Introduction to Infrared (IR) Spectroscopy

The light our eyes perceive is only a small portion of a much broader spectrum of electromagnetic radiation. This spectrum ranges from high-energy gamma rays and X-rays to low-energy radio waves. On the high-energy side of the visible spectrum lies the ultraviolet (UV) region, while on the low-energy side lies the infrared (IR) region. The infrared region, in particular, is of great importance in chemistry because it corresponds to the energy required to excite molecular vibrations.

The portion of the infrared spectrum most useful for analyzing organic compounds is not immediately adjacent to the visible region but spans wavelengths from 2,500 to 16,000 nm (nanometers). This corresponds to a frequency range of approximately 1.9 × 10¹³ to 1.2 × 10¹⁴ Hz (hertz). While these values are scientifically accurate, they are cumbersome to work with in practice. For this reason, chemists typically use wavenumber (expressed in cm⁻¹), which is the reciprocal of wavelength and is directly proportional to energy. The wavenumber scale for the IR region most relevant to organic compounds ranges from 400 to 4,000 cm⁻¹, making it a more convenient and intuitive unit for interpreting IR spectra.

Molecules vibrate and rotate in three dimensions at various discrete frequencies. Non-linear molecules have 3N–6 normal vibrational modes, where N is the number of atoms in the molecule. For example, methane (CH₄) has 3(5)-6 = 9 normal vibrational modes. The more atoms a molecule has, the more complex its vibrational spectrum becomes. These vibrations arise from different types of motions, such as stretching and bending. For methane, some of the important vibrational modes include C–H stretching and bending, as illustrated in the next page.

Why 3N–6?

Each atom in a non-linear molecule can move in three dimensions (x, y, z), hence the 3N term. However, if every atom in the molecule moves in the same direction (e.g., the x-direction), this corresponds to a translation of the entire molecule rather than an internal vibration. Therefore, we subtract 3 to account for translations in the x, y, and z directions. Additionally, we subtract another 3 to account for rotations about the x, y, and z axes. This leaves us with 3N–6 normal vibrational modes for non-linear molecules.

For linear molecules, the situation is slightly different. A linear molecule has 3N–5 vibrational modes. Can you explain why? (Hint: Think about how rotations differ in a linear molecule compared to a non-linear one.)

Infrared Radiation (IR) and Vibrational Spectroscopy

The vibrational modes of molecules have quantized energy levels, meaning they vibrate at specific frequencies. When a molecule is exposed to infrared radiation of the appropriate frequency, it can absorb photons, causing its vibrational modes to transition to higher energy levels. The energy differences between these vibrational states correspond to the energy of infrared radiation, which is why IR spectroscopy is often referred to as vibrational spectroscopy.

IR spectroscopy is a powerful tool for identifying functional groups in organic molecules. Each functional group has characteristic vibrational frequencies that appear as peaks in the IR spectrum. For example, the C–H stretching vibrations of an sp²-hybridized carbon (such as in benzene) typically appear around ~3300 cm⁻¹. To explore this further, use the interactive animation of benzene's vibrational modes. Select the frequency corresponding to the C(sp²)–H stretching mode to visualize how the molecule vibrates at this energy.

By analyzing the IR spectrum of a molecule, chemists can identify the presence of specific functional groups and gain insight into the molecular structure. As you progress through this chapter, you will learn how to interpret IR spectra and correlate vibrational frequencies with molecular features.

 Benzene Vibrations

Transmission and Absorption Spectra

Infrared (IR) spectroscopy exploits the interaction of infrared radiation with molecular vibrations. When IR light is passed through a sample, certain frequencies are absorbed by the molecule, corresponding to specific vibrational modes. The remaining light is transmitted. IR spectra can be recorded in two primary modes: transmission and absorption.

• Transmission IR: Measures the amount of IR light that passes through the sample. Peaks in a transmission spectrum correspond to lower transmittance (less light passing through), indicating absorption.  For example, the following is the Transmission IR spectrum for 1-propanol
  
• Absorption IR: Directly measures the amount of IR light absorbed by the sample. Peaks in an absorption spectrum correspond to higher absorbance, indicating stronger absorption.   While both modes provide the same fundamental information, absorption spectra are often preferred for quantitative analysis due to their linear relationship with concentration.  For example, the following is the absorption IR spectrum for 1-propanol