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Glossary

This glossary is intended to offer help in crossing disciplinary boundaries, especially for those beginning to explore the terminology-rich field of chemistry. The entries are neither exhaustive in scope nor definitional in quality. A small fraction of the entries define terms introduced in the present work. Crossreferences are marked with a small circle (for example, { }^{\circ}abstraction reaction); an alphabetical search will occasionally yield a different form of the indicated word.1 Some words in the main text are marked in the same way.

Abstraction reaction A\mathrm{A}^{\circ} reaction that removes an atom from a structure.

Acid In the Brønsted definition, an acid is a chemical species that can donate a proton to another species ( aa^{\circ} base). In the Lewis definition, an acid is a chemical species that can accept (and share) a pair of electrons from another species. Hydrochloric acid is a Brønsted acid; the proton it donates is a Lewis acid. A neutral Lewis acid and a neutral Lewis base can commonly form aa^{\circ} dipolar bond.

Activation energy Distinct states correspond to minima of aa^{\circ} potential energy surface in a { }^{\circ}configuration space. In this classical picture, the activation energy for transforming state AA into state BB is the maximum increase in energy (relative to the { }^{\circ}ground state of AA ) encountered on a minimum-energy path from AA to B. { }^{\circ}Energy here refers to potential energy; an analogous definition based { }^{\circ}{ }^{\circ} free energy can be constructed. When tunneling is considered, lower energy paths become possible, but an activation energy can be associated with the { }^{\circ}reaction (at a given { }^{\circ}temperature) via the relationship between temperature and reaction rate.

Acyclic Not { }^{\circ}cyclic.

Affinity constant The reciprocal of the { }^{\circ}dissociation constant; a measure of the { }^{\circ}binding energy of aa^{\circ} ligand in aa^{\circ} receptor.

AFM An\mathrm{An}^{\circ}{ }^{\circ} atomic force microscope.

Alkane A\mathrm{A}^{\circ} saturated, { }^{\circ}acyclic hydrocarbon structure; usually quite inert.

Alkene AA hydrocarbon containing a { }^{\circ}double bond; often rather reactive.

Alkyne AA^{\circ} hydrocarbon containing a { }^{\circ}triple bond; often rather reactive.

Amide A molecule containing an { }^{\circ}amine bonded to a carboxyl group; the resulting bond has substantial doublebond character. Also termed a { }^{\circ}peptide; { }^{\circ}amide bonds link { }^{\circ}amino acids in { }^{\circ}proteins.

Amine A molecule containing N\mathrm{N} with a single bond to C\mathrm{C} and two other single bonds to H\mathrm{H} or C\mathrm{C} (but not an { }^{\circ}amide); the amine group or moiety.

Amino acid A molecule containing both an { }^{\circ}amine and a { }^{\circ}carboxylic acid group; in the 20 genetically encoded amino acids in biology, both groups are bound to the same C\mathrm{C}. Amino acids joined by { }^{\circ}amide bonds form { }^{\circ}peptides and { }^{\circ}proteins; these do not contain amino acids as such, and are instead said to contain amino acid residues.

Anion A negatively charged { }^{\circ}ion.

Aromatic A term used to describe { }^{\circ}cyclic { }^{\circ}pi-bonded structures of special stability.

Assembler In recent popular usage, any { }^{\circ}nanomachine, usually assumed to offer magical, universal capabilities in an atom-sized package. In the author's usage, any programmable nanomechanical system able to perform a wide range of mechanosynthetic operations. See { }^{\circ}molecular manipulator, { }^{\circ}molecular mill.

Atomic force microscope A device in which the deflection of a sharp stylus mounted on a soft spring is monitored as the stylus is moved across a surface. If the deflection is kept constant by moving the surface up and down by measured increments, the result (under favorable conditions) is an atomic-resolution topographic map of the surface. Also termed a scanning force microscope.

Barrier height Roughly synonymous with activation energy.

Base In the Brønsted definition, a base is a chemical species that can accept a proton from another species. In the Lewis definition, a base is a chemical species that can donate (and share) a pair of electrons with another species. See { }^{\circ}acid.

Bearing A\mathbf{A}^{\circ} mechanical device that permits the motion of a component (ideally, with minimal resistance) in one or more degrees of freedom while resisting motion (ideally, with a stiff restoring force) in all other degrees of freedom.

Binding energy The reduction in the { }^{\circ}free energy of a system that occurs when aa^{\circ} ligand binds to aa^{\circ} receptor. Generally used to describe the total energy required to remove something, or to take a system apart into its constituent particles-for example, to separate two atoms from one another, or to separate an atom into electrons and nuclei.

Binding site The active region of a { }^{\circ}receptor; any site at which a chemical { }^{\circ}species of interest tends to bind.

Binding The process by which a molecule (or ligand) becomes bound, that is, confined in position (and often orientation) with respect to aa^{\circ} receptor. Confinement occurs because structural features of the receptor create aa^{\circ} potential well for the ligand; { }^{\circ}van der Waals and electrostatic interactions commonly contribute.

Bond Two atoms are said to be bonded when the energy required to separate them is substantially larger than the van der Waals attraction energy. Ionic bonds result from the electrostatic attraction between ions; { }^{\circ}covalent and metallic bonds result from the sharing of electrons among atoms; { }^{\circ}hydrogen bonds are weaker and result from dipole interactions and limited electron sharing. When used without modification, "bond" usually refers to a covalent bond.

Brownian assembly { }^{\circ}Brownian motion in a fluid brings molecules together in various positions and orientations. If molecules have suitable complementary surfaces, they can bind, assembling to form a specific structure. Brownian assembly is a less paradoxical name for self-assembly (how can a structure assemble itself, or do anything, when it does not yet exist?).

Brownian motion Motion of a particle in a fluid owing to thermal agitation, observed in 1827 by Robert Brown. (Originally thought to be caused by a vital force, Brownian motion in fact plays a vital role in the assembly and activity of the molecular structures of life.)

CAD Computer-aided design.

Cam A component that translates or rotates to move a contoured surface past aa{ }^{\circ} follower; the contours impose a sequence of motions (potentially complex) on the follower.

Carbanion A highly reactive { }^{\circ}anionic chemical species with an even number of electrons and an unshared pair of electrons on a tetravalent carbon atom.

Carbene A highly reactive chemical species containing an electrically neutral, divalent carbon atom with two nonbonding { }^{\circ}valence electrons; a prototype is CH2\mathrm{CH}_{2}.

Carbonium ion A highly reactive { }^{\circ}cationic chemical species with an even number of electrons and an unoccupied orbital on a carbon atom.

