 g and u
 gFactor
 γ
 Galvani Potential Difference
 Gas Constant
 Gas Laws
 Gaussian Function
 Gibbs–Duhem Equation
 Gibbs Energy
 Gibbs Energy of Formation
 Gibbs Energy of Reaction
 Gibbs–Helmholtz Equation
 Gibbs Surface Tension Equation
 Glory Scattering
 Grotrian Diagram
 Grotthuss Mechanism
 Ground State
 Group Theory
G

Published:17 May 2024
Concepts in Physical Chemistry, Royal Society of Chemistry, 2nd edn, 2024, pp. 129139.
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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 G; where appropriate, the entries also describe subsidiary but related concepts. Refer to the Directory for a full list of all the concepts treated.
g and u
The labels g (gerade, even) and u (ungerade, odd) denote the parity of a molecular orbital, its behaviour under inversion (Figure G.1). If the orbital does not change sign under inversion, it is denoted g; if it does change sign, it is denoted u. The classification is applicable only if the molecule has a centre of inversion (for example, a homonuclear diatomic molecule but not a heteronuclear diatomic molecule). The overall parity of a manyelectron molecule is obtained by multiplying the parities of the wavefunctions of all the electrons and using the rules g × g = g, g × u = u, and u × u = g. The parity classification is used in the specification of certain selection rules.
gFactor
γ
.  Atoms .  Linear molecules .  Nonlinear molecules . 

γ  5/3  7/5  4/3 
.  Atoms .  Linear molecules .  Nonlinear molecules . 

γ  5/3  7/5  4/3 
For other uses of the symbol γ see the discussion of the magnetogyric ratio in the entry on gfactor and the discussions of activities and surface tension.
Galvani Potential Difference
The Galvani potential difference, Δϕ, is the difference in electric potential between points in the metal electrode and the bulk solution.
Gas Constant
The (molar) gas constant, R, is defined as R = N_{A}k, where k is Boltzmann’s constant and N_{A} is Avogadro’s constant, both of which currently have defined, exact values which imply that R ≈ 8.314 462 618 J K^{−1} mol^{−1}. Its name arises from its original appearance in the perfect gas equation of state, pV = nRT. However, it appears in expressions unrelated to gases by virtue of its relation to the more fundamental Boltzmann’s constant.
Gas Laws
Avogadro’s contribution is called a principle rather than a law because it is based on the molecular model rather than being a direct summary of experience.
Gaussian Function
A Gaussian function is a bellshaped function of the form e^{−ax 2 } as illustrated in Figure G.2. Gaussian functions are encountered as components of the wavefunctions of the harmonic oscillator, as the shapes of certain spectral lines, and in expressions related to diffusion.
Gibbs–Duhem Equation
Gibbs Energy
Gibbs Energy of Formation
The Gibbs energy of formation of J, Δ_{f}G(J). is the Gibbs energy of reaction for the formation of J from its elements in their reference states expressed as a quantity per mole of J. The reference state of an element is its thermodynamically most stable form at the specified temperature. (The exception to this general rule is phosphorus, for which the reference state is white phosphorus.) The standard Gibbs energy of formation, Δ_{f}G ^{⦵}(J), adds to this definition that all components of the formation reaction are in their standard state (pure, 1 bar) at the specified temperature. To apportion values between cations and anions in solution, the standard Gibbs energy of formation of hydrogen ions in aqueous solution is defined as zero for all temperatures: Δ_{f}G ^{⦵}(H^{+}, aq)=0. Compounds for which Δ_{f}G ^{⦵}(J) > 0 are classified as endergonic and are unstable with respect to their elements (Figure G.4). Compounds for which Δ_{f}G ^{⦵}(J) < 0 are classified as exergonic and are stable with respect to their elements. The principal application of standard Gibbs energies of formation is to the calculation of the standard Gibbs energy of reaction by taking the difference between the stoichiometrically weighted values for the products and reactants (see that entry).
Gibbs Energy of Reaction
Gibbs–Helmholtz Equation
Gibbs Surface Tension Equation
Glory Scattering
Glory scattering is the enhanced intensity of scattering in the forward direction; it arises when two paths interfere constructively (Figure G.6). One path is at large impact parameter and is undeflected by the target molecule. The other path is at low impact parameter and is deflected as it enters regions of attractive and repulsive regions of force but then continues in the forward direction.
Grotrian Diagram
A Grotrian diagram displays the energy of the states of an atom (or molecule) as a ladder of horizontal lines and depicts the observed transitions by lines connected the terms responsible for them. In some cases, the relative intensities of the transitions are depicted by the width of the lines.
Grotthuss Mechanism
In the Grotthuss mechanism of proton conduction in water, the migration of a hydrogen ion occurs by the coordinated adjustment of the locations of protons in a chain of neighbouring molecules rather than the actual motion of an identifiable proton through the liquid (Figure G.7). Its rate is determined by the ability of protons to tunnel through potential barriers and for the molecules to rotate in the chain.
Ground State
The ground state of an atom or molecule is its state of lowest energy. It is a characteristic of quantum mechanics that the wavefunction of the ground state of a system has no nodes.
Group Theory
Group theory is the mathematical theory of symmetry. The h members of a set of elements g_{i} form a group of order h if they satisfy the following conditions:

The set includes the identity E, an element for which gE = Eg = g for all elements of the set.

The set includes the inverse g ^{−1} for each member of the set, where gg ^{−1} = g ^{−1}g = E.

The rule of combination is associative; that is, g_{i}(g_{j}g_{k}) = (g_{i}g_{j})g_{k}.

All the elements of a set conform to the group property, that g_{i}g_{j} = g_{k}, a member of the set.
The link between this mathematical structure and symmetry is that the symmetry operations of an object fulfil the conditions for them to form a group. A point group consists of all symmetry operations that leave a single point unchanged; a space group extends that concept to include translational symmetry.
The theory is rendered quantitative in terms of numbers by representing the effect of symmetry operations by a set of matrices that obey the same multiplication properties as the symmetry operations. Each matrix is a representative of the corresponding symmetry operation and the entire set of matrices for a given basis is a matrix representation of the group. The representation is irreducible if a transformation of the basis cannot be found that simultaneously reduces all the matrices to block diagonal form. A matrix representation is characterized by the character of each representative, the sum of its diagonal elements. These characters are collected in character tables.
Group theory, particularly the information in character tables, is used to classify molecules according to the point group to which they belong, to establish selection rules, to classify orbitals, and to construct molecular orbitals from the appropriate symmetryadapted combinations of atomic orbitals.