Comprehensive Study Notes on Infrared Spectroscopy and Principles of Molecular Spectroscopy

Fundamentals of Spectroscopy and Electromagnetic Radiation

• Spectroscopy Definition: Spectroscopy is the study of the interaction between electromagnetic radiation (such as visible light, radio waves, or X-rays) and matter.
• Nature of Electromagnetic Radiation: All electromagnetic radiation consists of an electric field and a magnetic field that are orthogonal to each other (oriented at an angle of $90^\text{ degrees}$ relative to one another).
• Characterization Parameters:
  • Wavelength: The spatial distance between two consecutive peaks of either the electric field or the orthogonal magnetic field.
  • Frequency: The number of wave peaks that pass a fixed point per second. The standard unit of frequency is Hertz ($\text{Hz}$), which corresponds to inverse seconds ($\text{s}^{-1}$).

The Electromagnetic Spectrum and Analytical Techniques

• Spectrum Ordering: Electromagnetic radiation spans a continuous spectrum categorized by decreasing wavelength and increasing frequency (or energy):
  • Radio Waves and Microwaves: Possess very long wavelengths and very low frequencies. Used in Nuclear Magnetic Resonance (NMR) spectroscopy.
  • Infrared (IR) Radiation: Possesses shorter wavelengths and higher frequencies than microwaves. Used in infrared (IR) spectroscopy or vibrational spectroscopy.
  • Visible Light: Encompasses the visible colors of the rainbow, with shorter wavelengths than infrared. Used in ultraviolet-visible (UV-Vis) spectroscopy.
  • X-rays: Possess smaller wavelengths and higher frequencies than visible light. Used in X-ray diffraction techniques and medical/dental imaging.
  • Gamma Rays: Possess the smallest wavelengths and highest frequencies on the spectrum. Used in Positron Emission Topography/Scan (PET scans) to detect tumors.

Energy Quantization and Molecular Transitions

• Principle of Energy Quantization: Traditional classical mechanics breaks down when analyzing systems at the atomic and molecular scale. Energy at this level is quantized, meaning atoms and molecules exist only at specific, discrete energy levels rather than a continuous spectrum of energy states.
• Absorption and Emission Mechanics:
  • Absorption: For a molecule in a low energy quantum state to transition to a higher quantum state, it must absorb a photon containing an exact energy amount matching the energy difference between the two states.
  • Photon Energy Formula: The energy of an absorbed or emitted photon is calculated as:         $E = h \times \nu$         where $E$ is energy, $h$ is Planck's constant, and $\nu$ is the frequency of the radiation.
  • Emission: A molecule residing in a high energy quantum state that relaxes to a lower quantum state releases a photon carrying an exact energy equal to the difference between the states ($h \times \nu$).
• Excitation Modes:
  • Vibrational Excitation: Induced by infrared (IR) radiation.
  • Electronic Excitation: Promoted by ultraviolet (UV) or visible light, boosting electrons to higher energy quantum states.
  • Nuclear Magnetic Orientation: Probed by radio frequency radiation in Nuclear Magnetic Resonance (NMR) spectroscopy.

