is related to the magnitude of the change in dipole moment upon molecular vibration. This change in dipole moment is proportional with the band intensity. Since the change in dipole moment is also related to the inherent dipole moment of the group itself, then upon molecular vibration, the stronger the polarity of the group, the greater the change in dipole moment, and the stronger the absorption band. Likewise, the higher the symmetry of the molecule, the smaller the change of dipole moment, and the weaker the absorption band. This indicates that the functional groups and constituents of a substance can be judged according to the infrared spectra.

1.1.1 Energy Level

A very important concept in spectroscopy is the Born-Oppenheimer approximation, which is the basis for understanding molecular potential energy curves. It was introduced to simplify the representation of Coulomb interactions between electrons and nuclei in a molecule by separating their motions. This approximation stands on the ground that since electrons are much lighter than the nuclei, they move so fast that they can be assumed to be moving in a field of fixed nuclei. Thus, for each relative position of the nuclei, a potential energy can be calculated relative to the position of the nuclei upon which the electronic energy parametrically depends. Figure 1.2a shows the potential energy curve of a diatomic molecule as a function of the distance between the nuclei.

Figure 1.2 (a) Potential energy curve for a diatomic molecule. The minimum value corresponds to the bond length, and is the dissociation energy. (b) Harmonic approximation of the potential energy curve.

When the two atoms are far away from each other, they do not feel any interaction, and the potential energy is zero. As they approach each other, however, attraction occurs between electrons and nuclei, whereas nuclei-nuclei and electron-electron repulsion occurs, giving rise to a nonattractive term. The attractive forces are prevalent at not too small distances. However, as the internuclear distance goes toward zero, the potential energy rises toward infinity, reflecting the importance of nucleus repulsion at small distances. The minimum value corresponds to the equilibrium distance between two nuclei. This value is most often referred to as the bond length, . In order to dissociate the molecule, an energy corresponding to at least the dissociation energy must be used.

Potential curves for diatomic molecules can be calculated accurately using a very good approximation called Morse potential, given by Equation (1.1):

where is the dissociation energy, is the distance separating the two nuclei, designates the equilibrium value, and is a parameter which influences the width of the Morse curve.

In vibrational spectroscopy, the bottom of the potential energy curve is the most important, as will be shown below. This part of the potential energy curve can be approximated, in most cases, by a parabola described by a harmonic oscillator, given by Equation (1.2), and illustrated in Figure 1.2b. This approximation is called harmonic approximation.

where is the force constant. At high potential energies, the harmonic approximation certainly performs bad as the dissociation energy goes toward infinity.

In classical view, all values for the potential energy are acceptable. However, this is not the case from quantum mechanical approach wherefrom only certain values of the potential energy are possible. Based on this approach, the values of the potential energy are given as:

where is Planck's constant, and is the quantum number taking values of positive integers (including zero). For possible values for the potential energy, the energy levels in the harmonic approximation are shown in Figure 1.3. Note that in this approximation, the energy difference between two consecutive levels is the same. This is sometimes called the distance between the levels, so that the distance is measured in energy units! The energy levels for the more realistic Morse potential are not equidistant as shown in Figure 1.3. For this potential, the distance between consecutive levels decreases with increasing quantum numbers. However, at the bottom of the Morse potential energy curve, the energy levels are nearly equidistant, consistent with the fact that the harmonic approximation is a good choice.

Figure 1.3 Energy levels for a Morse potential and a harmonic potential. The numbers are the vibrational quantum numbers.

Quite often, the potential energy curves are not shown, but only the energy levels as illustrated for both harmonic and anharmonic potentials are shown in Figure 1.4. When the energy is given in cm-1 instead of Joule (or J/mol), the picture in Figure 1.4 is referred to as term diagram. The state with the lowest energy is the fundamental state or ground state, while other states are the excited states. When a molecule moves from one energy state to another, this process is called a transition. When a transition is from lower to a higher state, the energy is said to be...