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Transfer of an oxidant oxygen atom to an unsaturated substrate, including controlled formation of an epoxide.

Isotope abundance, nuclear separation energies, spin and nuclear magnetic moments supply complementary tests: abundance concerns which atomic nuclei survive and accumulate, removal energy concerns binding, and magnetic properties test the angular momentum assignments. Agreement across these observables is more informative than fitting one list of numbers.

In her 1963 lecture, Maria Goeppert Mayer recalled excess abundances at $N=50$ and $82$. She contrasted the strong binding of the last neutron in oxygen isotope ${}^{16}\mathrm{O}$ with the weaker extra neutron in oxygen isotope ${}^{17}\mathrm{O}$, and displayed beta decay energies near $N=20$ and $50$. These are compiled empirical patterns, rather than readings from an apparatus she built.^[ref]

Her 1949 letter compared observed spins and nuclear magnetic moments with orbital assignments. For example, lead isotope ${}^{207}\mathrm{Pb}$ was assigned a $p_{1/2}$ neutron hole near $N=126$, whereas bismuth's odd proton began the next shell as $h_{9/2}$. The moments tested orbital character as well as spin.^[ref]

A useful comparison holds $Z$ fixed when comparing neighboring isotopes, and examines odd-even staggering separately from a shell discontinuity. Abundance additionally depends on production and decay history. Neither the abundance pattern nor a successful spin assignment directly images orbiting particles; neither fixes a unique nuclear mean field. The experimental techniques themselves include mass spectrometry and nuclear magnetic resonance, whose preparation and readout differ. The Hofstadter nuclear electron scattering experiment separately constrains nuclear size and nuclear charge distributions, rather than measuring these occupancies.

By National Institute of Standards and Technology. Handbook of Basic Atomic Spectroscopic Data, neutral oxygen O I table.

The first configuration block specifies $2s^{2}2p^4{}^3{P}_2$ as the zero-energy level, followed by its $J=1,0$ fine-structure partners.

Enolate alkylation forms a carbon–carbon bond by attack of an enolate carbon on an alkyl electrophile, commonly through an SN2 reaction. Solvent, counterion, aggregation and electrophile identity affect competition with oxygen alkylation.

An ether with oxygen directly attached to an alkene carbon. Electrophilic activation and hydrolysis can convert an appropriate enol ether back to a carbonyl compound.

The carboxylic acid-derived ester linkages in a triglyceride or typical glycerophospholipid have the form $\mathrm{R}-\mathrm{C}(=\mathrm{O})-\mathrm{O}-{\mathrm{R}}^{\prime }$. Here the acyl group is attached through oxygen to the glycerol-derived part. See IUPAC Blue Book, P-65.6: esters.

An ethoxy group is $-\mathrm{OC}{\mathrm{H}}_2\mathrm{C}{\mathrm{H}}_3$. An aryl ethoxy group can donate an oxygen lone pair into an aromatic ring.

Evolution is descent with inherited modification. Within a population, changes in allele frequencies provide a precise genetic description; over longer histories, branching descent connects populations through common descent. An individual growing larger is biological development, whereas an inherited variant becoming more frequent across generations is evolution. See UC Museum of Paleontology: the definition of evolution.

Mutation supplies new alleles, genetic recombination reshuffles inherited material, natural selection favors variants with greater reproductive contribution in a specified environment, and genetic drift changes frequencies through chance. Gene flow moves variants between populations. Consequently, an increasing allele frequency alone does not identify natural selection. See Clark, Douglas and Choi, Biology 2e: population genetics.

Evidence includes ordered fossils, shared inherited structures and similarities in DNA; phylogenetics uses such observations to infer relationships. A phylogenetic tree is an inferred historical account, with uncertainty about particular branches. See Clark, Douglas and Choi, Biology 2e: evidence of evolution. Evidence also comes from experiments: Blount, Borland and Lenski reported an Escherichia coli lineage able to use citrate with oxygen present by 31,500 generations, and tested historical dependence by replaying evolution from stored ancestors. See Blount, Borland and Lenski, 2008: original experimental report. Such observations constrain explanations; no single frequency equation captures every evolutionary process.

