12 Infrared Absorption

Whereas the absorption of UV and visible light is associated with electronic transitions in molecules, the absorption of infrared (IR) light is associated with vibrational transitions. The bonds in molecules are quantized oscillators with discrete energy levels. A molecule transitions to a higher energy vibrational state when the incident photon has energy resonant with that transition.

Vibrational Transitions

For a true quantum mechanical harmonic oscillator, there is a selection rule that vibrational transitions must be between adjacent vibrational levels. The transition from the ground vibrational state, v₀, to the first excited vibrational state, v₁, is the fundamental transition and is the strongest type of transition in an IR absorption spectrum.

Notably, real molecules have some anharmonic character (i.e. a Morse curve), such that transitions between non-adjacent vibrational levels are sometimes observed. These transitions are, for example, from v₀ to v₂ and v₀ to v₃, and are called overtones. Whereas a harmonic oscillator has equal energy spacing between all vibrational levels, the energy levels of an anharmonic oscillator are not equally spaced. Overtones thus occur at slightly lower wavenumbers than integer multiples of the wavenumber for the fundamental transition. The first overtone (v₀ to v₂) is stronger in an IR spectrum than the second overtone (v₀ to v₃), and so on. Transitions such as v₁ to v₂ and v₂ to v₃ are called hot bands because of the requirement of an excited initial state. As per the Boltzmann distribution, the intensity of these bands is very weak because few molecules occupy excited vibrational states at typical measurement temperatures. Combination bands may also be observed in IR absorption spectra. These bands correspond to the excitation of two or more vibrational modes simultaneously.

Spectral Region

Given the resonance with vibrational transitions, IR absorption spectra are rich in information about chemical structure and composition. IR spectra are usually plotted with transmittance on the y-axis and wavenumber (1/λ, units of cm^–1) on the x-axis. The x-axis frequently spans from 2.5–25 µm, which is equivalent to 4000–400 cm^–1 (higher wavenumber is higher energy). This mid-IR region is resonant with many fundamental vibrational transitions. The higher-energy half of this region is often called the group frequency region because the absorption peaks are diagnostic of certain functional groups. In turn, the lower-energy half of this region is often called the fingerprint region because the many absorption peaks are challenging to correlate to specific functional groups, but are generally a unique pattern for a given molecule.

IR-Active Vibrations

Not all vibrational modes of a molecule are IR-active—photon absorption is only observed if the vibration causes a net change in dipole moment (a selection rule). For example, the symmetric stretching vibration of CO₂ is IR inactive because it produces no net change in dipole moment (the opposing motions of each C=O bond cancel out one another), whereas the asymmetric stretching vibration is IR active because there is a net change in dipole moment.

Connections

• The energy of light absorbed must match the energy of the transition induced: UV-visible light is matched to electronic transitions (Ch. 6, Ch. 10); less-energetic IR light is matched to vibrational transitions.
• The Boltzmann distribution determines the occupancy of both electronic states (Ch. 10) and vibrational states.
• At most measurement temperatures,  almost all molecules occupy their ground vibrational state, just like they occupy their ground electronic state (Ch. 6)
• Visible absorption spectra tend to plot absorbance (peaks go up) versus wavelength (Ch. 7), whereas IR absorption spectra tend to plot transmission (peaks go down) versus wavenumber.
• Although the details are different versus the absorption of visible light (Ch. 6), selection rules still apply to the absorption of IR light by molecules.

Post-Reading Questions

1. What general type of transition will produce the most intense peaks in an infrared absorption spectrum?
2. Convert 1650 cm^–1 to a wavelength in units of microns.
3. HCl gas has a fundamental vibrational transition at 2886 cm^–1. Which of the following wavenumbers corresponds to its first overtone transition: 5668, 5772, or 5876 cm^–1?
4. Propose of an advantage and a disadvantage for the identification of analytes using (a) the group frequency region and (b) the fingerprint region of an infrared absorption spectrum.
5. Consider the molecular geometry of carbon dioxide. Why does the symmetric stretch produce no change in net dipole moment whereas the asymmetric stretch does?

Topic Learning Objectives

The chapter is a primer for the following learning objectives, which will be covered in lecture and/or with additional assigned reading:

• Draw energy level diagrams that show vibrational transitions.
• Given a small molecule or functional group, predict whether a specified vibration is IR active or not.
• Estimate the number of vibrational modes for a simple small molecule.
• Correlate knowledge of bond energies with anticipated vibrational frequencies (i.e. wavenumbers).
• Know where to find and how to use tables of infrared resonances for functional groups.