Infrared Spectroscopy Summary Notes

Fundamentals of Infrared Spectroscopy

• Spectroscopy Definition: The study of the absorption and emission of light and other electromagnetic radiation by matter.

• Photon Energy Equation:     $E = h\nu$

• Infrared Spectrum Regions:

  • Near-Infrared (NIR): $800\text{ nm}$ to $2500\text{ nm}$ ($4000\text{ cm}^{-1}$)

  • Mid-Infrared (MIR): $2500\text{ nm}$ ($4000\text{ cm}^{-1}$) to $25\,\mu\text{m}$ ($400\text{ cm}^{-1}$); used primarily for molecular vibration analysis

  • Far-Infrared (FIR): $25\,\mu\text{m}$ ($400\text{ cm}^{-1}$) to $500\,\mu\text{m}$ ($20\text{ cm}^{-1}$)

• Dipole Requirement: A molecular bond must possess a dipole moment that changes during vibration to absorb infrared radiation.

• Types of Vibrations:

  • Stretching: Symmetric stretch, Antisymmetric stretch

  • In-plane Bending: Rocking, Deformation

  • Out-of-plane Bending: Wagging, Twisting

Hooke's Law and Wavenumber Factors

• Wavenumber Formula:     $\bar{\nu} = \frac{1}{2\pi c} \sqrt{\frac{f}{\mu}}$

• Reduced Mass Formula:     $\mu = \frac{m_1 m_2}{m_1 + m_2}$

• Key Relationships:

  • Wavenumber $\bar{\nu}$ is directly proportional to the force constant $f$ (bond strength).

  • Wavenumber $\bar{\nu}$ is inversely proportional to the reduced mass $\mu$.

  • Stronger, shorter bonds vibrate faster and absorb higher energy (higher wavenumber).

  • Bonds to lighter atoms (such as $\text{H}$) vibrate faster and absorb at higher wavenumbers.

Spectral Regions and Range Assignments

• Diagnostic Region: > 1500\text{ cm}^{-1}; contains fewer, distinct peaks providing structural information about functional groups.

• Fingerprint Region: < 1500\text{ cm}^{-1}; contains complex vibrational signals from most single bonds.

• Functional Group Wavenumber Ranges:

  • $\text{X-H}$ bonds ($\text{O-H}$, $\text{N-H}$, $\text{C-H}$): $2700\text{ cm}^{-1}$ to $4000\text{ cm}^{-1}$

  • Triple bonds ($\text{C}\equiv\text{C}$, $\text{C}\equiv\text{N}$): $2100\text{ cm}^{-1}$ to $2300\text{ cm}^{-1}$

  • Double bonds ($\text{C=O}$, $\text{C=C}$, $\text{C=N}$): $1600\text{ cm}^{-1}$ to $1850\text{ cm}^{-1}$

  • Single bonds: $400\text{ cm}^{-1}$ to $1500\text{ cm}^{-1}$

Signal Characteristics: Wavenumber, Intensity, and Shape

• Resonance Effects:

  • Conjugation increases single-bond character, weakening the bond and shifting absorption to a lower wavenumber.

  • Isolated ketone carbonyl ($\text{C=O}$): $1720\text{ cm}^{-1}$

  • Conjugated ketone carbonyl ($\text{C=O}$): $1680\text{ cm}^{-1}$

• Signal Intensity: Proportional to the magnitude of the dipole moment change during vibration; stronger dipole changes produce stronger absorption signals.

• Hydrogen Bonding Effects:

  • $\text{O-H}$ participating in hydrogen bonding displays a broad peak due to a distribution of weakened bond strengths.

  • Free $\text{O-H}$ (absence of hydrogen bonding) exhibits a sharp, narrow peak.

• Amine Signal Multiplicity:

  • Primary amines ($\text{R-NH}_2$) produce two signals in the $\text{N-H}$ region due to symmetric and asymmetric stretching.

  • Secondary amines ($\text{R}_2\text{NH}$) produce a single $\text{N-H}$ signal.