The Position of Absorption Bands

The Position of Absorption Bands

The position of an absorption band in an IR spectrum, expressed as wavenumber (cm⁻¹), directly correlates with the frequency of the vibrational mode. This frequency is fundamentally determined by the strength of the bond and the masses of the atoms involved, a relationship that can be understood through Hooke's Law. Additionally, electronic and intermolecular interactions contribute to fine-tuning the band position.

Hooke's Law and Vibrational Frequency

Hooke's Law, typically used to describe the behavior of springs, provides a simplified model for understanding the vibrational frequency of a diatomic molecule. In this context, the chemical bond is treated as a spring connecting two masses (the atoms).

The vibrational frequency (ν) is related to the force constant (k) of the bond and the reduced mass (μ) of the atoms by the following equation:

ν = (1 / (2π)) * √(k / μ)

where:

• ν (nu) is the vibrational frequency.
• k is the force constant, which represents the strength of the bond (a higher force constant means a stronger bond).
• μ (mu) is the reduced mass, calculated as:

μ = (m₁ * m₂) / (m₁ + m₂)

where m₁ and m₂ are the masses of the two atoms.

Implications for IR Spectroscopy

• Bond Strength (k): A stronger bond (higher k) results in a higher vibrational frequency (higher wavenumber). This explains why triple bonds (stronger) appear at higher wavenumbers than double or single bonds.
• Atomic Masses (μ): A smaller reduced mass (lighter atoms) results in a higher vibrational frequency. This explains why bonds to hydrogen (lightest atom) have high stretching frequencies, even though they are single bonds.

While Hooke's Law provides a simplified model for diatomic molecules, it serves as a foundational concept for understanding the factors that influence vibrational frequencies in polyatomic molecules. However, in larger molecules, we must also consider coupling of vibrations and other more complex interactions.

Electronic and Intermolecular Interactions

Beyond Hooke's Law, electronic effects such as conjugation, inductive effects, and intermolecular interactions like hydrogen bonding can further shift the positions of absorption bands. These effects alter the effective force constant of the bonds and the vibrational frequencies.

1. Effect of Bond Order (Bond Strength and Stiffness)

Bond order significantly influences the position of absorption bands.

• General Trend: Higher bond orders correspond to stronger and stiffer bonds, leading to higher vibrational frequencies (higher wavenumbers).
  • Therefore, triple bonds (C≡C, ~2100-2260 cm⁻¹; C≡N, ~2210-2260 cm⁻¹) exhibit stretching vibrations at higher wavenumbers than double bonds (C=C, ~1620-1680 cm⁻¹; C=O, ~1650-1800 cm⁻¹), which in turn occur at higher wavenumbers than single bonds (C–C, ~800-1300 cm⁻¹; C–O, ~1000-1300 cm⁻¹).
  • This trend is a direct result of the increased force constant associated with higher bond orders.
• Exception: Bonds to Hydrogen: Bonds to hydrogen (C–H, ~2850-3300 cm⁻¹; O–H, ~3200-3600 cm⁻¹; N–H, ~3300-3500 cm⁻¹) are an exception to the strict bond order rule. Despite being single bonds, they have high stretching frequencies due to the low mass of hydrogen.
  • Lighter atoms vibrate at higher frequencies.

2. Effect of Electronic Effects

Electronic effects play a crucial role in fine-tuning the position of absorption bands.

• Electron Delocalization (Conjugation/Resonance): Delocalization of electrons, such as in conjugated systems, weakens the bond and reduces the force constant.
  • This results in a decrease in the stretching frequency.
  • For example, the C=O stretch in α,β-unsaturated ketones (~1660-1680 cm⁻¹) appears at lower wavenumbers compared to saturated ketones (~1710-1750 cm⁻¹) due to the delocalization of π-electrons.
• Electron Donation/Withdrawal (Inductive Effects): Electron-withdrawing groups increase the electron density in antibonding orbitals, effectively strengthening the bond, and therefore, increasing the wavenumber of the stretch.
  • Electron donating groups do the opposite.
  • For example, the presence of electronegative halogens or nitro groups can increase the frequency of nearby stretching vibrations.

3. Effect of Intermolecular Interactions (Hydrogen Bonding)

Intermolecular interactions, particularly hydrogen bonding, have a significant impact on the position and shape of absorption bands.

• Hydrogen Bonding: Hydrogen bonding weakens the O–H or N–H bond, leading to a decrease in the stretching frequency.
  • It also broadens the absorption band due to the variety of hydrogen bond strengths present in the sample.
  • Free O–H stretches typically appear around 3600 cm⁻¹, while hydrogen-bonded O–H stretches are observed in the 3200–3400 cm⁻¹ range.
  • Hydrogen bonding is concentration dependent. Dilute solutions will show less hydrogen bonding.
• Other intermolecular forces: Other intermolecular forces can also have smaller effects on the position of IR absorptions.

4. Other Factors

• Ring Strain: In cyclic compounds, ring strain can affect bond angles and bond strengths, leading to shifts in absorption frequencies.
• Hybridization: The hybridization state of carbon atoms affects C–H stretching frequencies. sp³ C–H stretches are typically below 3000 cm⁻¹, sp² C–H stretches are above 3000 cm⁻¹, and sp C–H stretches are around 3300 cm⁻¹.

Importance of Position Information:

• The position of absorption bands provides valuable information about the types of bonds and functional groups present in a molecule.
• It can be used to distinguish between different structural isomers.
• Changes in the position of absorption bands can indicate the presence of specific interactions or structural features.