Carbonyl A chemical moiety consisting of O\mathrm{O} with a double bond to C\mathrm{C}. If the C\mathrm{C} is bonded to N\mathrm{N}, the resulting structure is termed an { }^{\circ}amide; if it is bonded to O\mathrm{O}, it is termed a { }^{\circ}carboxylic acid or an { }^{\circ}ester linkage.

Carboxylic acid A molecule that includes a C\mathrm{C} having a { }^{\circ}double bond to O\mathrm{O} and aa^{\circ} single bond to OH\mathrm{OH}.Catalyst A chemical { }^{\circ}species or other structure that facilitates a chemical { }^{\circ}reaction without itself undergoing a permanent change.

Cation A positively charged { }^{\circ}ion.

Classical mechanics Classical mechanics describes a { }^{\circ}mechanical system as a set of particles (which in a limiting case can form continuous media) having a well-defined geometry at any given time, and undergoing motions determined by applied forces and by the initial positions and velocities of the particles. The forces themselves may have electromagnetic or { }^{\circ}quantum mechanical origins. Classical 'statistical mechanics uses the same physical model, but treats the geometry and velocities as uncertain, statistical quantities subject to random thermally-induced fluctuations. Classical mechanics and classical statistical mechanics give a good account of many mechanical properties and behaviors of molecules; but for describing the { }^{\circ}electronic properties and behaviors of molecules, they are often useless.

CMOS An acronym for complementary metal-oxide-semiconductor, as in CMOS transistor and CMOS logic.

Col In describing landforms, a pass between two valleys is sometimes termed a col. In describing molecular { }^{\circ}potential energy functions, this term is commonly used to describe analogous features of the PES; a col is the region around a saddle point having negative curvature along one axis and positive curvature along all orthogonal axes.

Compliance The reciprocal of { }^{\circ}stiffness; in a linear elastic system, displacement equals force times compliance.

Configuration space A mathematical space describing the three-dimensional configuration of a system of particles (e.g., atoms in a { }^{\circ}nanomechanical structure) as a single point; the configuration space for an NN particle system has 3N3 N dimensions.

Conformation A molecular geometry that differs from other geometries chiefly by rotation about single or triple bonds; distinct conformations (termed conformers) are associated with distinct { }^{\circ}potential wells. Typical biomolecules and products of organic synthesis can interconvert among many conformations; typical { }^{\circ}diamondoid structures are locked into a single potential well, and thus lack conformational flexibility.

Conjugated A conjugated { }^{\circ}pi system is one in which pi bonds alternate with single bonds. The resulting electron distribution gives the intervening single bonds partial double-bond character, the pi electrons become delocalized, and the energy of the system is reduced.

Conservative In design and analysis, a conservative model or a conservative assumption is one that departs from accuracy in such a way that it reduces the chances of a false-positive assessment of the feasibility of the system in question. Conservative assumptions overestimate problems and underestimate capabilities.

Covalent bond A\mathrm{A}^{\circ} bond formed by sharing a pair of electrons between two atoms.

Covalent radius Given a set of NN elements that can form { }^{\circ}covalent { }^{\circ}single bonds in molecules, with N(N1)N(N-1) possible elemental pairings, it has proved possible to define a covalent radius for each element such that the actual bond length between any two elements that form a covalent single bond is roughly equal to the sums of their covalent radii.

CPU The central processing unit of a computer, responsible for executing instructions to process information.

Cyclic A structure is termed cyclic if its { }^{\circ}covalent bonds form one or more rings.

Cycloaddition AA^{\circ} reaction in which two unsaturated molecules (or moieties within a molecule) join, forming a ring.

Dative bond A\mathrm{A}{ }^{\circ} dipolar bond.

Diamondoid As used in this volume, this term describes structures that resemble diamond in a broad sense: strong, stiff structures containing dense, threedimensional networks of { }^{\circ}covalent bonds, formed chiefly from first and second row atoms with aa^{\circ} valence of three or more. Many of the most useful diamondoid structures will in fact be rich in tetrahedrally coordinated carbon.

Diamondoid is used more narrowly elsewhere in the literature.

Dipolar bond A\mathrm{A}^{\circ} covalent bond in which one atom supplies both bonding electrons, and the other atom supplies an empty orbital in which to share them. Also termed a dative bond.

Dissociation constant For systems in which ligands { }^{\text {ligands }} of a particular kind bind to a { }^{\circ}receptor in a solvent there will be a characteristic frequency with which existing ligand-receptor complexes dissociate as a result of thermal excitation, and a characteristic frequency with which empty receptors bind ligands as a result of Brownian encounters, forming new complexes. The frequency of binding is proportional to the concentration of the ligand in solution. The dissociation constant is the magnitude of the ligand concentration at which the probability that the receptor will be found occupied is 1/21 / 2.

Double bond Two atoms sharing electrons as in a { }^{\circ}single bond (that is, aa^{\circ} sigma bond) may also share electrons in an orbital with a node passing through the two atoms. This adds a second, weaker bonding interaction ( api\mathrm{a}^{\circ} \mathrm{pi} bond); the combination is termed a double bond. A twisting motion that forces the nodal plane at one atom to become perpendicular to the nodal plane on the other atom eliminates the (signed) { }^{\circ}overlap between the atomic orbitals, destroying the pi bond. The energy required to do this cre- ates a large barrier to rotation about the bond (see { }^{\circ}triple bond).

Doublet The electronic state of a molecule having one unpaired spin is termed a doublet (see { }^{\circ}radical). This term is derived from spectroscopy: an unpaired spin can be either up or down with respect to a magnetic field, and these states have different energy, resulting in field-dependent pairs, or doublets, of spectral lines. (See { }^{\circ}triplet, { }^{\circ}singlet.)

Effective mass In a vibrating system, a particular vibrational mode can be described as a harmonic oscillator with some mass and stiffness. Given some measure of vibrational amplitude, there exists a unique choice of mass and stiffness that yields the correct values for both frequency and energy; these are the effective mass and effective stiffness.

Effective stiffness See { }^{\circ}effective mass.

Elastic An object behaves elastically if it returns to its original shape after a force is applied and then removed. (If an applied force causes a permanent deformation, the behavior is termed plastic.) In an elastic system, the internal potential energy is a function of shape alone, independent of past forces and deformations.

Electron density The location of an electron is not fixed, but is instead described by a probability density function. The sum of the probability densities of all the electrons in a region is the electron density in that region.