The formal charge of a chemical atom in a Lewis structure assigns it all of its nonbonding electrons and half of the electrons in its connections:Here $v$ is the neutral chemical atom's valence electron count, $n$ is the number of nonbonding electrons assigned to it, and $b$ is the number of bonding electrons incident on it. Count electrons, not electron pairs: two lone pairs mean $n=4$, and two double connections mean $b=8$. The number $\mathrm{FC}$ gives electric charge in units of the positive elementary charge. Equal splitting is a bookkeeping convention, regardless of the actual electron density. See the IUPAC Gold Book, formal charge.

For $\mathrm{O}=\mathrm{C}=\mathrm{O}$, each oxygen has $v=6$, $n=4$, $b=4$, giving formal charge $6-4-4/2=0$. Carbon has $v=4$, $n=0$, $b=8$, giving formal charge $4-0-8/2=0$. For ${\mathrm{O}}^{-}-\mathrm{C}\equiv {\mathrm{O}}^{+}$, the left oxygen has formal charge $6-6-2/2=-1$, carbon still has formal charge zero, and the right oxygen has formal charge $6-2-6/2=+1$. The net electric charge is zero in either drawing.

The Lewis structure with no separated formal charges is the dominant contributor in this elementary comparison; the charge-separated drawing is a less important contributor, rather than an equally dominant alternative. This is a qualitative selection rule, not a calculation of energy or numerical chemical resonance weights. See Flowers et al., Chemistry 2e, 7.4: comparing carbon dioxide structures. A zero formal charge does not imply zero partial atomic charge: the latter depends on partitioning the actual electron density, which a Lewis structure does not supply.

As a short consistency derivation, summing $n+b/2$ over all chemical atoms counts every drawn electron once: a nonbonding electron is assigned once, and a bonding electron contributes half at each of its two endpoints. Thuswhere $N_{\mathrm{valence}}$ is the total drawn valence electron count. The right side is the net electric charge in units of elementary charge. This catches a wrong budget even when individual octet rule checks look plausible.

For a chosen homogeneous composition ${\mathrm{La}}_{2-x}{\mathrm{Ba}}_x{\mathrm{CuO}}_{4-\delta }$, assign formal oxidation states $+3$ to lanthanum, $+2$ to barium and $-2$ to oxygen. If $v$ is the mean formal copper oxidation state, charge neutrality requiresThe excess formal positive charge per copper relative to $+2$ is therefore $p_{\mathrm{formal}}=x-2\delta$. For stipulated $x=0.12$ and $\delta =0.01$, it is $0.10$; at $\delta =0.06$, it is zero. These are bookkeeping examples, not measurements of mobile carriers. The symbol $x$ here belongs to this declared formula, not the original mixed-phase recipe. A whole-pellet elemental ratio cannot simply be assigned to each constituent phase.

Charge neutrality alone does not locate holes. The lecture reviews oxygen-related carrier evidence and charge-$2e$ pairing from the Josephson effect and fluxoid and flux quantization in a superconductor. Pair charge does not establish phonon-mediated BCS theory for cuprate superconductors.^[ref]

Glucose is a monosaccharide with molecular formula ${\mathrm{C}}_6{\mathrm{H}}_{12}{\mathrm{O}}_6$. Its familiar biological form, D-glucose, is an aldohexose. In the open-chain Fischer projection, $\mathrm{CHO}$ is at the top and ${\mathrm{CH}}_2\mathrm{OH}$ at the bottom; the hydroxy groups at C2, C3, C4, and C5 point right, left, right, right. This full pattern distinguishes D-glucose from other six-carbon aldehyde sugars. See McMurry, Organic Chemistry, 25.4: configurations of the aldoses.

The molecular formula can be checked directly: one $\mathrm{CHO}$ group, four $\mathrm{CHOH}$ groups, and one ${\mathrm{CH}}_2\mathrm{OH}$ group give six carbon, twelve hydrogen, and six oxygen chemical atoms. All four interior carbon positions are stereocenters in this open-chain structure. Neither their orientations nor the arrangement of chemical bonds can be recovered from the molecular formula alone.

In water, glucose exists mainly in six-membered rings in chemical equilibrium with a small amount of open-chain glucose. Ring closure connects the hydroxy group at C5 to the aldehyde carbon at C1; the ring contains five carbon chemical atoms and one oxygen, with C6 outside it. No chemical atoms are lost, so the molecular formula remains ${\mathrm{C}}_6{\mathrm{H}}_{12}{\mathrm{O}}_6$. See McMurry, Organic Chemistry, 25.5: cyclic structures of monosaccharides.

