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doi:10.1039/BK9781837674244-00265

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Concepts in Physical Chemistry

DOI:

https://doi.org/10.1039/9781837674244

Hardback ISBN:

978-1-83767-386-5

PDF ISBN:

978-1-83767-424-4

EPUB ISBN:

978-1-83767-425-1

No. of Pages:

394

Publication date:

17 May 2024

Physical chemistry is the part of chemistry that seeks to account for the properties and transformations of matter in terms of concepts, principles, and laws drawn from physics. This glossary is a compilation of definitions, descriptions, formulae, and illustrations of concepts that are encountered throughout the subject. This section describes the concepts that begin with the letter Q; where appropriate, the entries also describe subsidiary but related concepts. Refer to the Directory for a full list of all the concepts treated.

Quadrupole

An electric quadrupole is an array of four charges with no net charge or electric dipole moment; see multipole. A quadrupole moment, with components Q_ij, is defined as

Q_{i j} = \frac{1}{2} \int (3 r_{i} r_{j} - δ_{i j} r^{2}) ρ (r) d τ

where ρ( r ) is the electron density. (Be aware that some sources use a slightly different definition.) A nucleus with I > 1/2 has a nuclear quadrupole moment due to a nonspherical distribution of charge over its surface. Electric quadrupole moments interact with the electric field gradient,

\nabla E

⁠, not the electric field itself.

Quantization

The quantization of a property, primarily energy and angular momentum, is its confinement to a discrete but possibly infinite set of values. Quantization is a consequence of the application of boundary conditions to solutions of the Schrödinger equation and criteria related to the acceptability of wavefunctions. The term space quantization is sometimes applied to the quantization of the component of angular momentum on an arbitrary axis, because in the vector model the vector representing the angular momentum is depicted as adopting only certain discrete orientations with respect to that axis.

Quantum Mechanics

The description of the properties of matter and radiation known as quantum mechanics is based on the following postulates:

The dynamical state of a system is fully described by a wavefunction, ψ( r ,t).
Observables, Ω, are represented by linear Hermitian operators, $\hat{Ω}$ ⁠, chosen to satisfy certain commutation relations.
When a system is described by a wavefunction ψ( r ,t), the mean value of the observable Ω is the expectation value of $\hat{Ω}$ ⁠.
If the wavefunction is an eigenfunction of $\hat{Ω}$ with eigenvalue ω, then the result of a measurement of Ω will be ω. If the wavefunction is not an eigenfunction of $\hat{Ω}$ ⁠, then any measurement will give one of its eigenvalues and the probability that the eigenvalue ω_i will be obtained is proportional to the square modulus of the linear combination coefficient c_i in the expansion $ψ = \sum_{i} c_{i} ψ_{i}$ ⁠.

In typical applications of quantum mechanics, the Schrödinger equation is set up for the system of interest and then solved either analytically or numerically, subject to the boundary conditions for the system of interest. Some dynamical properties can be inferred from the operators alone (angular momentum especially).

Quantum Number

A quantum number is a number used to label the state of a system and in many cases to assess the value of a dynamical variable. Quantum numbers are either integers or, for properties relating to the intrinsic angular momenta (spin) half-integers. In at least one case, a particle confined to an equilateral triangular surface, the quantum numbers are one-third integers. Some typical quantum numbers, their values, and their significance are listed in Table Q.1.

