Physical Chemistry: Spectroscopy and Intermolecular Forces

Vocabulary practice flashcards covering rotational, vibrational, and electronic spectroscopy, selection rules, quantum mechanical models (rigid rotor, harmonic and anharmonic oscillators), and non-covalent intermolecular forces.

Spectroscopy

The use of electromagnetic radiation to study the energy levels, transitions, and microscopic structures of atomic and molecular systems.

Rotational Spectroscopy

A spectroscopic method utilizing microwave radiation ($\lambda: 10^{-1} - 10^1\,\text{cm}$, $\nu: 10^9 - 10^{12}\,\text{Hz}$) to probe transitions between quantized rotational energy states ($\Delta E_{\text{rot}}$).

Vibrational Spectroscopy

A spectroscopic method employing infrared radiation ($\lambda: 10^{-2} - 10^{-4}\,\text{cm}$, $\nu: 10^{12} - 10^{14}\,\text{Hz}$) to probe transitions between quantized molecular vibrational states ($\Delta E_{\text{vib}}$).

Electronic Spectroscopy

A spectroscopic method using visible, ultraviolet ($\lambda: 100 - 1000\,\text{nm}$, $\nu: 10^{15} - 10^{17}\,\text{Hz}$), or X-ray radiation to probe transitions of electrons between different electronic energy levels.

Extinction Coefficient ($\varepsilon$)

A wavelength-dependent parameter measured in $\text{M}^{-1}\,\text{cm}^{-1}$ that quantifies how strongly a chemical species absorbs light in the Beer-Lambert law: $A = \varepsilon c l$.

Transition Dipole Moment ($\mu_{ij}$)

A quantum mechanical integral that measures the change in the electric dipole moment associated with the shift of charge during a transition between states $\psi_i$ and $\psi_j$; if $\mu_{ij} = 0$, no spectroscopic absorption occurs.

Gross Selection Rule

A general rule that specifies the overall structural or physical features a molecule must possess (such as having a permanent dipole moment or experiencing a change in dipole during vibration) to exhibit a specific type of spectrum.

Specific Selection Rule

A selection rule that defines which specific changes in quantum numbers (such as $\Delta J = \pm 1$ or $\Delta n = \pm 1$) are allowed during a transition between states.

Allowed Transition

A quantum transition that is permitted by both the gross selection rule and the specific selection rule.

Forbidden Transition

A transition that violates either a gross selection rule or a specific selection rule, yielding a transition dipole moment of zero and weak or unobserved absorption under ideal conditions.

Rigid Rotor

A quantum mechanical model describing a rotating diatomic molecule with a fixed bond length, whose energy levels are given by $E_J = B h J(J + 1)$ where $J = 0, 1, 2, \dots$ and $I = \mu r^2$.

Reduced Mass ($\mu$)

An effective mass representation used in two-body problems defined by the relation $\mu = \frac{m_1 m_2}{m_1 + m_2}$.

Normal Mode

An independent, collective vibrational motion in a polyatomic molecule where all atoms move in phase and with the same frequency; non-linear molecules exhibit $3N - 6$ normal modes and linear molecules exhibit $3N - 5$ normal modes.

Zero-Point Energy

The lowest possible vibrational energy state of a molecule, which cannot be zero due to quantum uncertainty; for a harmonic oscillator, it equals $E_0 = \frac{1}{2} \hbar \omega = \frac{1}{2} h c \tilde{\nu}$.

Anharmonic Oscillator

A realistic model of molecular vibration where the potential energy curve deviates from a parabola as bonds stretch toward dissociation, causing energy levels to converge and relaxing selection rules to allow $\Delta n > 1$.

Spin Selection Rule

A selection rule stating that electric dipole transitions cannot alter electron spin ($\Delta S = 0$, $\Delta m_s = 0$), meaning transitions between states of different spin multiplicity are formally forbidden.

Fluorescence

A radiative de-excitation process occurring between states of the same spin multiplicity, typically from an excited singlet state to the ground singlet state ($S_1 \rightarrow S_0$).

Phosphorescence

A radiative de-excitation process involving an intersystem spin conversion (such as an excited triplet state emitting to a ground singlet state, $T_1 \rightarrow S_0$), resulting in a long-lived emission lifetime.

Lattice Energy

The total potential energy stabilizing an ionic solid, calculated as the sum of all long-range coulombic attractions and repulsions throughout the crystal array and scaled by the Madelung constant ($A$).

Madelung Constant ($A$)

A dimensionless geometric factor in the lattice energy formula of an ionic solid that accounts for the specific three-dimensional spatial arrangement of ions (e.g., $A = 1.748$ for $\text{NaCl}$).

Polarizability ($\alpha$)

A measure of the ease with which an atom or molecule's electron cloud is distorted by an external electric field or nearby charge, possessing dimensions of volume ($\text{length}^3$).

London Dispersion Interactions

Attractive intermolecular forces arising from instantaneous fluctuations in electron density that induce temporary dipoles in adjacent molecules, displaying a $-\frac{1}{r^6}$ distance dependence.

Lennard-Jones 6-12 Potential

An empirical intermolecular potential model defined as $V(r) = 4\varepsilon [(\frac{\sigma}{r})^{12} - (\frac{\sigma}{r})^6]$, where $\varepsilon$ is the potential well depth, $\sigma$ is the finite distance where the potential equals zero, and $r_e = 2^{1/6}\sigma$ is the equilibrium separation.

Hydrogen Bond

A strong, directional non-covalent dipole-dipole interaction occurring between an electronegative atom ($\text{N, O, F}$) and a hydrogen atom that is covalently bonded to another electronegative atom, typically with bond energies of $8 - 30\,\text{kJ/mol}$.