Electronegativity A measure of the tendency of an atom (or moiety) to withdraw electrons from structures to which it is bonded. In most circumstances, for example, sodium tends to donate electron density (it has a low electronegativity) and fluorine tends to withdraw electron density (it has a high electronegativity).

Electronic Pertaining to the energies, distributions, and behaviors of electrons; see { }^{\circ}mechanical.

Endoergic A transformation is termed endoergic if it absorbs energy; such a { }^{\circ}reaction increases molecular { }^{\circ}potential energy. (Sometimes wrongly equated to the narrower term { }^{\circ}endothermic.)

Endothermic A transformation is termed endothermic if it absorbs energy in the form of heat. A typical endothermic\mathrm{mic}^{\circ} reaction increases both entropy{ }^{\circ} \mathrm{entropy} and molecular { }^{\circ}potential energy (and is thus analogous to a gas expanding while absorbing heat and compressing a spring).

Energy A conserved quantity that can be interconverted among many forms, including { }^{\circ}kinetic energy, { }^{\circ}potential energy, and electromagnetic energy. Sometimes defined as "the capacity to do "work," but in an environment at a uniform nonzero { }^{\circ}temperature, { }^{\circ}thermal energy does not provide this capacity. (Note, however, that all energy has mass, and thus can be used to do work by virtue of its gravitational potential energy; this caveat, however, is of no practical significance unless a really deep gravity well is available.) See { }^{\circ}free energy.

Enthalpy The enthalpy of a system is its actual { }^{\circ}energy (termed the internal energy) plus the product of its volume and the external pressure. Though sometimes termed "heat content," the enthalpy in fact includes energy not contained in the system. Enthalpy proves convenient for describing processes in gases and liquids in laboratory environments, if one does not wish to account explicitly for energy stored in the atmosphere by work done when a system expands. It is of little use, however, in describing processes in { }^{\circ}nanomechanical systems, where work can take many forms: internal energy is then more convenient. Enthalpy is to energy what the { }^{\circ}Gibbs free energy is to the Helmholtz{ }^{\circ} \mathrm{Helmholtz} free energy.

Entropy A measure of uncertainty regarding the state of a system: for example, a gas molecule at an unknown location in a large volume has a higher entropy than one known to be confined to a smaller volume. { }^{\circ}Free energy can be extracted in converting a low-entropy state to a high-entropy state: the (timeaverage) pressure exerted by a gas molecule can do useful work as a small volume is expanded to a larger volume. In the classical { }^{\circ}configuration space picture, any molecular system can be viewed as a single-particle gas in a high-dimensional space. In the quantum mechanical picture, entropy is described as a function of the probabilities of occupancy of different members of a set of alternative quantum states. Increased information regarding the state of a system reduces its entropy and thereby increases its free energy, as shown by the resulting ability to extract more work from it.

An illustrative contradiction in the simple textbook view of entropy as a local property of a material (defining an entropy per mole, and so forth) can be shown as follows: The third law of thermodynamics states that a perfect crystal at absolute zero has zero entropy;2 this is true regardless of its size. A piece of disordered material, such as a glass, has some finite entropy S0>0\mathscr{S}_{0}>0 at absolute zero. In the local-property view, NN pieces of glass, even (or especially) if all are atomically identical, must have an entropy of NS0N \mathscr{S}_{0}. If these NN pieces of glass are arranged in a regular three-dimensional lattice, however, the resulting structure constitutes a perfect crystal (with a large unit cell); at absolute zero, the third law states that this crystal has zero entropy, not Nφ0N \varphi_{0}. To understand the informational perspective on entropy, it is a useful exercise to consider (1) what the actual entropy of such crystal is as a function of NN, with and without information describing the structure of the unit cell, (2) how the third law can be phrased more precisely, and (3) what this more precise statement implies for the entropy of well-defined aperiodic structures. Note that any one unit cell in the crystal can be regarded as a description of all the rest.

Enzyme AA^{\circ} protein molecule that acts as a specific { }^{\circ}catalyst, binding to other molecules in a manner that facilitates a particular chemical { }^{\circ}reaction.

Equilibrium A system is said to be at equilibrium (with respect to some set of feasible transformations) if it has minimal { }^{\circ}free energy. A system containing objects at different { }^{\circ}temperatures is in disequilibrium, because heat flow can reduce the free energy. Springs have equilibrium lengths, reactants and products in solution have equilibrium concentrations, thermally excited systems have equilibrium probabilities of occupying various states, and so forth.

Ester A molecule containing an ester linkage, a\mathrm{a}^{\circ} carbonyl group bonded to an O\mathrm{O} that is in turn bonded to a C\mathrm{C}.

Ether A molecule containing a COC\mathrm{C}-\mathrm{O}-\mathrm{C} structure, termed an ether linkage (unless one of the CC atoms has a { }^{\circ}double bond to another O\mathrm{O}, making this part of an ester linkage, or some other exception holds).

Eutactic Characterized by precise molecular order, like that of a perfect crystal, the interior of a protein molecule, or a machine-phase system; contrasted to the disorder of bulk materials, solution environments, or biological structures on a cellular scale. Borderline cases can be identified, but perfection is not necessary. As a crystal with sparse defects is best described as a crystal (rather than as amorphous), so a eutactic structure with sparse defects is best described as (imperfectly) eutactic, rather than as disordered.

Excluded volume The presence of one molecule (or moiety) reduces the volume available for other molecules (or moieties); resulting reductions in their 'entropy are termed excluded volume effects.

Exoergic The opposite of { }^{\circ}endoergic; describes a transformation that releases energy.

Exothermic The opposite of { }^{\circ}endothermic; describes an { }^{\circ}exoergic transformation in which energy is released as { }^{\circ}heat. Exoergic { }^{\circ}reactions in solution are commonly exothermic.

Fail-stop Describes a component or subsystem that, in the event of a failure, produces no output (e.g., of material or data) rather than producing a damaged or incorrect output.

Fault-tolerant Describes a system that can suffer failure in a component or subsystem, yet continue to function correctly.

Follower A component in a { }^{\circ}cam system that is driven through a pattern of displacements as it rests against a moving contoured surface.

Free energy Free energy is a measure of the ability of a system to do work, such that a reduction in free energy could in principle yield an equivalent quantity of work. The Helmholtz{ }^{\circ} \mathrm{Helmholtz} free energy describes the free energy within a system; the Gibbs{ }^{\circ} \mathrm{Gibbs} free energy does not.

Free radical A\mathbf{A}^{\circ}{ }^{\circ} radical.

Gate In digital logic, a component that can switch the state of an output dependent on the states of one or more inputs.

