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polysulfur has a chain of S–S sigma bonds with filled lone-pair orbitals. Its occupied states do not supply a partly filled delocalized band, so the chain is an electrical insulator.

In polythiazyl, an approximately planar S–N chain permits overlap of orbitals perpendicular to the backbone. In an elementary pi bond electron picture, nitrogen supplies one electron and sulfur two to this manifold: three pi electrons per SN unit, rather than a completely filled, isolated two-centre bonding pair. The extended states are therefore not all fully occupied. More realistic descriptions include the crystallographic repeat, interchain interactions and overlapping bands crossing the Fermi level; the odd electron count of a chosen chemical repeat is suggestive, not by itself a proof of metallicity.

The essential distinction is occupied, localized bonding/lone-pair states in sulfur chains versus available extended states at the Fermi level in crystalline sulfur nitride. The measured high conductivity along the polymer fibres and its metallic temperature dependence provide the experimental basis, alongside the structural evidence for the chain. Conductivity depends on order and defects as well as chemical composition.^[ref]

The initial nucleophile attacks silicon, not the nitrile or an alkene carbon. Each trimethylsilyl group has an electrophilic Si center. A methyl group from methyllithium attacks Si, passing through a pentacoordinate silicon arrangement; Si–O cleavage releases $\mathrm{SiM}{\mathrm{e}}_4$ and the lithium salt of the oxygen-containing fragment. Cleaving the silyl enol ether generates a lithium enolate; cleaving the aryl silyl ether generates a phenoxide. Neither operation needs a new deprotonation at a carbon stereocenter.Here $R-O^{-}$ represents either the phenoxide or the oxygen-centered enolate contributor. Excess reagent permits both cleavages. The pre-existing methyl/nitrile stereocenter retains its configuration: it has no hydrogen to remove, and neither bond attached to that center is broken.

After HMPA is added, each anionic oxygen attacks the carbonyl carbon of allyl chloroformate. The C=O pi electrons move to the carbonyl oxygen, giving a tetrahedral intermediate; collapse expels chloride. The enolate becomes an allyl enol carbonate, and the phenoxide becomes an aryl allyl carbonate, each containing $\mathrm{O}-\mathrm{C}(\mathrm{O})-\mathrm{OC}{\mathrm{H}}_2\mathrm{CH}=\mathrm{C}{\mathrm{H}}_2$. oxygen acylation accounts for preservation of the enol double bond and for the two newly installed carbonate groups. carbon attack would give a different carbon skeleton. The two oxygens are trapped because they were selectively unmasked by desilylation, rather than because every ether oxygen in the molecule is equally reactive.

Lithium diisopropylamide removes an alpha proton from the ethyl side of the ketone. The C–H electrons form the C=C part of a lithium enolate, while the C=O pi electrons move to oxygen. The phenyl side has no competing alpha C–H site. Diisopropylamine is the conjugate-acid byproduct.The carbon end of this enolate attacks the primary carbon bearing iodine in $\mathrm{IC}{\mathrm{H}}_2\mathrm{C}{\mathrm{H}}_2\mathrm{C}{\mathrm{H}}_2\mathrm{OMe}$. The C–I bond breaks to iodide in an SN2 reaction, and carbonyl reformation givesThus a three-carbon methoxypropyl chain is attached at the ketone alpha carbon. The remote methyl ether survives. The hindered amide base is chosen to generate the enolate rather than to add to the carbonyl. No absolute stereochemical preference is specified for the new stereocenter under these achiral conditions.

The carbamate carbonyl oxygen attacks electrophilic sulfur of triflic anhydride, with cleavage of the anhydride S–O bond to release triflate. Donation of the nitrogen lone pair toward the carbonyl carbon then gives the indicated imidoyl-type cation: the former carbonyl oxygen now bears Tf, and the N–H nitrogen participates in a C=N${}^{+}$ bond. This converts a relatively unreactive carbamate carbonyl into a strongly electrophilic carbon bearing an excellent leaving group.

The aromatic pi bond para to ethoxy attacks that carbon. The C=N pi electrons move to nitrogen as the new aryl–carbon bond forms. Loss of the aromatic proton restores aromaticity; nitrogen donation and departure of the O-triflylated group restore the imine bond. proton transfers during the sequence and carbonate workup remove the remaining N–H proton. The surviving five-membered ring is an oxazoline: the product is 2-(4-ethoxyphenyl)-2-Oxazoline. An equivalent arrow order can eliminate the triflyloxy leaving group before arene capture; these are limiting descriptions of the activated electrophile, not a need to postulate an unactivated carbamate undergoing ordinary Friedel–Crafts acylation.

Ethoxy donates a lone pair into the ring, stabilizing the ortho and para Wheland intermediates. The para pathway avoids the crowding of an incoming heterocycle beside ethoxy, giving the observed position. Mechanistic experiments on this transformation include in situ carbon NMR of the activated reagent, competition experiments and isotope-effect measurements supporting electrophilic aromatic substitution; they do not directly image every intermediate.^[ref]

In the strongly acidic nitrating mixture, the dimethylamino nitrogen is predominantly protonated. The substituent is therefore $-\mathrm{NM}{\mathrm{e}}_2{\mathrm{H}}^{+}$ during aromatic substitution, rather than the neutral electron-donating $-\mathrm{NM}{\mathrm{e}}_2$ group. Its lone pair is unavailable for conjugation. Ortho or para attack would generate a sigma-complex contributor with positive ring charge at the carbon attached to an already positive nitrogen; meta attack avoids that especially unfavorable contributor.

