I

A regular solution is one for which the entropy of mixing has its ideal value (so the solute is distributed randomly) but the enthalpy of mixing is nonzero; see excess functions. Note that in an ideal system the interactions are all the same but in a perfect system (that is, a perfect gas) they are not only the same but also zero. This distinction between ideal and perfect is not always made.

The identity operation, E, is the act of doing nothing. It is required in the formal structure of group theory. The largest character of the identity in a character table for a point group is the maximum degeneracy possible for a system (and atom, ion, or molecule) that belongs to that point group.

The impact parameter, b, is the initial perpendicular distance between the line of approach of a projectile molecule and the target molecule (Figure I.5).

An n-fold improper rotation axis (or axis of improper rotation), S_n, is a combination of an n-fold axis and a horizontal mirror plane: S_n = σ_hC_n. Note that S₁ is equivalent to a mirror plane and that S₂ is equivalent to a centre of inversion. Molecules that do not possess an S_n axis are chiral (Figure I.6).

Incongruent melting is the decomposition of a compound as it melts. The corresponding feature in the phase diagram is indicated in Figure I.7 by the ringed area.

Indexing reflections is the procedure in which a reflection in X-ray crystallography is ascribed to planes with the Miller indices {hkl}.

An inexact differential (or incomplete differential) is one for which its integral depends on the path of integration. They are sometimes denoted đx. Examples of inexact differentials are dw and dq for work and heat, respectively. An inexact differential can be converted into an exact differential by multiplication by an integrating factor. An example is the conversion of the inexact differential dq_rev into the exact differential dS by multiplication by 1/T.

Of the four normal modes of an ABA linear molecule, two are degenerate (in the sense that they have the same frequency. The allowed transitions, those for which $Δ v = 1$ ⁠, are the first harmonics. When the motion is anharmonic (when the restoring force deviates from Hooke’s law), then overtones with $Δ v > 1$ (the higher harmonics) are allowed with low intensity. In the gas phase, vibrational transitions are accompanied by rotational transitions, giving rise to a branch structure of the vibrational spectrum.

The vibrational spectra of large molecules can be very complex. The fingerprint region of complex structure is characteristic of the substance, and can be used to recognize it by reference to a library of spectra.

Inhibition in biochemistry is the reduction in efficiency of an enzyme. Inhibitors are classified in terms of their binding properties, or equivalently in terms of their effect on the values of the maximum velocity, $v max$ ⁠, and the Michaelis constant, K_M, of the uninhibited enzyme. They can be distinguished experimentally by making a Lineweaver−Burk plot (Figure I.8).

The y-intercept of a Lineweaver–Burk plot is unchanged, but the slope increases by a factor 1 + [I]/K_d,EI. Thus, $K M inhibited$ increases as [I] increases, but $v max$ is unaffected.

In this case K_d,EI → ∞ because EI does not form. The slope of the Lineweaver–Burk plot is unchanged, but the y-intercept of the plot increases by a factor of 1 + [I]/K_d,ESI. Thus, as [I] increases uncompetitive inhibition reduces $K M inhibited$ and $v max inhibited$ by the same amount.

Both the slope and intercept of the Lineweaver–Burk plot increase upon addition of the inhibitor.

A property is classified as intensive if it is independent of the amount of substance in the sample. More precisely, if the sample is imagined to be divided into smaller samples, then a property is intensive if its value for the original sample is the same as the values for each of the smaller samples. Properties that are not intensive are extensive. Examples of intensive properties are temperature, pressure, mass density, and all molar quantities. In some cases (temperature and pressure, for instance) the properties are intrinsically independent of the size of the sample. In others (density and molar quantities, for instance), the property is a ratio of two extensive properties.

Interference is the interaction between the amplitudes of waves (including wavefunctions) that results in a wave with altered amplitude. In constructive interference the waves have the same phase in the region where they overlap and the total amplitude is larger than either component alone. In destructive interference the phases of the components are opposite and the amplitude of one wave subtracts from the other to result in a diminished amplitude.

Intermolecular forces are the forces of interaction of attraction and repulsion that act between closed shell atoms and molecules. Some of the interactions are universal, in the sense that (apart from their strength) they act regardless of the identity of the species. These universal interactions are electromagnetic in origin and most can be traced to the Coulombic interaction between permanent or transient charges. The distance dependence of their potential energies are as follows (where z is the charge number of an ion, μ is the dipole moment of a polar molecule, and α is the molecular polarizability):

1. Ion–ion interaction. The electrostatic interaction between charges; V ∝ z₁z₂/r.

2. Ion–dipole interaction. The electrostatic interaction between the charge of an ion and the partial charges of a permanent electric dipole; V ∝ z₁μ₂/r ².

3. Dipole–dipole interaction. The electrostatic interaction between the partial charges of two polar molecules. V ∝ μ₁μ₂/r ³ if the dipoles are locked in position; V ∝ (μ₁μ₂)²/Tr ⁶ if they are freely rotating at a temperature T.

4. Dipole–induced dipole interaction. In this interaction, the partial charges of a polar molecule induces a dipole moment in a neighbouring molecule (which might already be polar) and the initial and induced dipoles interact. V ∝ (μ₁α₂)²/r ⁶.