Gibbs free energy The Gibbs { }^{\circ}free energy is the Helmholtz{ }^{\circ} \mathrm{Helmholtz} free energy plus the product of the system volume and the external pressure. Changes in the Gibbs free energy at a constant pressure thus include work done against external pressure as a system undergoes volumetric changes. This proves convenient for describing equilibria in gases and liquids at a constant pressure (e.g., at one atmosphere), but is of little use in describing machine-phase chemical processes.

Changes in the Gibbs free energy caused by a change in the applied pressure (at constant volume) have no direct physical significance. (See also { }^{\circ}enthalpy.)

Ground state The lowest-energy state of a system. The electronic ground state of a system cannot reduce its energy by an electronic transition, but may contain vibrational energy ( { }^{\circ}kinetic and { }^{\circ}potential energy associated with the motions and positions of its atoms); extended systems at ordinary temperatures are always vibrationally excited, and so "ground state" is often taken to mean "electronic ground state."

Group A set of linked atoms in a molecule; a defined substructure. Typically, a set that is usefully regarded as a unit in chemical { }^{\circ}reactions of interest.

Group velocity In wave propagation, the speed of the waveform (e.g., of a peak) can be different from the speed of a group of waves (e.g., of a set of ripples in water). The latter is the group velocity, and is the speed of propagation of information and wave energy. The waveform speed is the phase velocity.

Harmonic oscillator A system in which a mass is subject to a linear restoring force, like an ideal spring. A harmonic oscillator vibrates at a fixed frequency, independent of amplitude.

Heat As defined in thermodynamics, heat is the energy that flows between two systems as a result of { }^{\circ}temperature differences (a system contains neither heat nor { }^{\circ}work, but can produce heat or do work). Heat thus differs from { }^{\circ}thermal energy.

Heat capacity The ratio of the { }^{\circ}heat input to the { }^{\circ}temperature increase in a system. Note that this definition does not imply that a system contains heat, despite the name heat capacity.

Helmholtz free energy The internal energy of a system minus the product of its { }^{\circ}entropy and { }^{\circ}temperature; see { }^{\circ}free energy.

Hydrocarbon A molecule consisting only of H\mathrm{H} and C\mathrm{C}.

Hydrogen bond A hydrogen atom { }^{\circ}covalently bound to an electronegative atom (e.g., nitrogen, oxygen) has a significant positive charge and can form a weak bond to another electronegative atom; this is termed a hydrogen bond.

Hydrophobic force Water molecules are linked by a network of hydrogen { }^{\text {hydrogen }} bonds. A nonpolar, nonwetting, surface (e.g., wax) cannot form hydrogen bonds. To form their full complement of hydrogen bonds, the nearby water molecules must form a more orderly (hence lower { }^{\circ}entropy) network. This both increases { }^{\circ}free energy and causes forces that tend to draw hydrophobic surfaces together across distances of several nanometers.

Intermolecular Describes an interaction (e.g., a chemical { }^{\circ}reaction) between different molecules.

Internal energy The sum of the { }^{\circ}kinetic and { }^{\circ}potential energies (including electromagnetic field energies) of the particles that make up a system.

Intramolecular Describes an interaction (e.g., a chemical { }^{\circ}reaction) within a single molecule. Intramolecular interactions between widely separated parts of a molecule resemble { }^{\circ}intermolecular interactions in most respects.

Ion An atom or { }^{\circ}molecule with a net charge.

Ionic bond A chemical { }^{\circ}bond resulting chiefly from the electrostatic attraction between positive and negative { }^{\circ}ions.

Isoelectronic Two molecules are described as isoelectronic if they have the same number of valence electrons in similar orbitals, although they may differ in their distribution of nuclear charges (e.g., HCN\mathbf{H}-\mathbf{C} \equiv \mathrm{N} and HN+C\mathbf{H}-\mathrm{N}^{+} \equiv \mathrm{C}^{-}are isoelectronic).

Kinetic Pertaining to the rates of chemical { }^{\circ}reactions. A fast reaction is said to have fast kinetics; if the balance of products in a reaction is controlled by reaction rates rather than by thermodynamic equilibria, the reaction is said to be kinetically controlled.

Kinetic energy Energy resulting from the motion of masses.

Ligand In { }^{\circ}protein chemistry, a small molecule that is (or can be) bound by a larger molecule is termed a ligand. In organometallic chemistry, a moiety bonded to a central metal atom is also termed a ligand; the latter definition is more common in general chemistry.

Linear Aside from its geometric meaning, linear describes systems in which an output is directly proportional to an input. In particular, a linear { }^{\circ}elastic system is one in which the internal displacements are (at equilibrium) directly proportional to applied forces.

London dispersion force An attractive force caused by quantum-mechanical electron correlation. For example, a neu- tral spherical molecule (such as a single argon atom) has no charge and produces no external electric field, yet a pair of molecules has a distribution of electron configurations weighted toward those with lesser electron-electron repulsions; this creates a small net attraction.

Lone pair Two valence electrons of an atom that share an orbital but do not participate in a bond.

Machine-phase chemistry The chemistry of systems in which all potentially reactive moieties follow controlled trajectories (e.g., guided by molecular machines working in vacuum).

Mechanical Pertaining to the positions and motions of atoms, as defined by the positions of their nuclei; see { }^{\circ}electronic. A purely mechanical device can be described in terms of atomic positions and motions without reference to electronic properties, save through their effect on the { }^{\circ}potential energy function.

Mechanochemistry In this volume, the chemistry of processes in which { }^{\circ}mechanical systems operating with atomic-scale precision either guide, drive, or are driven by chemical transformations. In general usage, the chemistry of processes in which energy is converted from mechanical to chemical form, or vice versa.

Mechanosynthesis Chemical { }^{\circ}synthesis controlled by { }^{\circ}mechanical systems operating with atomic-scale precision, enabling direct positional selection of { }^{\circ}reaction sites; synthetic applications of { }^{\circ}mechanochemistry. Suitable mechanical systems include AFM{ }^{\circ} \mathrm{AFM} mechanisms, { }^{\circ}molecular manipulators, and { }^{\circ}molecular mill systems. Processes that fall outside the intended scope of this definition include reactions guided by the incorporation of reactive { }^{\circ}moieties into a shared { }^{\circ}covalent framework (i.e., conventional intramolecular reactions), or by the binding of reagents to { }^{\circ}enzymes or enzymelike { }^{\circ}catalysts.

