LEARNING OUTCOMES - Explain the fundamentals of IR (Infrared Spectroscopy). - Understand IR and molecular vibrations. - Discuss Hooke’s Law and degrees of freedom. - Review selection rules for infrared absorption regarding stretching and bending vibrations. - Interpret IR spectra and identify functional groups present in molecular structures. ### General Aspects of Spectroscopy - Many materials have the capacity to absorb electromagnetic radiation. - A spectrum represents a plot of a function representing attenuation of radiation versus wavelength, frequency, or wavenumber. - Electromagnetic radiation may be treated as either waves or particles (known as wave/particle duality). #### Key Units - Frequency, $\nu$ ($\mathrm{s^{-1}}$ or Hz) - Wavelength, $\lambda$ (meters or derived units) - Wavenumber, $\overline{\nu}$ ($\mathrm{cm^{-1}}$) - Speed of light, $c = 2.99792 \times 10^{8} \mathrm{ms^{-1}}$ #### Fundamental Relationship - $\nu = \frac{c}{\lambda}$ - $\overline{\nu} = \frac{1}{\lambda} = \frac{\nu}{c}$ ### Graphical Representation of an IR Spectrum - X-axis: Represented as Wavenumber ($\overline{\nu}$) in units of $\mathrm{cm^{-1}}$, typically decreasing from $4000 \mathrm{cm^{-1}}$ on the left to $400 \mathrm{cm^{-1}}$ on the right. - Y-axis: Represented as Percent Transmittance ($\%T$). High transmittance (near $100\%$) indicates little to no absorption. - Absorption Peaks: In IR graphs, absorbance is visualized as downward-pointing peaks or 'valleys'. Each peak corresponds to a specific vibrational frequency of a molecular bond. ### Wave-Particle Duality of Light #### Classical Mechanics - Light is categorized as a waveform, where: - $c = \nu \lambda$ #### Quantum Mechanics - Light can also be conceptualized as a stream of particles termed photons (energy packets), calculated using: - $E = h \nu$ - $E$: energy - $h$: Planck’s constant ($6.626 \times 10^{-34} \mathrm{Js}$) ### Spectroscopy and Molecular Transition Types - Branches of Molecular Spectroscopy: - Ultraviolet and visible: Electronic transitions. - Infrared: Vibrational transitions. - Far infrared and microwave: Rotational and nuclear spin transitions. ### Infrared Spectroscopy (IR) #### Overview - Infrared spectroscopy utilizes electromagnetic radiation in the infrared range to ascertain molecular structure and perform quantitative analysis. - It pertains specifically to the vibrational motions of molecules. #### Selection Rules - A vibration is IR active only if it induces a change in the electric dipole moment. - Bonds with no dipole moment change during vibration (e.g., symmetrical diatomic molecules) are IR inactive. ### Types of Vibrational Motions 1. Stretching: Rhythmic displacement along the bond axis, altering interatomic distances. 2. Bending: Alterations in bond angles between two bonds sharing a common atom. ### Harmonic Oscillator Model #### Frequency Calculation - The vibrational frequency ($\nu$) is determined by: - $\nu = \frac{1}{2\pi} \sqrt{\frac{k}{\mu}}$ where: - $k$: force constant (bond stiffness) - $\mu$: reduced mass, where $\mu = \frac{m<em>1 m</em>2}{m<em>1 + m</em>2}$ ### Calculation of Stretching Frequency - Given: $k = 5 \times 10^{5} \mathrm{dyne/cm}$ for a C-H bond. - The wavenumber ($\overline{\nu}$) can be computed as: - $\overline{\nu} \mathrm{(C-H)} \approx 3023 \mathrm{cm^{-1}}$ ### Characteristic Group Wavenumbers | Functional Group | Wavenumber ($\mathrm{cm^{-1}}$) | Intensity | | :--- | :--- | :--- | | O-H (alcohol) | 3600-3200 | Strong (broad) | | N-H | 3500-3300 | Medium (broad) | | O-H (carboxylic) | 3300-2500 | Strong (broad) | | C-H | 3000-2850 | Medium | | C=O | 1820-1650 | Strong | | C=C | 1680-1620 | Medium | ### Analysing IR Spectra - High-Frequency End: Start at $4000 \mathrm{cm^{-1}}$ and identify functional groups (O-H, N-H, C-H) first. - Fingerprint Region: Below $1500 \mathrm{cm^{-1}}$, the spectrum is often crowded and unique to specific molecules; use it for identifying specific compounds by comparison. - Coherence Check: Ensure identified groups align with the known molecular formula.