Molecular Spectroscopy and Analytical Techniques

Molecular Spectroscopy

The branch of science dealing with the interaction of matter (atoms or molecules) with electromagnetic radiation, involving the production, measurement, and interpretation of absorption or emission spectra.

Absorption Spectrum

A spectrum consisting of dark lines formed when an atom or molecule transitions from a lower energy level to a higher energy level by absorbing a photon of energy $h\nu$ equal to the energy difference.

Emission Spectrum

A spectrum consisting of bright lines obtained when an atom or molecule transitions from a higher energy level to a lower energy level with the emission of a photon of energy $h\nu$, requiring the higher energy state to be more populated.

Atomic Spectra

Spectra obtained due to the interaction of isolated atoms with electromagnetic radiation, characterized by sharp individual lines (line spectra) originating from electronic transitions.

Molecular Spectra

Spectra obtained from the interaction of molecules with electromagnetic radiation, consisting of bands (band spectra) where each band contains closely spaced lines from associated vibrational and rotational transitions.

Electronic Energy Levels

Quantized molecular energy states where electrons occupy bonding, non-bonding, or antibonding molecular orbitals; transitions between these levels fall in the UV-Visible region ($200\text{ to }800\,nm$).

Vibrational Energy Levels

Quantized energy levels associated with the to-and-fro motion of nuclei in a molecule about their equilibrium positions while the center of mass remains constant; transitions between them fall in the infrared (IR) region.

Rotational Energy Levels

Quantized energy levels arising from the rotation of a molecule about an axis perpendicular to its internuclear axis passing through the center of mass; transitions between them fall in the microwave region.

Translational Energy Levels

Energy levels of a molecule whose center of mass changes with time; these levels are negligibly small and only quantized when the molecule is enclosed in a box of nano-dimensions.

Beer-Lambert's Law

The law stating that the rate of decrease in radiation intensity with path length ($-\frac{dI}{dx}$) through an absorbing solution is directly proportional to the incident intensity ($I$) and the solute concentration ($C$).

Molar Absorption Coefficient

A constant ($\epsilon$) dependent on the nature of the absorbing molecule and absorption wavelength, given by $\epsilon = \frac{A}{Cx}$ with units of $mol^{-1}\,dm^2$.

Absorbance

The logarithm of the ratio of incident light intensity ($I_0$) to transmitted light intensity ($I$), defined as $A = \log\left(\frac{I_0}{I}\right) = -\log(T) = \epsilon C x$.

Transmittance

The ratio of transmitted light intensity ($I$) to incident light intensity ($I_0$), represented as $T = \frac{I}{I_0} = e^{-\epsilon C x}$, which decreases exponentially with increasing concentration.

UV-Visible Spectroscopy

An electronic spectroscopy method based on promoting valence electrons from ground state to higher energy molecular orbitals via absorption of ultraviolet ($200\text{ to }400\,nm$) or visible ($400\text{ to }800\,nm$) radiation.

Electronic Transitions

Promotions of electrons between bonding ($\sigma$, $\pi$), non-bonding ($n$), and antibonding ($\sigma^*$, $\pi^*$) orbitals upon the absorption of UV or visible light.

$\sigma \rightarrow \sigma^*$ Transition

A high-energy electronic transition in saturated hydrocarbons (e.g., methane, ethane) exciting a bonding $\sigma$ electron to an antibonding $\sigma^*$ orbital at wavelengths shorter than $150\,nm$.

$\pi \rightarrow \pi^*$ Transition

An electronic transition observed in unsaturated systems (alkenes, alkynes) from HOMO to LUMO, shifting by approximately $30\,nm$ to longer wavelengths with each additional conjugated double bond.

$n \rightarrow \pi^*$ Transition

A low-intensity, symmetry-forbidden electronic transition occurring in molecules containing both heteroatoms with non-bonding lone pairs and $\pi$ bonds, such as aldehydes and ketones.

$n \rightarrow \sigma^*$ Transition

A low-intensity electronic transition observed in saturated compounds with non-bonding lone pairs on heteroatoms ($S$, $N$, $O$), such as alcohols and haloalkanes, requiring less energy than $$\sigma \rightarrow \sigma^*$.

Double-Beam Spectrophotometer

An optical instrument where monochromatic light selected by a slit is divided into two beams passing simultaneously through sample and reference cells before reaching photocell detectors.

Infrared Spectroscopy

A vibrational spectroscopy technique studying the absorption of IR radiation ($500\,nm\text{ to }4000\,cm^{-1}$) to identify functional groups and establish the structural fingerprint of a molecule.

Infrared Active Molecules

Molecules that experience a net change in dipole moment during vibrational motion, permitting the absorption of IR radiation (e.g., $H_2O$, $SO_2$, $NH_3$, $HCN$, $HBr$, $HCl$, $HF$, $CO$).

Infrared Inactive Molecules

Molecules that undergo no change in dipole moment during vibration and consequently do not absorb IR radiation (e.g., $Br_2$, $Cl_2$, $N_2$, $H_2$, $O_2$, $F_2$).

Fundamental Vibrational Frequency

The characteristic oscillation frequency ($\nu_0$) of a diatomic molecule treated as a simple harmonic oscillator, calculated by $\nu_0 = \frac{1}{2\pi}\sqrt{\frac{k}{\mu}}$.

Reduced Mass

The effective inertial mass ($\mu$) of a two-particle vibrating system, defined as $\mu = \frac{m_1 m_2}{m_1 + m_2}$.

Force Constant

A parameter ($k$) measuring the bond strength between two bonded atoms, derived from vibrational frequency as $k = 4\pi^2 c^2 \mu \bar{\nu}^2$, where $k$ increases from single to triple bonds ($C-C < C=C < C\equiv C$).

Vibrational Degrees of Freedom (Non-linear Molecule)

The number of fundamental vibrational modes in a non-linear molecule of $n$ atoms, equal to $3n - 6$ because 3 degrees correspond to translation and 3 to rotation.

Vibrational Degrees of Freedom (Linear Molecule)

The number of fundamental vibrational modes in a linear molecule of $n$ atoms, equal to $3n - 5$ because 3 degrees correspond to translation and 2 to rotation.

Vibrational Modes of Carbon Dioxide

The four fundamental vibrational modes ($3\times 3 - 5 = 4$) of linear $CO_2$: one symmetric stretching mode (IR inactive) and three IR active modes (one asymmetric stretch and two bending vibrations).

Vibrational Modes of Water

The three fundamental modes of non-linear $H_2O$ ($3\times 3 - 6 = 3$)—antisymmetric stretch, symmetric stretch, and scissoring bend—all of which cause a net dipole moment change and are IR active.

Intramolecular Hydrogen Bonding

Hydrogen bonding occurring internally within a single molecule (e.g., o-hydroxy phenol) whose characteristic $-OH$ stretching absorption frequency does not shift upon dilution.

Intermolecular Hydrogen Bonding

Hydrogen bonding formed between adjacent molecules (e.g., p-hydroxy phenol) that weakens and dissociates upon dilution, causing a detectable shift in the $-OH$ absorption frequency.

Dielectric Thermal Analysis

A thermal analysis technique (DETA) measuring changes in dielectric properties (conductance $G$ and capacitance $C$) of a material placed under an alternating electric field across varying temperatures.

Dielectric Loss Tangent

The dissipation factor ($$\tan(\delta) = \frac{\epsilon_{11}}{\epsilon_