Metastable A classical system is metastable if it is above its minimum-energy state, but requires an energy input before it can reach a lower-energy state; accordingly, a metastable system can act like a { }^{\circ}stable system, provided that energy inputs (e.g., thermal fluctuations) remain below some threshold. Systems with strong metastability are commonly described as stable. Quantum mechanical effects can permit metastable states to reach lower energies by tunneling, without an energy input; an associated, broader definition of metastable embraces all systems that have a long lifetime (by some standard) in a state above the minimum-energy state.

Misreaction A chemical { }^{\circ}reaction that fails by yielding an unwanted product.

MM2 A molecular mechanics program developed by Norman Allinger and coworkers; the "MM2 model" is the molecular { }^{\circ}potential energy function described by the equations, rules, and parameters embodied in that program.

MM2/CSC A molecular mechanics program developed by Cambridge Scientific Computing that closely follows the MM2 model, adding a graphical user interface and other features.

Modulus Any of several measures of { }^{\circ}strain versus applied { }^{\circ}stress. See { }^{\circ}shear modulus, { }^{\circ}Young's modulus.

Moiety A portion of a molecular structure having some property of interest.

Mole A number of instances of something (typically a molecular species) equaling 6.022×1023\sim 6.022 \times 10^{23}. Mole ordinarily means gram-mole; a kilogram-mole is 6.022×1026\sim 6.022 \times 10^{26}.

Molecular machine AA^{\circ} mechanical device that performs a useful function using components of nanometer scale and defined molecular structure; includes both artificial ^{\circ} nanomachines and naturally occurring devices found in biological systems.

Molecular manipulator A programmable device able to position molecular tools with high precision, for example, to direct a sequence of { }^{\circ}mechanosynthetic steps; a molecular { }^{\circ}assembler.

Molecular manufacturing The production of complex structures via nonbiolog- ical { }^{\circ}mechanosynthesis (and subsequent assembly operations).

Molecular mechanics models Many of the properties of molecular systems are determined by the molecular { }^{\circ}potential energy function. Molecular mechanics models approximate this function as a sum of 2-atom, 3-atom, and 4-atom terms, each determined by the geometries and bonds of the component atoms. The 2-atom and 3-atom terms describing bonded interactions roughly correspond to linear springs.

Molecular mill A\mathrm{A}^{\circ} mechanochemical processing system characterized by limited motions and repetitive operations without programmable flexibility (see { }^{\circ}molecular manipulator).

Molecular nanotechnology See ^{\circ} nanotechnology.

Molecule A set of atoms linked by { }^{\circ}covalent bonds. A macroscopic piece of diamond is technically a single molecule. (Sets of atoms linked by bonds of other kinds are sometimes also termed molecules.)

Nanomachine An artificial { }^{\circ}eutactic { }^{\circ}mechanical device that relies on nanometer-scale components; see { }^{\circ}molecular machine.

Nanomechanical Pertaining to { }^{\circ}nanomachines.

Nanoscale On a scale of nanometers, from atomic dimensions to 100 nm\sim 100 \mathrm{~nm}.

Nanosystem AA^{\circ} eutactic set of nanoscale components working together to serve a set of purposes; complex nanosystems can be of macroscopic size.

Nanotechnology In recent general usage, any technology related to features of nanometer scale: thin films, fine particles, chemical synthesis, advanced microlithography, and so forth. As introduced by the author, a technology based on the ability to build structures to complex, atomic specifications by means of mechanosynthesis; this can be termed molecular nanotechnology.

NMOS An acronym for n-channel metal-oxide-semiconductor, as in NMOS transistor and NMOS logic.

Nucleus The positively charged core of an atom, an object of 0.00001\sim 0.00001 atomic diameters containing >99.9%\mathbf{> 9 9 . 9} \% of the atomic mass. Nuclear positions define atomic positions.

Olefin An\mathrm{An}^{\circ} alkene.

Omitted reaction A chemical { }^{\circ}reaction that fails by not occurring (see { }^{\circ}misreaction).

Orbital In the approximation that each electron in a molecule has a distinct, independent { }^{\circ}wave function, the spatial distribution of an electron wave function corresponds to a molecular orbital. These, in turn, can be approximated as sums of contributions from the orbitals characteristic of the isolated atoms. An electron added to a molecule-or, similarly, one excited to a higher-energy state within a moleculewould occupy a state with a different wave function from the rest; an unoccupied state of this kind corresponds to an unoccupied molecular orbital. Orbitalsymmetry effects on reaction rates arise when a reaction requires { }^{\circ}overlap between two lobes of the orbitals on each of two { }^{\circ}reagents: if the algebraic signs of the wave functions in the facing lobes do not match, bond formation between those orbitals is prohibited.

Overlap { }^{\circ}Orbitals lack sharply defined surfaces, declining in amplitude exponentially in their surface regions. When two orbitals are brought together, regions of substantial amplitude overlap. The resulting system can be described as two new orbitals, one formed by joining the two original orbitals without introducing a node in the { }^{\circ}wave function, and the other formed with a node between them. The nodeless joining reduces the energy of the electrons relative to the separate orbitals, resulting in a bonding interaction; joining with a node raises the energy, producing an antibonding interaction. If both new orbitals are occupied, antibonding forces dominate, resulting in { }^{\circ}overlap repulsion. { }^{\circ}Molecular mechanics models give an approximate description of overlap (and other) forces for a certain range of atoms and geometries.

Overlap repulsion A repulsive force resulting from the nonbonding { }^{\circ}overlap of two atoms.

Partition function A function determined by the probability distribution (over { }^{\circ}phase space in the { }^{\circ}classical treatment; over { }^{\circ}quantum states in the quantum treatment) describing a thermally equilibrated system; many thermodynamic quantities can be expressed in terms of the partition function and its derivatives.

PDF See { }^{\circ}probability density function

Peptide A short chain of amino acids; see { }^{\circ}protein.

FES See { }^{\circ}potential energy surface.

Phase space A classical system of NN particles can be described by its 3N3 N position and 3N3 N momentum coordinates. The phase space associated with the system is the 6N6 N dimensional space defined by these coordinates.

Phonon A quantum of acoustic energy, analogous to the quantum of electromagnetic radiation, the photon. Thermal excitations in a crystal or in an elastic continuum can be described as a population of phonons (analogous to blackbody electromagnetic radiation). In highly inhomogeneous solids, a description in terms of phonons breaks down and localized vibrational modes become important.

Pi bond A\mathrm{A}^{\circ} covalent bond formed by { }^{\circ}overlap between two pp orbitals on different atoms ( see sp^{\circ} s p ). Pi bonds are superimposed on { }^{\circ}sigma bonds, forming { }^{\circ}double or { }^{\circ}triple bonds.

