The Latin phrase ab initio means (loosely) ‘from scratch’. It is applied to calculations of the electronic structures and properties of molecules starting from only the atomic numbers of the elements and the mass and charge of an electron. They are in contrast to semi-empirical methods, which import empirical information into the calculation as a substitute for calculating certain integrals.

In spectroscopy, absorption is the process by which electromagnetic radiation excites an atom or molecule into a state of higher energy. Absorption is most intense when the energy, hν, of a photon of the incident radiation matches the energy difference, ΔE, between the initial and final states. For electric dipole transitions, the intensity of absorption is proportional to the square of the transition dipole moment. The intensity is reported as the absorbance (at a specified frequency, wavelength, or wavenumber) or, when the absorption spans a range of frequencies, as the integrated absorption coefficient. When the upper state is already populated, the net intensity of absorption is the difference between the intensity of absorption from the ground state and the intensity of emission from the upper state.

Accommodation in surface science is the dissipation of energy that leads to the adsorption of a gas-phase molecule on to a substrate.

An Arrhenius acid is a compound that releases hydrogen ions in aqueous solution. A Brønsted acid, HA, is a proton donor (with ‘proton’, in this context, a hydrogen ion, H⁺). Loss of the proton results in the formation of the conjugate base of the acid, A⁻. Conversely, the acquisition of a proton by a base, B, result in the formation of its conjugate acid, HB⁺. A strong acid is effectively fully deprotonated in solution; a weak acid is only partially deprotonated at normal concentrations. In terms of acidity constants, K_a, a weak acid has K_a ≪ 1. A Lewis acid is an electron-pair acceptor. A hard acid is a Lewis acid that tends to bond strongly to a hard base; a soft acid is a Lewis acid that tends to bond strongly to a soft base. Hard acid–hard base combinations are largely ionic whereas soft acid–soft base combinations are largely covalent.

The acidity constant is a measure of the proton-donating strength of the acid to water. A low value of K_a, and therefore a high value of pK_a, indicates a weak acid.

Thermodynamic expressions are typically developed for ideal solutions and perfect gases, with expressions such as $μ J = μ J ⦵ +RT ln x J$ (where $μ J ⦵$ is the standard chemical potential and x_J is the mole fraction of J). The activity of a species J, a_J or a(J), is introduced principally to retain the form of these expressions for systems that are not ideal. Thus, for a real solution the chemical potential is written $μ J = μ J ⦵ +RT ln a J$ ⁠. The activity is therefore an ‘effective’ version of the mole fraction (or other measures of abundance, such as molar concentration [J] and molality b_J). Activities are dimensionless. For reversion to ideal expressions (as in many elementary applications) given an expression in terms of activity, use the relations a_J = p_J/p ^⦵ (for a gas) and either a_J = [J]/c ^⦵ or a_J = b_J/b ^⦵ for a solute; for any pure solid, a_J = 1.

Activities can be measured by making observations on the vapour pressure of a solvent and comparing it with the vapour pressure of the pure solvent (at the same temperatures): a_J = p_J/p_J*. The activity of the solute can then be inferred from this value by using the Gibbs–Duhem equation. Electrochemical measurements in conjunction with the Nernst equation can be used if the solute is ionic.

Thermodynamic equations expressed in terms of activities are exact (by definition). For them to be useful, activities need to be related to measures of abundance. To do so, it is common to introduce the activity coefficient, γ_J, by the relation a_J = γ_Jx_J (or analogous expressions in terms of molar concentration and molality), and to focus on the activity coefficient. For the the solvent, Raoult’s law implies that γ_J → 1 as x_J → 1. For the solute, Henry’s law implies that γ_J → 1 as x_J → 0. Models and theories are then needed to relate γ_J to measurable properties. Typically, these theories are limiting laws, reliable only in the Raoult’s or Henry’s law limits. An example is the Debye–Hückel limiting law for electrolyte solutions. The utility of these limiting-law expressions is best regarded as a guide to how measurements should be extrapolated to low concentrations rather than as the basis for making reliable estimates of numerical values.

