Infrared spectroscopy Knowledge-Based Study

Study notes

1. Introduction to Infrared Spectroscopy

   Infrared (IR) spectroscopy is an analytical technique used primarily to identify functional groups in organic and inorganic compounds. It relies on the interaction between matter and electromagnetic radiation in the infrared region, which corresponds to wavelengths from approximately 2.5 to 25 $\mu\text{m}$, or wavenumbers ranging from $4000\text{ cm}^{-1}$ to $400\text{ cm}^{-1}$.

   The Wavenumber Scale

   In IR spectroscopy, radiation is conventionally expressed in terms of wavenumber, denoted as $ilde{\nu}$, which represents the number of waves per unit length:

   $$ilde{\nu} = \frac{1}{\lambda} = \frac{\nu}{c}$$

   where $\lambda$ is wavelength in centimeters, $\nu$ is frequency, and $c$ is the speed of light. The standard unit is the reciprocal centimeter ($\text{cm}^{-1}$). Wavenumber is directly proportional to frequency and energy ($E = hc ilde{\nu}$), making it a convenient measure of vibrational transition energies.

   The IR Selection Rule

   For a molecular vibration to absorb infrared radiation and appear as a peak in an IR spectrum, the vibration must cause a net change in the molecular dipole moment during the motion:

   • IR Active: Heteronuclear bonds such as $\text{C}=\text{O}$, $\text{O}-\text{H}$, and $\text{C}-\text{Cl}$ possess permanent dipole moments that change magnitude or direction as bonds stretch or bend, resulting in strong absorptions.
   • IR Inactive: Symmetrical diatomic molecules (such as $\text{O}_2$ and $\text{N}_2$) and completely symmetrical vibrations of centrosymmetric molecules (such as the symmetric stretch of trans-dichloroethene or carbon dioxide) produce no change in dipole moment, and thus exhibit no IR absorption.

   Modes of Molecular Vibration

   Molecules possess specific degrees of vibrational freedom depending on their geometry. For a molecule with $N$ atoms:

   • Linear molecules: have $3N - 5$ fundamental vibrational modes.
   • Non-linear molecules: have $3N - 6$ fundamental vibrational modes.

   These fundamental modes fall into two main categories:

   1. Stretching Vibrations: Involve continuous change in interatomic distance along the bond axis. These can be symmetric (atoms moving in-phase) or asymmetric (atoms moving out-of-phase).
   2. Bending Vibrations: Involve changes in the angle between two bonds. These include in-plane bending (scissoring and rocking) and out-of-plane bending (wagging and twisting). Bending motions require less energy than stretching motions and occur at lower wavenumbers.

   Hooke's Law and Vibrational Frequency

   To a first approximation, the stretching vibration of a chemical bond behaves as a simple harmonic oscillator governed by Hooke's Law:

   $$ilde{\nu} = \frac{1}{2\pi c} \sqrt{\frac{k}{\mu}}$$

   where $k$ is the bond force constant (representing bond stiffness or strength) and $\mu$ is the reduced mass of the two vibrating atoms, given by $\mu = \frac{m_1 m_2}{m_1 + m_2}$.

   Hooke's Law illustrates two fundamental trends in IR spectra:

   • Bond Order Effect: Stronger bonds have higher force constants ($k_{\text{triple}} > k_{\text{double}} > k_{\text{single}}$) and absorb at higher wavenumbers ($\text{C}\equiv\text{C} \approx 2200\text{ cm}^{-1}$, $\text{C}=\text{C} \approx 1650\text{ cm}^{-1}$, $\text{C}-\text{C} \approx 1200\text{ cm}^{-1}$).
   • Mass Effect: Bonds involving lighter atoms vibrate at higher frequencies. For instance, bonds to hydrogen ($\text{C}-\text{H}$, $\text{O}-\text{H}$, $\text{N}-\text{H}$) appear at significantly higher wavenumbers ($2800\text{--}3600\text{ cm}^{-1}$) than bonds between heavier atoms ($\text{C}-\text{C}$, $\text{C}-\text{O}$, $\text{C}-\text{Cl}$).

   Dividing the IR Spectrum

   An infrared spectrum is divided into two primary zones: the functional group region and the fingerprint region.