Poisson's ratio A bar of an isotropic, elastic material ordinarily shrinks laterally when it is stretched longitudinally. The lateral contracting strain divided by the applied tensile strain is Poisson's ratio, which varies from material to material.

Polycyclic AA^{\circ} cyclic structure contains rings of bonds; a structure having many such rings is termed polycyclic. In the polycyclic structures of interest in this volume, a large fraction of the atoms are members of multiple small rings, resulting in considerable rigidity.

Potential energy The energy associated with a configuration of particles, as distinct from their motions. In macroscopic experience, potential energy can be increased (for example) by stretching a spring or by lifting a mass against a gravitational force; in molecular systems, potential energy can be increased (for example) by stretching a bond or by separating molecules against avan\mathbf{a}^{\circ} \mathbf{v a n} der Waals attraction.

Potential energy surface The { }^{\circ}potential energy of a ground-state molecular system containing NN atoms is a function of its geometry, defined by 3N3 N spatial coordinates ( aa^{\circ} configuration space). If the energy is imagined as corresponding to a height in a 3N+13 N+1 dimensional space, the resulting landscape of hills, hollows, and valleys is the potential energy surface.

Potential well In a { }^{\circ}potential energy surface, the region surrounding a local energy minimum. Typically taken to include at least those points in { }^{\circ}configuration space such that a path of steadily declining energy can be found that leads to the minimum in question, and such that no similar path can be found to any other minimum. If the PES were a landscape, this would be the region around the minimum that could be filled with water without any flowing down and away toward another minimum.

Probability density function Consider an uncertain physical property and a corresponding space describing the range of values that the property can have (e.g., the configuration of a thermally excited NN particle system and the corresponding 3N3 N dimensional configuration space). The probability density function associated with a property is defined over the corresponding space; its value at a particular point is the probability per unit volume that the property has a value in an infinitesimal region around that point.

Protein Living cells contain many molecules that consist of amino acid polymers folded to form more-or-less definite three-dimensional structures; these are termed proteins. Short polymers lacking definite three-dimensional structures are termed { }^{\circ}peptides. Many proteins incorporate structures other than amino acids, either as { }^{\circ}covalently attached side chains or as bound ligands. Molecular objects made of protein form much of the molecular machinery of living cells.

Quantum mechanics Quantum mechanics describes a system of particles in terms of a { }^{\circ}wave function defined over the { }^{\circ}configuration space of the system. Although the concept of particles having distinct locations is implicit in the { }^{\circ}potential energy function that determines the wave function (e.g., of a { }^{\circ}ground-state system), the observable dynamics of the system cannot be described in terms of the motion of such particles from point to point. In describing the energies, distributions, and behaviors of electrons in nanometer-scale structures, quantum mechanical methods are necessary. Electron { }^{\circ}wave functions help determine the { }^{\circ}potential energy surface of a molecular system, which in turn is the basis for { }^{\circ}classical descriptions of molecular motion. Nanomechanical{ }^{\circ} \mathrm{Nanomechanical} systems can almost always be described in terms of classical mechanics, with occasional quantum mechanical corrections applied within the framework of a classical model.

Radiation damage Chemical changes (bond breakage, ionization) caused by high-energy radiation (e.g., x-rays, gamma rays, high-speed electrons, protons, etc.).

Radical A structure with an unpaired electron (but excluding certain metal ions). In organic molecules, a radical is often associated with a highly reactive site of reduced valence (see { }^{\circ}doublet). The term radical is sometimes used to describe a substructure within a molecule; the term free radical then describes a radical in this sense, viewed as the result of cleaving the bond linking the substructure to the rest of the molecule.

Reaction A process that transforms one or more chemical { }^{\circ}species into others. Typical reactions make or break 'bonds; others change the state of ionization or other properties taken to distinguish chemical species.

Reagent A chemical { }^{\circ}species that undergoes change as a result of a chemical { }^{\circ}reaction.

Reagent device A large { }^{\circ}reagent structure (or a large structure that binds a smaller reagent) serving as a component of a { }^{\circ}mechanochemical system. A reagent device exists chiefly to hold, position, and manipulate the environment of a { }^{\circ}reagent moiety.

Reagent moiety The portion of a { }^{\circ}reagent device that is intimately involved in a chemical { }^{\circ}reaction.

Receptor A structure that can capture a molecule (often of a specific type in a specific orientation) owing to complementary surface shapes, charge distributions, and so forth, without forming a { }^{\circ}covalent bond. See { }^{\circ}dissociation constant.

Reconstruction A crystal consists of a regular array of atoms, and the simplest model of a crystal surface would be generated by simply discarding all atoms to one side of a surface without changing the positions of the rest. In reality, however, the positions of the remaining atoms do change. A pattern of displacements that lowers the symmetry of the surface (relative to the ideally terminated crystal) is termed a surface reconstruction; some reconstructions alter the pattern of bonds.

Reduced mass Many dynamical properties of a system consisting of two interacting masses, m1m_{1} and m2m_{2}, are equivalent to those of a system in which one mass is fixed in space and the other has a mass (the reduced mass) with the value m1m2/(m1+m2)m_{1} m_{2} /\left(m_{1}+m_{2}\right). The reduced mass description has fewer dynamical variables.

Register A temporary storage location for an array of bits within a digital logic system.

Relaxation time A measure of the rate at which a disequilibrium distribution decays toward an { }^{\circ}equilibrium distribution. The electron relaxation time in a metal, for example, describes the time required for a disequilibrium distribution of electron momenta (e.g., in a flow- ing current) to decay toward equilibrium in the absence of an ongoing driving force and can be interpreted as the mean time between scattering events for a given electron.

Representative point The point in a { }^{\circ}configuration space that represents the geometry of a system.

Rigid structure As used in this volume, a { }^{\circ}covalent structure that is reasonably stiff. In a typical rigid structure, all modes of deformation encounter firstorder restoring forces resulting from some combination of bond stretching and angle bending; such a structure cannot undergo deformation by bond torsion alone. Meeting this condition usually requires a { }^{\circ}polycyclic { }^{\circ}diamondoid structure.

Salt bridge An ionic bond between charged { }^{\circ}groups that are part of larger { }^{\circ}covalent structures; salt bridges occur in many { }^{\circ}proteins.

Saturated An organic molecule is described as saturated if it is a closed shell species lacking { }^{\circ}double or { }^{\circ}triple bonds; forming a new bond to a saturated molecule requires the cleavage of an existing bond.