Molecular Vibrations and Hooke's Law Model

• Infrared Excitation Mechanisms: Organic molecules absorb light in the IR region (often perceived as heat) to undergo vibrational excitation. Key vibrational modes include:
  • Stretching Vibration: Rhythmic movement along the bond axis between two bonded atoms.
  • Scissoring: In-plane bending movement involving three bonded atoms.
  • Twisting: Out-of-plane rotational movement involving three bonded atoms.
• Hooke's Law Mathematical Model: The vibrational frequency (expressed as wave number) of a molecular bond is modeled by a mathematical derivative of Hooke's Law:     $\tilde{\nu} = \frac{1}{2 \times \text{π} \times c} \times \text{sqrt}​​$     Wait, let's format LaTeX cleanly:     $\tilde{\nu} = \frac{1}{2 \times \pi \times c} \times \sqrt{\frac{f}{\mu}}$     where:
  • $\tilde{\nu}$ is the wave number (indicative of vibrational frequency and energy).
  • $c$ is the speed of light.
  • $f$ is the force constant, representing bond strength or spring stiffness.
  • $\mu$ is the reduced mass, converting a two-body problem (two atoms with masses $m_1$ and $m_2$ connected by a bond) into a single term calculated as:         $\mu = \frac{m_1 \times m_2}{m_1 + m_2}$
• Factors Increasing Vibrational Frequency ($\tilde{\nu}$):
  • High Force Constant ($f$): Stronger bonds (higher bond order) increase the force constant, raising the wave number/energy of vibration.
  • Low Reduced Mass ($\mu$): Bonds containing lighter atoms (such as hydrogen) result in a smaller reduced mass denominator, significantly increasing the wave number/energy of vibration.
• Reduced Mass Comparisons:
  • $\text{C-Cl}$ Bond: Heavy chlorine atom creates a large reduced mass ($\mu$), yielding a low vibrational frequency around $700\,\text{cm}^{-1}$.
  • $\text{C-H}$ Bond: Light hydrogen atom yields a very small reduced mass ($\mu$), resulting in a high vibrational frequency around $3000\,\text{cm}^{-1}$.
• Force Constant Comparisons (Bond Order):
  • $\text{C-N}$ Single Bond: Stretching frequency occurs around $1100\,\text{cm}^{-1}$.
  • $\text{C=N}$ Double Bond: Increased bond strength raises stretching frequency to around $1600\,\text{cm}^{-1}$.
  • $\text{C}\equiv\text{N}$ Triple Bond (Nitrile): Strongest bonding interaction raises stretching frequency to around $2200\,\text{cm}^{-1}$.

Sample Preparation Techniques for IR Spectroscopy

• Salt Plates:
  • Substances such as calcium chloride ($\text{CaCl}_2$), potassium chloride ($\text{KCl}$), or potassium bromide ($\text{KBr}$) do not absorb IR radiation significantly.
  • Liquid organic samples can be applied directly as a drop between clear salt plates.
• Potassium Bromide ($\text{KBr}$) Pellets:
  • Solid organic samples are ground with $\text{KBr}$ salt powder and compressed into a transparent disk using a hydraulic press prior to spectroscopic analysis.
• Nujol Mull:
  • For liquid or solid samples incompatible with plain salt plates, the sample is mixed with Nujol (a specific brand of mineral oil that has minimal IR absorption) to form a non-homogeneous slurry/mull, which is sandwiched between salt plates.
• Attenuated Total Internal Reflectance IR (ATIR / ATR-IR):
  • Utilizes a sample stage made of diamond.
  • Infrared light reflects off the diamond stage interface, bypassing the need for traditional IR-transparent window plates. Samples are placed directly onto the ATIR stage (such as the instrument manufactured by Thermo Fisher Scientific used at North Central College).

Analysis and Regions of an IR Spectrum

• Spectrum Axes:
  • X-axis: Wave number ($\tilde{\nu}$), spanning from $400\,\text{cm}^{-1}$ to $4000\,\text{cm}^{-1}$.
  • Y-axis: Percent Transmittance ($\%\,\text{Transmittance}$), representing the proportion of infrared light that passes through the sample to the detector. Strong absorption peaks appear as downward dips on the spectrum.
• Fingerprint Region ($400\,\text{cm}^{-1}$ to $1500\,\text{cm}^{-1}$):
  • Contains a complex series of overlapping bending and stretching absorbances unique to each specific compound.
  • Difficult to assign individual peaks; evaluated by directly comparing the spectrum to an authentic standard spectrum of a known molecule.
• Diagnostic Region ($1500\,\text{cm}^{-1}$ to $4000\,\text{cm}^{-1}$):
  • Contains distinct, strong absorption bands that correlate directly with specific chemical functional groups.
  • Example: The IR spectrum of 2-butanol exhibits a distinct, broad $\text{O-H}$ stretching peak alongside aliphatic $\text{C-H}$ bond stretching resonances in this region.

