M.Sc. Chemistry - Physical Chemistry III 2-Mark Questions & Answers

Vocabulary revision flashcards based on the 29 2-mark questions and answers for M.Sc. Physical Chemistry III, covering Group Theory, Quantum Chemistry, Approximation Methods, Molecular Spectroscopy, and Magnetic Resonance Spectroscopy.

Symmetry element

A geometrical entity (a point, line or plane) about which a symmetry operation is performed so that the molecule is brought into an indistinguishable configuration.

Point group

The complete set of symmetry operations of a molecule that leave at least one point unchanged. Molecules are classified into point groups according to their symmetry.

Reducible representation

A representation of a group that can be expressed as a direct sum of two or more irreducible representations.

Irreducible representation

A representation of a group that cannot be further decomposed into simpler representations of that group.

Character table

A tabular arrangement of the irreducible representations of a point group that lists the characters for the symmetry-operation classes and commonly shows the symmetry behaviour of coordinates and molecular functions.

Subgroup

A subset of the elements of a group that itself forms a group under the same operation, containing the identity element and being closed under the group operation and inverses.

Wave function

A mathematical function ($\psi$) that describes the quantum state of a particle or system. The modulus squared gives the probability density of finding the particle at a given position ($|\psi|^2 = \text{probability density}$), and for a normalized wave function, the total probability over all space is $1$.

Eigenvalue

The constant ($a$) obtained when an operator ($\hat{A}$) acts on one of its eigenfunctions ($\psi$) and reproduces the same function multiplied by that constant ($\hat{A}\psi = a\psi$).

Degeneracy

The condition in which two or more different quantum states have the same energy. The number of states with the same energy is called the degree of degeneracy.

Zero-point energy

The lowest energy that a quantum mechanical system can possess, even at absolute zero temperature. For a harmonic oscillator, it is given by $E_0 = \frac{1}{2}h\nu$, where $h$ is Planck's constant and $\nu$ is the oscillator frequency.

Angular momentum

The physical quantity associated with rotational motion. In quantum mechanics, the magnitude of orbital angular momentum is quantized as $L = \sqrt{l(l + 1)}\,\hbar$, where $l$ is the orbital angular momentum quantum number and $\hbar = \frac{h}{2\pi}$.

Zeeman effect

The splitting of an atomic or molecular spectral line into two or more components when the emitting or absorbing species is placed in an external magnetic field.

Variation principle

An approximation principle stating that the energy expectation value calculated using any acceptable, normalized trial wave function is greater than or equal to the true ground-state energy ($E_{\text{trial}} \ge E_0$).

Perturbation theory

An approximate method used to calculate the energies and wave functions of a system when a small additional interaction or disturbance is applied to a system whose solution is already known.

Slater determinant

A determinant form used to construct the wave function of a many-electron system. It ensures that the electronic wave function is antisymmetric when any two electrons are exchanged, as required by the Pauli principle.

Effective nuclear charge

The net positive charge experienced by an electron in a multi-electron atom after the shielding effect of other electrons is taken into account, defined by $Z_{\text{eff}} = Z - S$, where $Z$ is the atomic number and $S$ is the shielding constant.

Self-consistent field (SCF) method

An iterative method in which approximate electron wave functions are used to calculate an average field, and the wave functions are recalculated until the input and output fields agree within a chosen tolerance.

Raman effect

The inelastic scattering of monochromatic light by molecules, in which the scattered light has a frequency different from that of the incident light because energy is exchanged with molecular rotational or vibrational motion.

Fermi resonance

The interaction between two vibrational states that have nearly the same energy and the same symmetry, causing a shift in their frequencies and a change in band intensities.

Fluorescence

The emission of light when an excited molecule returns from an excited singlet state to a lower singlet state, commonly the ground state, usually occurring rapidly after excitation.

Phosphorescence

The emission of light when a molecule returns from an excited triplet state to a singlet ground state. Because the transition is spin-forbidden, it is generally slower than fluorescence.

Franck–Condon principle

The principle stating that an electronic transition occurs so rapidly compared with nuclear motion that the internuclear positions remain practically unchanged during the transition, represented as vertical transitions on an energy diagram.

Mutual exclusion principle

The principle stating that, for a molecule with a centre of symmetry, a normal vibration that is IR-active is Raman-inactive, and a Raman-active vibration is IR-inactive.

g-value

A dimensionless quantity (spectroscopic splitting factor) that describes the magnetic response of an electron in an external magnetic field. For a simple ESR resonance: $g = \frac{h\nu}{\mu_B B}$, where $h$ is Planck's constant, $\nu$ is the microwave frequency, $\mu_B$ is the Bohr magneton, and $B$ is the magnetic field at resonance.

Hyperfine splitting

The splitting of an ESR signal into multiple lines due to interaction between the magnetic moment of an unpaired electron and the magnetic moment of nearby magnetic nuclei.

Chemical shift

The difference in resonance frequency of a nucleus relative to a reference compound, usually tetramethylsilane (TMS), in NMR spectroscopy. Expressed in parts per million ($\text{ppm}$) as $\delta = \left[\frac{\nu_{\text{sample}} - \nu_{\text{reference}}}{\nu_{\text{spectrometer}}}\right] \times 10^6$.

Spin density

The local distribution of unpaired electron spin in an atom or molecule, indicating where the unpaired electron spin is concentrated.

Nuclear electric quadrupole moment

A measure of the deviation of a nucleus's charge distribution from spherical symmetry. A non-zero electric quadrupole moment is possible for nuclei with spin quantum number $I \ge 1$.

Kramers degeneracy

The theorem stating that, in the absence of a magnetic field and when time-reversal symmetry is preserved, a system with half-integer total angular momentum has at least two states of equal energy (commonly applying to systems with an odd number of electrons).