Adiabatic demagnetization is a procedure for cooling objects to very low temperatures. A sample of electron or nuclear spins (on their parent atoms or ions) at a given temperature has a certain entropy. The application of a magnetic field on the sample in thermal contact with its surroundings partially aligns the spins and therefore lowers the entropy of the spin system. Then, with the thermal contact broken to make the subsequent step adiabatic, the field is slowly reduced to zero (Figure A.5). This step is adiabatic and reversible, so it is also isentropic (that is, occurs without change of entropy). The result of this step is a sample in which the newly partially aligned spins survive in the absence of a magnetic field. The lower entropy of this spin distribution corresponds to a temperature lower than it was initially. The process can be repeated to reach successively lower temperatures. When the spins are those of nuclei, the technique is called adiabatic nuclear demagnetization.

Adsorption is the attachment of a species, the adsorbent, to a surface, the substrate. If no chemical bonds are formed between adsorbent and substrate, it is called physisorption; if chemical bonds are formed, then the process is called chemisorption. The reverse of adsorption is desorption.

An allowed transition is a spectroscopic transition that is permitted by the selection rules. A transition that is forbidden may become allowed by perturbations or departures from the assumed symmetry of the molecule. Allowed transitions are identified by consideration of the transition dipole moment, which in turn can be assessed by considerations of symmetry.

The amount of substance, n, is a measure of the number of specified entities in a sample of matter. It is the physical quantity that is measured in moles, and hence is still widely colloquially referred to as the ‘number of moles’. The term ‘amount of substance’ is somewhat unwieldy, so it is often abbreviated to ‘amount’ or, preferably, ‘chemical amount’. For a sample of a substance of mass m and molar mass M, n = m/M. To avoid ambiguity, the value of n should always include the identity of the species; thus 1 mol H(g) or 1 mol H₂(g), not 1 mol of hydrogen.

An amphiprotic species is one that can act as both a proton donor and a proton acceptor. Water is an example. See autoprotolysis.

An antibonding orbital is a molecular orbital with an energy higher than that of its constituent atomic orbitals. In dihydrogen, the antibonding orbital is ψ = ψ_A1s − ψ_B1s. When discussing polyatomic molecules, it is appropriate to refer to the antibonding character of a molecular orbital in relation to pairs of neighbouring atoms and to identify an orbital as antibonding between two atoms if there is an internuclear nodal plane (Figure A.9).

A mathematical function f(x) is antisymmetric if f(−x) = −f(x). A many-particle wavefunction is said to be antisymmetric with respect to particle interchange if it changes sign under the interchange of the labels of two identical particles: ψ(…,i,…,j,…) = −ψ(…,j,…,i,…). See Pauli principle. A normal mode of vibration of a centrosymmetric polyatomic molecule is classified as antisymmetric if the extension of one bond is mirrored by the contraction of an equivalent bond (as in Figure A.10). The term antisymmetry should be distinguished from asymmetry, which means the absence of symmetry.

The Arrhenius parameters are the activation energy, E_a, and the frequency factor (formerly the pre-exponential factor), A, which occur in the expression $k r =A e − E a / R T$ or equivalently $ln k r =lnA− E a /RT$ for the temperature dependence of the rate constant of a chemical reaction. They are determined experimentally by making an Arrhenius plot of ln k_r against 1/T, the intercept at 1/T = 0 being ln A and the slope −E_a/R. A high activation energy signifies a strong dependence of the rate constant on the temperature (Figure A.11).

An asymmetric unit is the entity (an atom, ion, or molecule) from which a crystal is built. The location of an asymmetric unit is denoted by a lattice point. The crystal structure itself is the array of asymmetric units obtained by associating each one with a lattice point (Figure A.12).

The atmosphere (atm) is a unit of pressure defined as 1 atm = 101 325 Pa exactly. The unit is used in the current definitions of normal melting and boiling points. It is a component of the definition of standard temperature and pressure (STP).

The atomic number, Z, of an element is the number of protons in the nucleus of one of its atoms. The nuclear charge is Ze, where e is the fundamental charge. It follows that the number of electrons in an electrically neutral atom is also Z. See also effective nuclear charge.

