Foundations

A primary amine adds to a suitable aldehyde or ketone and dehydration of the carbinolamine produces an iminium intermediate, which can lose an N proton to give an imine.

Alcohol addition to a carbonyl forms a hemiacetal.

In a Wittig transformation, a phosphorus ylide and an aldehyde or ketone give an alkene and a phosphine oxide.

For identical sample aliquots diluted to a common final volume, blank-corrected linear response satisfies S=k(c₀V₀+cstdVstd)/Vf.

A distinct internal standard added to standards and samples permits calibration of SA/SIS=K cA/cIS, where K is the relative response.

An extraction distribution ratio D compares total solute concentrations in two immiscible phases.

In a buffered capillary, an analyte's velocity combines electrophoretic migration with electroosmotic solvent motion: v=(μep+μeo)E.

Atomic absorption measures attenuation at element-specific transitions after atomization.

Potentiometry measures the potential difference between an analyte-responsive indicator electrode and a reference electrode with negligible measurement current.

Aminoacyl-tRNA synthetases couple amino acids to cognate tRNAs using ATP-dependent activation.

A protein sequence and its chemical environment constrain a conformational energy landscape.

Rubisco's oxygenase activity produces a three-carbon phosphoglycerate and a two-carbon phosphoglycolate from RuBP.

In a common C4 route, PEP carboxylation supplies four-carbon acids that deliver CO₂ to Rubisco in a spatially separated compartment.

A molecular internal partition function sums the Boltzmann weights and degeneracies of its internal states.

A linear rigid rotor has rotational levels proportional to J(J+1), with magnetic degeneracy 2J+1.

For one harmonic normal mode, a geometric sum gives its vibrational partition function.

In an electric-dipole description, a pure rotational transition requires a molecular permanent dipole, while a normal-mode vibrational transition requires a changing dipole along that coordinate.

An electronic transition is fast relative to nuclear motion, so its initial nuclear coordinates are approximately unchanged during the transition.

In an isotropic Fickian transport model, diffusive mass flux is proportional to the negative local mass-density gradient.

Matrices representing symmetry operations on a chosen basis must reproduce group composition.

A transition matrix element ⟨initial|O|final⟩ can be nonzero only when Γinitial*⊗Γoperator⊗Γfinal contains the totally symmetric representation.

Coordination compounds can share composition while differing in ligand connectivity or spatial arrangement.

Neutral-fragment and oxidation-state counting consistently allocate ligand and metal electrons when their conventions are used throughout.

Dissociative ligand substitution loses a ligand before addition, while an associative route adds an incoming ligand before loss.

Ligand-field MO models combine metal and ligand orbitals with compatible symmetry, adding covalent interactions beyond a point-charge crystal field.

Hydrogen in an ionic hydride is formally H− and can act as a strong base or reducing species; proton transfer with water produces hydrogen gas and hydroxide.

Boron trihalides have trigonal-planar molecular reference structures and can accept donor electron pairs; BF3 and fluoride form BF4−.

Nitrogen forms oxides with several formal oxidation states.

Phosphorus(III) and phosphorus(V) oxides have different oxygen content and formal oxidation states.

Oxide O²−, peroxide O₂²− and superoxide O₂− contain different numbers and arrangements of oxygen atoms and electrons.