Scanning tunneling microscope A device in which a sharp conductive tip is moved across a conductive surface close enough to permit a substantial tunneling current (typically a nanometer or less). In a common mode of operation, the voltage is kept constant and the current is monitored and kept constant by controlling the height of the tip above the surface; the result, under favorable conditions, is an atomic-resolution map of the surface reflecting a combination of topography and electronic properties. The STM has been used to manipulate atoms and molecules on surfaces.

Self assembly A term commonly used for { }^{\circ}Brownian assembly.

Shear modulus Shear { }^{\circ}stress divided by shear { }^{\circ}strain; has the units of force per unit area.

Shear A shear deformation is one that displaces successive layers of a material transversely with respect to one another, like a crooked stack of cards. Shear is a dimensionless quantity measured by the ratio of the transverse displacement to the thickness over which it occurs.

Sigma bond AA^{\circ} covalent bond in which { }^{\circ}overlap between two atomic { }^{\circ}orbitals (e.g., of sp,sp2{ }^{\circ} s p, s p^{2}, or sp3s p^{3} hybridization) produces a single bonding orbital in which the distribution of shared electrons has a roughly cylindrical symmetry about the axis linking the two atoms; see pi{ }^{\circ} \mathrm{pi} bond, { }^{\circ}single bond, { }^{\circ}double bond, { }^{\circ}triple bond. By themselves, sigma bonds present little barrier to rotation of one substructure with respect to another, although { }^{\circ}steric effects and { }^{\circ}cyclic structures may hinder or block rotation.

Single bond A\mathrm{A}^{\circ} sigma bond having no associated pi{ }^{\circ} \mathrm{pi} bonds.

Singlet An electronic state of a molecule in which all spins are paired; see { }^{\circ}doublet, { }^{\circ}triplet.

sp,sp2,sp3s p, s p^{2}, s p^{3} \quad An isolated carbon atom has four { }^{\circ}valence { }^{\circ}orbitals: three mutually perpendicular pp orbitals, each with a single nodal plane, and one spherically symmetric ss orbital. A carbon atom in a typical molecule can be regarded as bonding with four orbitals consisting of weighted sums (termed hybrids) of these ss and pp orbitals. One common pattern has four equivalent orbitals, each formed by combining the three pp orbitals with the ss orbital; this is sp3s p^{3} hybridization. An sp3s p^{3} carbon atom forms four { }^{\circ}sigma bonds, usually in a roughly tetrahedral arrangement. Another common pattern has three equivalent orbitals formed by combining two pp orbitals with the ss orbital; this is termed sp2s p^{2} hybridization. An sp2s p^{2} carbon atom forms three roughly coplanar sigma bonds, usually separated by 120\sim 120^{\circ}, and one pi{ }^{\circ} \mathrm{pi} bond (or several fractional pi bonds). If a single pp orbital is combined with the ss orbital, the result is sps p hybridization, forming two sigma bonds and two pi bonds (usually in a straight line). Atoms of other kinds (e.g., N\mathrm{N} and O\mathrm{O} ) can hybridize in an analogous manner.

Species In chemistry, a distinct kind of { }^{\circ}molecule, { }^{\circ}ion, or other structure.

Stable Strictly speaking, a system is termed stable if no rearrangement of its parts can form a system of lower { }^{\circ}free energy. In practice, the term is used with an implicit proviso regarding the transformations to be considered. Hydrogen is not considered unstable merely because it is subject to nuclear fusion at extreme temperatures. A system is usually regarded as stable (more precisely, as kinetically stable) if its rate of transformation to a state of lower free energy is negligible (by some standard) under the ambient conditions. In { }^{\circ}nanomechanical systems, a structure can commonly be regarded as stable if it has an extremely low rate of transformations when subjected to its intended operating conditions.

State A physical system is said to be in a particular state when its physical properties fall within some particular range; the boundaries of the range defining a state depend on the problem under consideration. In a { }^{\circ}classical world, each point in { }^{\circ}phase space could be said to correspond to a distinct state. In the real world, time-invariant systems in { }^{\circ}quantum mechanics have a set of discrete states, particular superpositions of which constitute complete descriptions of the system. In practice, broader boundaries are usually drawn. A molecule is often said to be in a particular excited { }^{\circ}electronic state, regardless of its state of { }^{\circ}mechanical vibration. In { }^{\circ}nanomechanical systems, the PES{ }^{\circ} \mathrm{PES} often corresponds to a set of distinct { }^{\circ}potential wells, and all points in configuration space within a particular well can be regarded as one state. Definitions of state in the thermodynamics of bulk matter are analogous, but extremely coarse by these standards.

Statistical mechanics Statistical mechanics treats the detailed { }^{\circ}state of a system (its { }^{\circ}quantum state or, in { }^{\circ}classical models, its position in { }^{\circ}phase space) as unknown and subject to statistical uncertainties; { }^{\circ}entropy is a measure of this uncertainty. Statistical mechanics describes the distribution of states in an { }^{\circ}equilibrium system at a given { }^{\circ}tempera- ture (describing either the distribution of probabilities of quantum states or the { }^{\circ}probability density function in phase{ }^{\circ} \mathrm{phase} space), and can be used to derive { }^{\circ}thermodynamic properties from properties at the molecular level. These equilibrium results are useful in { }^{\circ}nanomechanical design.Steric Pertaining to the spatial relationships of atoms in a molecular structure, and in particular, to the space-filling properties of a molecule. If molecules were rigid and had hard surfaces, steric properties would merely be an opaque way of saying "shape"; a flexible sidechain, however, has definite steric properties but no fixed shape. { }^{\circ}Nanomechanical systems make extensive use of the steric properties of relatively rigid molecules, for which the term "shape" has essentially its conventional meaning so long as one remembers that the surface interactions are soft on small lengthscales.

Steric hindrance Slowing of the rate of a chemical { }^{\circ}reaction owing to the presence of structures on the { }^{\circ}reagents that mechanically interfere with the motions associated with the reaction, typically by obstructing the reaction site.

Stiffness The stiffness of a system with respect to a deformation (e.g., the stiffness of a spring with respect to stretching) is the second derivative of the energy with respect to the corresponding displacement; this measures the curvature of the { }^{\circ}potential energy surface along a particular direction. Positive stiffness is associated with stability, and a large stiffness can result in a small positional uncertainty in the presence of thermal excitation. Negative stiffnesses correspond to unstable locations on the potential energy surface. Alternative terms for stiffness include force gradient and rigidity.

STM A { }^{\circ}scanning tunneling microscope.