   1. Functional Group Region ($4000\text{ to }1500\text{ cm}^{-1}$)

   This region contains characteristic absorption bands that correspond directly to specific functional groups, largely independent of the rest of the molecular skeleton:

   • $4000\text{--}2500\text{ cm}^{-1}$ (Single bonds to hydrogen):
     • Alcohol $\text{O}-\text{H}$: Broad, intense peak at $3200\text{--}3600\text{ cm}^{-1}$ due to intermolecular hydrogen bonding.
     • Carboxylic acid $\text{O}-\text{H}$: Extremely broad band spanning $2500\text{--}3300\text{ cm}^{-1}$, often overlapping the $\text{C}-\text{H}$ region.
     • Amine/Amide $\text{N}-\text{H}$: Sharp band(s) at $3300\text{--}3500\text{ cm}^{-1}$ (primary amines show a doublet; secondary show a singlet).
     • Alkynyl $\text{C}-\text{H}$: Sharp, strong absorption near $3300\text{ cm}^{-1}$.
     • Aliphatic $\text{C}_{sp^3}-\text{H}$: Just below $3000\text{ cm}^{-1}$ ($2850\text{--}2960\text{ cm}^{-1}$).
     • Aromatic/Alkenyl $\text{C}_{sp^2}-\text{H}$: Just above $3000\text{ cm}^{-1}$ ($3010\text{--}3100\text{ cm}^{-1}$).
   • $2500\text{--}2000\text{ cm}^{-1}$ (Triple bonds):
     • Alkyne $\text{C}\equiv\text{C}$: Weak-to-medium band around $2100\text{--}2260\text{ cm}^{-1}$.
     • Nitrile $\text{C}\equiv\text{N}$: Sharp, medium-to-strong band around $2220\text{--}2260\text{ cm}^{-1}$.
   • $2000\text{--}1500\text{ cm}^{-1}$ (Double bonds):
     • Carbonyl $\text{C}=\text{O}$: Highly intense and diagnostic peak at $1650\text{--}1780\text{ cm}^{-1}$. Conjugation shifts this band to lower wavenumbers, whereas ring strain (in cyclic ketones) shifts it higher.
     • Alkene $\text{C}=\text{C}$: Medium-to-weak band at $1620\text{--}1680\text{ cm}^{-1}$.
     • Aromatic ring $\text{C}=\text{C}$: Characteristic multiple peaks around $1450\text{--}1600\text{ cm}^{-1}$.

   2. Fingerprint Region ($1500\text{ to }400\text{ cm}^{-1}$)

   The fingerprint region contains complex vibrational patterns resulting from coupled bending vibrations and single-bond stretches ($\text{C}-\text{C}$, $\text{C}-\text{O}$, $\text{C}-\text{N}$). While assigning individual bands here is difficult, this region produces a unique spectral pattern for every compound (except enantiomers), allowing definitive identification by direct library comparison.

   Sample Preparation Techniques

   Analytical IR measurements require appropriate sample handling because water and glass strongly absorb IR radiation:

   • Liquid Samples: Examined as neat liquid films pressed between polished alkali halide plates (such as $\text{NaCl}$ or $\text{KBr}$), which are transparent in the mid-IR range.
   • Solid Samples: Can be prepared as a potassium bromide ($\text{KBr}$) pellet by grinding the analyte with dry $\text{KBr}$ and pressing it under high pressure, or as a Nujol mull (suspension in mineral oil).
   • Attenuated Total Reflectance (ATR): A modern sampling accessory utilizing an internal reflection element (typically diamond, zinc selenide, or germanium). ATR requires minimal or no sample preparation and works on solids, liquids, and pastes.

   Systematic Interpretation Strategy

   When analyzing an unknown infrared spectrum, follow a structured workflow:

   1. Check for Carbonyl ($\text{C}=\text{O}$): Look for an intense absorption peak between $1650\text{ cm}^{-1}$ and $1780\text{ cm}^{-1}$. If absent, exclude aldehydes, ketones, esters, and carboxylic acids.
   2. Check for $\text{O}-\text{H}$ or $\text{N}-\text{H}$: Look for broad or distinct bands in the $3200\text{--}3600\text{ cm}^{-1}$ zone.
   3. Analyze $\text{C}-\text{H}$ Stretching: Check whether absorptions fall below $3000\text{ cm}^{-1}$ (saturated $sp^3$), above $3000\text{ cm}^{-1}$ (unsaturated $sp^2$), or near $3300\text{ cm}^{-1}$ (terminal $sp$ alkyne).
   4. Look for Unsaturation or Triple Bonds: Inspect $2100\text{--}2260\text{ cm}^{-1}$ for $\text{C}\equiv\text{C}$ and $\text{C}\equiv\text{N}$, and $1600\text{--}1680\text{ cm}^{-1}$ for alkene or aromatic unsaturation.
   5. Consult the Fingerprint Region: Match the spectrum to reference databases to confirm the exact compound.