Glucose is useful both as a substrate in cellular metabolism and as a building block of polysaccharides. Cellulose chains assembled from glucose units help support plant cell walls. The same small sugar thus connects chemical fuel to a structural material; its role depends on how it is transformed or linked. See Cooper, The Cell: A Molecular Approach, the molecular composition of cells.

Glutamine has a neutral side-chain amide. Its N–H groups can donate hydrogen bonds and its carbonyl oxygen can accept them; its amide nitrogen is not an ordinary amine base.

Glycolysis converts one glucose into two pyruvates, yielding two net ATP and reducing two NAD+ to two NADH in the canonical pathway. It first spends two ATP, then produces four by substrate-level phosphorylation. The pathway itself consumes no molecular oxygen; sustained operation nevertheless requires regeneration of NAD+.^[ref]

The useful organizing idea is three separate ledgers: carbon chemical atoms, transfers between ADP and ATP, and redox transfers between NAD+ and NADH. Splitting the carbon skeleton doubles the number of downstream conversions; recycling a cofactor permits repeated operation. These counts explain the yield without memorizing a drawing of every enzyme. The two net ATP belong to glycolysis alone, not to complete cellular respiration.

In the payoff stage of glycolysis, oxidation of glyceraldehyde 3-phosphate is coupled to reduction of NAD+. Each NADH carries a two-electron reducing equivalent. The formal half-chemical equationmakes the electron count explicit: two NADH per glucose carry four electrons. This is redox bookkeeping, not a claim that free electrons travel through the chemical solution or that NADH is itself ATP.

Fermentation can return NADH to NAD+ by reducing an organic substrate; reduction of pyruvate to lactate is one example. In aerobic cellular respiration, reducing equivalents reach an electron transport chain, reducing molecular oxygen. Other forms of cellular respiration use other electron acceptors, so absence of oxygen does not uniquely imply fermentation.^[ref]

The need for NAD+ regeneration follows from a finite-pool argument. In a hypothetical closed preparation with $12\mu \mathrm{mol}$ of initially oxidized NAD+ and no regeneration, at most $6\mu \mathrm{mol}$ of glucose can complete the two NAD+-consuming conversions per glucose. This is an upper bound even with excess glucose, not a predicted stopping time: other limitations can stop the preparation earlier. With an intact fixed nicotinamide adenine dinucleotide pool and no side reactions, converting NAD+ into NADH preserves their sum but depletes the usable oxidized form.

ATP recycling imposes a second condition. Glycolysis needs some initial ATP for investment and consumes two net ADP and two inorganic phosphate per completed glucose. In a closed ideal preparation with only $8\mu \mathrm{mol}$ of initial ADP, no other source of ADP, and enough initial ATP and inorganic phosphate, at most $4\mu \mathrm{mol}$ of glucose can finish. This bound follows from the net ADP consumption, even though investment temporarily produces additional ADP. Initial investment also means that adequate final inventories alone cannot guarantee the route can start.

For continued operation at fixed carrier inventories, other chemical reactions must match the two net ATP formed per glucose with ATP use that restores ADP and inorganic phosphate, or exchange must supply those reactants. ATP hydrolysis coupled to cellular work is one route. Thus glycolysis can sustain useful energy coupling while neither its ATP inventory nor its NADH inventory grows indefinitely; matter cycles while glucose supplies fresh chemical free energy.

An oxocarbenium ion at the anomeric carbon of a cyclic glycosyl fragment. Positive charge is delocalized between that carbon and the ring oxygen. A counterion can remain nearby and influence which face a nucleophile approaches.

A Lewis acid whose acceptor interaction favours small, weakly polarizable donor atoms. High charge density favours hard character; Eu(III) typically favours oxygen and nitrogen donors over a softer sulfur donor.

A helium-burning shell converts helium into carbon and oxygen outside a helium-exhausted stellar core. Thin-shell burning on the Asymptotic giant branch can develop a thermal pulse of an asymptotic-giant-branch star.

The helium mass fraction is the fraction of a material's mass carried by helium nuclei. Hydrogen burning raises it, whereas core helium burning lowers it while producing carbon and oxygen.

Hemoglobin is an oxygen-binding protein; its oxygenation can supply a spectroscopic molecular oxygen readout, as in the early Hill reaction work.

A prism with two hexagonal faces and six quadrilateral side faces. Its twelve vertices and eighteen edges provide an alternating aluminium–oxygen cage model when the graph is coloured bipartitely.