An atomic orbital is a one-electron wavefunction for an atom. Most developments in chemistry are based on hydrogenic atomic orbitals, which are the orbitals found by solving the Schrödinger equation for a hydrogenic atom. Each of these wavefunctions can be expressed as the product of a radial wavefunction, R(r), and an angular wavefunction, Y(θ,ϕ), where r, θ, and ϕ are the polar coordinates of a point relative to the nucleus. Each orbital is specified by three quantum numbers:

• principal quantum number n, with n = 1, 2,…

• orbital angular momentum quantum number l, with l = 0,1, 2,…, n − 1

• magnetic quantum number m_l = 0, ±1, ±2,…, ±l

It follows that there are n ² orbitals that can have the quantum number n and which in a hydrogenic atom are degenerate.

Atomic orbitals are referred to according to the following notation:

The value of l specifies the orbital angular momentum of the electron it describes. The angular wavefunctions are the spherical harmonics. See that entry and also the entries for individual types of orbital for their shapes. The radial wavefunction has n − l − 1 nodes where the wavefunction passes through zero. An s orbital is unique in having a nonzero value at the nucleus: in classical terms, there is no orbital angular momentum to fling an electron away from the nucleus. An electron that ‘occupies’ (that is, is described by) an atomic orbital with quantum number n is called an ns-electron (if l = 0) an np-electron (if l = 1), and so on. See also shell, subshell, and hydrogenic atom.

According to the nuclear model, an atom consists of a small, central, positively charged, massive nucleus surrounded by shells of electrons. The electronic structures of atoms are expressed in terms of the atomic orbitals that are occupied by the Z electrons that are present in a neutral atom of atomic number Z. The structure is reported in terms of the electron configuration, the list of occupied orbitals such as 1s¹ for hydrogen, 1s² for helium, 1s²2s¹ for lithium, and so on. The electron configuration is determined spectroscopically and magnetically and can be rationalized in terms of the building-up principle. The orbitals available to the electrons lie in a series of concentric shells labelled as follows:

An attractive surface is a potential energy surface for a chemical reaction in which the saddle point occurs early in the reaction coordinate (Figure A.13). Reactions with attractive surfaces take place more readily if the energy of the reactants is principally in their relative translational motion. A surface is repulsive if the saddle point occurs late in the reaction coordinate (right illustration). Reactions with such surfaces take place most readily if the excess energy of the reactants is in the form of molecular vibration.

The Auger effect is the emission of a secondary electron after high-energy radiation (either X-ray or, more commonly, a beam of fast electrons) has expelled another electron. The first electron to depart leaves a vacancy in the low-lying orbital and an electron falls into it from an upper level (Figure A.14). The energy released ejects the secondary electron. The latter’s kinetic energy is characteristic of the solid. Its use in determining composition is called Auger electron spectroscopy (AES). Instead of the released energy ejecting a second electron, it might result in the generation of an X-ray photon, which is observed as X-ray fluorescence.

Autocatalysis is the acceleration of a reaction as a result of a product acting as a reactant. Thus, the reaction A + B → C followed by C → A + D is autocatalytic.

Avogadro’s constant, N_A, is the number of entities per mole of a substance. It has the defined value N_A = 6.022 140 76 × 10²³ mol⁻¹ (a value chosen to be close to the traditional definition, which was the number of atoms in exactly 12 g of carbon-12). See mole.

An axis of symmetry is the symmetry element corresponding to a symmetry rotation of a body. An n-fold axis of symmetry is the symmetry element associated with a rotation through 2π/n.

An azeotrope is a liquid mixture that boils to give a vapour of the same composition as the liquid. A high-boiling azeotrope has a boiling temperature higher than that of both its components (Figure A.16). A low boiling azeotrope has a boiling point that is lower than that of both its components. Azeotropes have important consequences for fractional distillation. When a mixture that forms a high-boiling azeotrope is fractionally distilled, the more volatile component vaporizes until the remaining liquid has reached its azeotropic composition; the mixture then distils unchanged. When a mixture that forms a low-boiling azeotrope is distilled, the vapour has the composition of the azeotropic mixture.