5. Induced-dipole–induced-dipole interaction (or London interaction, dispersion interaction). A fluctuation in the electron distribution in one molecule gives rise to a transient electric dipole, which induces an electric dipole in a neighbouring molecule, and the two transient dipoles interact. V ∝ (α₁α₂)²/r ⁶.

6. Repulsion. Once the two molecules come into contact and their wavefunctions start to overlap, they repel each other. This repulsion increases sharply with decreasing distance.

All the interactions may be present, depending on the charge and polarity of the molecules involved. The interactions that are proportional to 1/r ⁶ are classified as van der Waals interactions, although the term is often applied to all nonbonded interactions. Note that the force is proportional to dV/dr, so a potential energy proportional to 1/r ⁿ is associated with a force proportional to 1/r ⁿ⁺¹. At large molecular separations, the potential energy of the dispersion interaction becomes proportional to 1/r ⁷. This weakening is due to the time it takes for information to pass between the molecules.

A specific interaction, one that does depend on the identity of the molecules, is hydrogen bonding; see that entry.

Internal conversion is the process by which a molecule in one electronic state converts non-radiatively into another electronic state of the same multiplicity (Figure I.12). The conversion occurs in accord with the Franck–Condon principle and takes place at the intersection of the two molecular potential energy curves.

Intersystem crossing (ISC) is the radiationless transition of a molecule from one electronic state into another with a different multiplicity (Figure I.13). An example is the singlet-to-triplet crossing that occurs as a step in the mechanism of phosphorescence.

Intersystem crossing is brought about by spin−orbit coupling and entails the transfer of orbital angular momentum to spin angular momentum (the change from S = 0 to S = 1 in singlet-to-triplet ISC). The mechanism of this transfer is the magnetic field due to orbital motion of the electron acting on its own spin and thereby reversing its orientation relative to a second spin (↑↓ → ↑↑, Figure I.14). The opportunity for ISC, which conforms to the Franck–Condon principle, arises where the two molecular potential energy curves intersect. The intersection of curves effectively opens the door to the crossing and the spin–orbit coupling pushes the molecules through. As heavy atoms have strong spin–orbit couplings, ISC is most likely to occur in molecules that contain them.

An ionic bond is an electrostatic attraction between oppositely charged ions. Except in the case of the formation of ion pairs in the gas phase, it is best regarded as a global property of an aggregation of ions rather than a localized interaction between one cation and one anion. The formation of an ionic bond involves transfer of an electron from one atom to another, so its formation is facilitated by a low ionization energy of the element that is to form the cation. Low ionization energies are associated with metallic elements, so ionic bonds are typically characteristic of a metal in combination with a nonmetal. There are major exceptions, such as the formation of compounds containing NH₄ ⁺. The energetics of formation of an ionic bond take into account the ionization energy of one element, the electron affinity of the other, and the global Coulombic interaction energy of the ions they form; the net result of the first two alone only rarely accounts for the lower energy of an ionic solid relative to the free atoms.

The ionic radius is the notional radius of an ion in a solid. Its value depends on a largely arbitrary apportioning of the internuclear separation of the two ions, and a typical scale is based on ascribing the value 140 pm to the ionic radius of the O²⁻ ion. Other scales are sometimes more appropriate, such as for halides. Ionic radii vary periodically, with values typically increasing down a group and decreasing from left to right across a period. The d-block elements show some subtle variations. Cations are smaller than their parent atoms and anions are larger. The lanthanide contraction is a marked decrease in atomic and ionic radius following the lanthanoids.

An isenthalpic process is a process taking place at constant enthalpy. An example is the isothermal reversible expansion of a perfect gas (which is isenthalpic but endothermic). See Joule–Thomson effect.

An isobaric process is a process taking place at constant pressure. For an isobaric process in a closed (constant composition) system, ΔH = q_p.

An isochoric process is a process taking place at constant volume. For an isochoric process in a closed (constant composition) system, ΔU = q_V.

The isoelectric point of a macromolecule is the pH of a solution in which its net electric charge is zero.

The isolation method is a technique for examining the influence of an individual reactant on the rate of a chemical reaction and for determining the order of the reaction with respect to that reactant. In the procedure, each reactant except the one of interest is present in a large excess so that its concentration is effectively constant throughout the course of the reaction. The concentration of the remaining reactant is varied and the rate law for that component is inferred in the normal way.

Isomorphous replacement is a technique used in X-ray crystallography in which a modification to the diffraction pattern is obtained by the substitution of atoms of one element for those of another without significantly changing the structure of the crystal. The replacement can result in a greatly simplified diffraction pattern, especially if the replacement atoms dominate the diffraction, and so be a guide to the determination of the normal structure of the crystal.

An isopleth is a line of constant composition in a phase diagram (Figure I.15).

An isosteric process is a process that occurs at constant surface coverage.

An isothermal process is a process that occurs at constant temperature. An isotherm is a line in a graphical representation of a process occurring at constant temperature; for example, the variation of the pressure of a gas with volume at constant temperature (Figure I.16).

An adsorption isotherm is an expression for the variation of the extent of surface coverage with pressure. The work done by a gas expanding isothermally and reversibly is equal to the area below its isotherm and enclosed between the initial and final volumes (Figure I.17).