Foundations

Halogens and halides have distinct oxidizing and reducing roles; for example, chlorine can oxidize bromide under suitable solution conditions.

In the elementary alkene hydroboration model, C–H and C–B bonds form together from the same face without a free carbocation intermediate.

Adding hydration equivalents to an alkyne initially produces an enol, which can tautomerize to a carbonyl compound.

A nucleophile can add to an activated aryl system, forming an anionic intermediate before leaving-group elimination restores aromaticity.

An amine's basicity can be described by the acidity of its conjugate ammonium species under specified conditions.

In chain-growth polymerization, monomer addition regenerates a growing active centre.

Step-growth polymerization joins compatible functional groups on monomers and oligomers rather than requiring all growth at one persistent chain centre.

For a reversible one-to-one receptor/ligand interaction at equilibrium, the dissociation constant relates free receptor, free ligand and complex concentrations.

Ligand binding at one site can alter affinity or activity at another through coupling of protein states.

Coulometry infers reacting amount from integrated charge and electron stoichiometry.

Voltammetry records current while controlling the working-electrode potential relative to a reference; a counter electrode carries the balancing current.

Fluorescence emission follows optical excitation while competing with nonradiative relaxation.

Oxidation states assign electrons formally rather than measuring atomic partial charge.

For a balanced redox reaction transferring n electrons per reaction event, the molar reaction Gibbs energy is ΔrG=−nFE at the same temperature and composition when E is its reversible cell potential.

A semicrystalline polymer contains ordered crystallites and amorphous material.

For an ideal linear step-growth model, the number-average length Xn counts monomer-derived units per product molecule, including unreacted monomers in the counted population.

Green chemistry evaluates product and process design to reduce hazardous inputs, releases and waste over a stated lifecycle.

Theoretical atom incorporation and actual process material use answer different questions.

For a normalized trial state of the same Hermitian, lower-bounded Hamiltonian, the Rayleigh energy cannot be below its ground-state energy.

Basis convergence must be tested separately for SCF and correlation contributions.

Small energy and orbital-gradient residuals identify a stationary SCF solution, which may be unstable to allowed orbital rotations.

A larger orbital basis does not remove exchange-correlation functional error.

Counterpoise compares the complex energy with fragment energies evaluated in the complex basis, including partner basis functions without partner nuclei.

Near electronic degeneracy, nuclear motion can couple electronic states through derivative couplings, so a single Born–Oppenheimer potential surface can fail.

A computed vertical electronic excitation is not automatically a measured spectral maximum.

In classical transition-state trajectory counting, recrossing the dividing surface reduces the fraction of nominal crossings that contributes to net reaction; this recrossing transmission coefficient is bounded by one.

In an overdamped diffusive reaction-coordinate model, the flux contains both potential-driven drift and concentration spreading.

The classical harmonic reorganization model gives an electron-transfer barrier depending jointly on driving force and reorganization energy.

Species transport is driven by chemical and electrical contributions to electrochemical potential.

A dilute-solution Nernst–Planck flux combines diffusion, electric migration and convection.