Strain In mechanical engineering, strain is a measure of the deformation resulting from { }^{\circ}stress (that is, force per unit area); the displacement of one point with respect to another, divided by their { }^{\circ}equilibrium separation in the absence of stress. In chemistry, a molecular fragment generally has some equilibrium geometry (bond lengths, interbond angles, etc.) when the rest of the molecular structure does not impose special constraints (e.g., bending bonds to form a small ring). Deviations from this equilibrium geometry are described as strain, and increase the energy of the molecule. Strain in the mechanical engineering sense causes strain in the chemical sense.

Stress Force per unit area applied by one part of an object to another. Pressure is an isotropic compressive stress. Suspending a mass from a fiber places it in tensile stress. Gluing a layer of rubber between two plates and then sliding one over the other (while holding their separation constant) places the rubber in { }^{\circ}shear stress.

Structural volume The interior of a { }^{\circ}diamondoid structure typically consists of a dense network of { }^{\circ}covalent bonds; aa larger { }^{\circ}excluded volume, however, is determined by nonbonded repulsions at the surface. The structural volume corresponds to a region smaller than the excluded volume, chosen to make properties such as the strength and { }^{\circ}modulus nearly size independent by correcting for surface effects.

Synthesis The production of a specific { }^{\circ}molecular structure by a series of chemical { }^{\circ}reactions.

System In scientific usage, usually equivalent to "a collection of matter and energy being analyzed as a unit." In engineering usage, usually equivalent to "a set of components working together to serve a set of purposes."

Temperature A system in which internal vibrational modes have equilibrated with one another can be said to have a particular temperature. Two systems A and BB are said to be at different temperatures if, when brought into contact, { }^{\circ}heat flows from (say) A to B, increasing the { }^{\circ}thermal energy of BB at the expense of the thermal energy of AA.

Thermal energy The internal energy present in a system as a result of the energy of thermally equilibrated vibrational modes and other motions (including both { }^{\circ}kinetic energy and molecular { }^{\circ}potential energy). The mean thermal energy of a classical { }^{\circ}harmonic oscillator is kTk T.

Thermal expansion coefficient The rate of change of length with respect to { }^{\circ}temperature for a particular material.

Thermal fluctuations The { }^{\circ}thermal energy of a system (or of a particular part or mode of motion in a system) has a mean value determined by the { }^{\circ}temperature and by the structure of the system. Statistical deviations about that mean are termed thermal fluctuations; these are of great importance in determining both rates of chemical { }^{\circ}reactions and error rates in { }^{\circ}nanomechanical systems.

Thermodynamics A field of study embracing energy conversion among various forms, including { }^{\circ}heat, { }^{\circ}work, and { }^{\circ}potential and { }^{\circ}kinetic energy.

Thermoelastic Both { }^{\circ}stress and { }^{\circ}temperature changes alter the dimensions of an object having a finite { }^{\circ}stiffness and a nonzero thermal expansion coefficient. Applying a stress then produces a temperature change; this can result in a heat flow which then changes the stress: these are thermoelastic effects, and result in losses of { }^{\circ}free energy.

Thiol An SH group, or a molecule containing one. Also known as a sulfhydryl or mercapto group.

Tight-receptor structures A receptor structure in which a bound ligand of a particular kind is confined on all sides by repulsive interactions (note that favorable binding energies are compatible with repulsive forces). A tight-receptor structure discriminates strongly against all molecules larger than the target.

Transition state At the saddle point of aa^{\circ} col linking two { }^{\circ}potential wells, the direction of maximum negative curvature defines the reaction coordinate; the transition state is a hypothetical system of reduced dimensionality, free to move only on a hypersurface perpendicular to the reaction coordinate at its point of maximum energy.

Transition state theory Any of several theories that give approximate descriptions of chemical { }^{\circ}reaction rates based on the PES{ }^{\circ} \mathrm{PES} of the system, and in particular, on the properties of two { }^{\circ}potential wells and { }^{\circ}transition state between them.

Triple bond A\mathrm{A}^{\circ} double bond is formed when a pi bond is superimposed on a { }^{\circ}single bond; adding a second pi bond results in a triple bond. The two pi bonds have perpendicular nodal planes, and their sum has roughly cylindrical symmetry, permitting rotation in much the same manner as a single bond.

Triplet An electronic state of a molecule in which two spins are aligned. This term is derived from spectroscopy: a system of two aligned spins has three possible orientations with respect to a magnetic field; each has a different energy, resulting in sets of three fielddependent spectral lines (see { }^{\circ}doublet, { }^{\circ}singlet.)

TST { }^{\circ}Transition state theory.

Tunneling A classical particle or system could not penetrate regions in which its energy would be negative, that is, barrier regions in which the { }^{\circ}potential energy is greater than the system energy. In the real world, however, aa^{\circ} wave function of significant amplitude may extend into and beyond such a region. If the wave function extends into another region of positive energy, the barrier is crossed with some probability; this process is termed tunneling (since the barrier is penetrated rather than climbed).

Unimolecular Occurring to or within a single molecule; like { }^{\circ}intramolecular, but can refer to fragmentation reactions.

Unsaturated Possessing { }^{\circ}double or { }^{\circ}triple bonds.

Valence electrons Electrons that can participate in bonds and in chemical reactions; { }^{\circ}lone-pair electrons are valence electrons, although not participating in a bond.

Valence In { }^{\circ}covalent compounds, the valence of an atom is the number of bonds it forms to other atoms.

Van der Waals force Any of several intermolecular attractive forces not resulting from ionic charges; in this volume, only { }^{\circ}London dispersion forces are described by this name. Descriptions of the potential energy of nonbonded interactions follow the convention of expressing van der Waals attractive forces and overlap repulsion forces as a single van der Waals potential.

Wave function In { }^{\circ}quantum mechanics, a complex function extending over the { }^{\circ}configuration space of a system; its complex conjugate yields the { }^{\circ}probability density function, and other mathematical operations yield other physical quantities.

Work Energy transferred by applying a force over a distance; lifting a mass does work against gravity, and stores gravitational { }^{\circ}potential energy.

Young's modulus A\quad \mathrm{A}^{\circ} modulus relating tensile (or compressive) { }^{\circ}stress to { }^{\circ}strain in a rod that is free to contract or expand transversely in accord with its { }^{\circ}Poisson's ratio. The relevant measure of strain is the elongation divided by the initial length.

Footnotes

  1. This system is modeled on Atkins (1974).

  2. Some textbooks state a slightly weaker form: a reaction that converts perfect crystals at absolute zero into other perfect crystals at absolute zero results in no change in entropy. This is essentially equivalent.