Table Q.1

Common quantum numbers. ^a

Quantum number	Name	Comment
F	Total angular momentum quantum number	Includes nuclear spin; nonnegative values only; significance as for j.
I	Nuclear spin quantum number	Significance as for j; nonnegative values only; integer or half-integer.
j, J	Total angular momentum quantum number (excluding nuclear spin for molecules) and angular momentum quantum number in general	Nonnegative values only.
		Magnitude of angular momentum is {j(j + 1)}^1/2ħ.
		Number of projections is 2j + 1; see m.
		Permitted values given by the Clebsch–Gordan series.
J	Rotational quantum number	Nonnegative values only. Significance as for j. May have 2J + 1 projections on external axis and (except for linear molecules), 2J + 1 projections on an internal axis.
K	Angular momentum projection quantum number	Angular momentum about internal axis of a molecule; takes the values K = 0, ±1,…, ±J for nonlinear molecules; K = 0 for linear molecules.
l, L	Orbital angular momentum quantum number; l formerly called the azimuthal quantum number.	Nonnegative values only; significance as for j.
m, M	Magnetic quantum number	Designated m_X, M_X for angular momentum source X, with X = l, s, j, J, etc. Specifies component of angular momentum on z-axis as m_Xħ with m_X = X, X – 1,…, −X.
n	Generic quantum number; principal quantum number	Used generically. For a particle in a box and for hydrogenic atoms n = 1, 2,….
s, S	Spin quantum number	Nonnegative values only; significance as for j.
$v$	Vibrational quantum number	Specifies state and energy of harmonic oscillator as $(v + \frac{1}{2}) ℏ ω$ ⁠, $v = 0, 1, 2, \dots$
α, β	Spin states of spin-1/2 particle	α denotes m_s = +1/2, β denotes m_s = −1/2.
Λ	Orbital angular momentum projection quantum number on figure axis	For a linear molecule.
Σ	Spin angular momentum projection quantum number on figure axis	For a linear molecule.
Ω	Total electronic angular momentum projection quantum number on figure axis	For a linear molecule.

Quantum number	Name	Comment
F	Total angular momentum quantum number	Includes nuclear spin; nonnegative values only; significance as for j.
I	Nuclear spin quantum number	Significance as for j; nonnegative values only; integer or half-integer.
j, J	Total angular momentum quantum number (excluding nuclear spin for molecules) and angular momentum quantum number in general	Nonnegative values only.
		Magnitude of angular momentum is {j(j + 1)}^1/2ħ.
		Number of projections is 2j + 1; see m.
		Permitted values given by the Clebsch–Gordan series.
J	Rotational quantum number	Nonnegative values only. Significance as for j. May have 2J + 1 projections on external axis and (except for linear molecules), 2J + 1 projections on an internal axis.
K	Angular momentum projection quantum number	Angular momentum about internal axis of a molecule; takes the values K = 0, ±1,…, ±J for nonlinear molecules; K = 0 for linear molecules.
l, L	Orbital angular momentum quantum number; l formerly called the azimuthal quantum number.	Nonnegative values only; significance as for j.
m, M	Magnetic quantum number	Designated m_X, M_X for angular momentum source X, with X = l, s, j, J, etc. Specifies component of angular momentum on z-axis as m_Xħ with m_X = X, X – 1,…, −X.
n	Generic quantum number; principal quantum number	Used generically. For a particle in a box and for hydrogenic atoms n = 1, 2,….
s, S	Spin quantum number	Nonnegative values only; significance as for j.
$v$	Vibrational quantum number	Specifies state and energy of harmonic oscillator as $(v + \frac{1}{2}) ℏ ω$ ⁠, $v = 0, 1, 2, \dots$
α, β	Spin states of spin-1/2 particle	α denotes m_s = +1/2, β denotes m_s = −1/2.
Λ	Orbital angular momentum projection quantum number on figure axis	For a linear molecule.
Σ	Spin angular momentum projection quantum number on figure axis	For a linear molecule.
Ω	Total electronic angular momentum projection quantum number on figure axis	For a linear molecule.

Uppercase letters are used for many-electron systems.

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Quantum Yield

In photochemistry, the primary quantum yield, ϕ, is the number of specified primary products for each photon absorbed. The overall quantum yield, Φ, is the number of reactant molecules that generated for each proton absorbed.

Quenching

A chemical reaction is quenched if the conditions are suddenly changed and it ceases to generate products. Quenching may be achieved by lowering the temperature, diluting the system, or adding a new reagent.

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