Structural Diagnostic Bands in IR Spectroscopy

• Carbonyl and Multiply Bonded Species ($1600\,\text{cm}^{-1}$ to $2200\,\text{cm}^{-1}$):
  • Carbonyl groups ($\text{C=O}$) in acyl halides, esters, carboxylic acids, ketones, and amides exhibit strong absorption bands in the range of $1650\,\text{cm}^{-1}$ to $1850\,\text{cm}^{-1}$.
  • Carbon-carbon double bonds ($\text{C=C}$) absorb in the range of $1600\,\text{cm}^{-1}$ to $1700\,\text{cm}^{-1}$.
  • Carbon-nitrogen triple bonds ($\text{C}\equiv\text{N}$) absorb around $2200\,\text{cm}^{-1}$.
• Conjugation Effect on Carbonyl Absorption:
  • Conjugation (presence of an unsaturated double bond situated one carbon away from the carbonyl) lowers the carbonyl stretching energy/frequency.
  • Resonance contributions from single-bonded carbon-oxygen forms ($\text{C}^{+}\text{-O}^{-}$) weaken the overall carbon-oxygen bond force constant, shifting absorption to lower wave numbers.
• Carbon-Hydrogen ($\text{C-H}$) Stretch Identification ($3000\,\text{cm}^{-1}$ Baseline):
  • $sp^3$ Hybridized $\text{C-H}$ Stretch: Observed directly to the right of $3000\,\text{cm}^{-1}$ (below $3000\,\text{cm}^{-1}$).
  • $sp^2$ Hybridized $\text{C-H}$ Stretch: Observed directly to the left of $3000\,\text{cm}^{-1}$ (above $3000\,\text{cm}^{-1}$). The higher energy is due to the $sp^2$ orbital holding electron density closer to the carbon nucleus, forming a stronger bond than an $sp^3$ orbital.
  • $sp$ Hybridized $\text{C-H}$ Stretch: Observed further to the left, around $3250\,\text{cm}^{-1}$, reflecting an even stronger bond due to the greater s-character of $sp$ orbitals.
• Hydroxyl ($\text{O-H}$) Stretches:
  • Unassociated / Free $\text{O-H}$ Stretch: Appears as a sharp peak at higher wave numbers/energy when hydrogen bonding is absent.
  • Hydrogen-Bonded $\text{O-H}$ Stretch: Hydrogen bonding weakens the individual $\text{O-H}$ bond strength, shifting the absorption to lower energy and producing a very broad peak due to varying extents of hydrogen bonding throughout the sample.
• Carboxylic Acid Functional Group Features:
  • Exhibits a carbonyl ($\text{C=O}$) stretch around $1700\,\text{cm}^{-1}$.
  • Exhibits an extremely broad $\text{O-H}$ stretch that spans nearly one-third of the total spectrum (or approximately half of the diagnostic region). Extensive hydrogen bonding dimerization (as seen in 2-methylbutanoic acid) weakens and attenuates the $\text{O-H}$ bond strength over a wide energy range.
• Amine ($\text{N-H}$) Stretches ($3400\,\text{cm}^{-1}$):
  • Absorb near $3400\,\text{cm}^{-1}$ due to low reduced mass and strong bond character.
  • Primary Amines ($\text{R-NH}_2$): Display a doublet (two distinct peaks) in the $3400\,\text{cm}^{-1}$ region.
  • Secondary Amines ($\text{R}_2\text{NH}$): Display a singlet (one peak) in the $3400\,\text{cm}^{-1}$ region.
  • Mechanism of Primary Amine Peak Splitting: The doublet in primary amines is not caused by having two separate protons, but by two distinct vibrational stretching modes:
    • Symmetric Stretch: Both $\text{N-H}$ bonds extend and contract simultaneously.
    • Asymmetric Stretch: One $\text{N-H}$ bond shortens while the other extends, producing a different energy absorption mode.