Sulfuric acid protonates nitric acid, and loss of water produces the nitronium ion. Aromatic attack at a meta position forms a Wheland intermediate; deprotonation restores aromaticity. The bicarbonate workup then returns the amino group to its neutral form. $A$ is 3-nitro-N,N-dimethylaniline.

There are six inequivalent aromatic carbons in this unsymmetrical meta-disubstituted ring and one carbon environment for the two equivalent N-methyl groups, giving seven carbon NMR signals. The para isomer would have only four aromatic environments plus the methyl environment. An ortho isomer could also give seven signals, so signal counting supports but does not alone establish the meta assignment; protonation-dependent directing effects are essential.

The same base first makes $\mathrm{Ph}{\mathrm{C}}^{-}(\mathrm{OPh})\mathrm{CN}$. This time addition occurs at a carbon bearing hydrogen para to the nitro group, giving a sigma-H adduct. The attacked carbon temporarily bears both its original H and the new carbon substituent. Negative charge is again delocalized through the ring toward the nitro oxygens.

A further base removes the hydrogen on that aromatic addition site. Its C–H electrons form an exocyclic bond toward the incoming carbon, while that carbon expels phenoxide. This is a base-induced elimination across the new ring–side-chain bond. Redistribution of the nitronate/quinoid pi system restores an aromatic ring and gives the side-chain carbanion $\mathrm{p}-\mathrm{N}{\mathrm{O}}_2{\mathrm{C}}_6{\mathrm{H}}_4-{\mathrm{C}}^{-}(\mathrm{Ph})\mathrm{CN}$. protonation during acidic workup yields $\mathrm{p}-\mathrm{N}{\mathrm{O}}_2{\mathrm{C}}_6{\mathrm{H}}_4-\mathrm{CH}(\mathrm{Ph})\mathrm{CN}$.

This is vicarious nucleophilic substitution: the ring loses hydrogen while the nucleophile sacrifices its phenoxy leaving group. hydrogen is not expelled as hydride, and the product's side-chain hydrogen can be supplied on workup rather than moving directly from the ring in a compulsory hydride shift. Base and isotope experiments in the primary mechanistic work support reversible addition followed by base-induced elimination, while not uniquely choosing every E2/E1cb limit.^[ref] The displayed para product is consistent with access to the less crowded activated position.

Base again generates $\mathrm{Ph}{\mathrm{S}}^{-}$ catalytically. In $\mathrm{P}{\mathrm{h}}_2\mathrm{P}(\mathrm{O})-\mathrm{CH}=\mathrm{C}=\mathrm{C}{\mathrm{H}}_2$, attack at the central allene carbon moves the adjacent C=C pi electrons onto the phosphorus-bearing carbon. This makes the stabilized alpha-phosphoryl carbanionprotonation at that carbon gives $\mathrm{P}{\mathrm{h}}_2\mathrm{P}(\mathrm{O})-\mathrm{C}{\mathrm{H}}_2-\mathrm{C}(\mathrm{SPh})=\mathrm{C}{\mathrm{H}}_2$, the second product drawn above. The remaining double bond is terminal, so no E/Z pair is possible. The new sulfur bond is at the central carbon of the original allene, not at the terminal methylene.

This regiochemistry places the developing negative charge beside the electron-withdrawing phosphine-oxide group, instead of at a less stabilized vinylic position. It is an ionic addition/proton-transfer cycle, rather than radical thiol–ene chemistry. proton donation by another thiophenol molecule regenerates thiolate. One thiophenol is incorporated without loss of atoms, giving ${\mathrm{C}}_{21}{\mathrm{H}}_{19}\mathrm{OPS}$.

The alkene undergoes concerted oxygen transfer from the terminal peroxide oxygen of mCPBA. In the cyclic electron-flow description, the alkene pi bond begins one C–O bond, the peroxide oxygen supplies the second, O–O breaks, and proton transfer/carboxyl rearrangement gives m-chlorobenzoic acid. Both C–O bonds are installed from the same alkene face, so the alkene's relative substituent geometry is retained in the epoxide. There is no freely rotating carbocation intermediate.

The neighboring free OH hydrogen-bonds to the approaching peracid and favors a cyclic, organized transition-state geometry. oxygen is delivered from the OH-directed face, giving the indicated syn relationship between epoxide oxygen and the allylic hydroxyl. In the supplied projection, the epoxide C–O bonds and the original C–OH bond are on the rear/hashed face. Steric interactions still influence the preferred hydrogen-bonded conformer, but “attack from the least hindered face” alone misses the positive directing role of OH. The distant benzyl ether is not the directing free hydroxyl.

The classical experimental comparison of allylic alcohols and protected derivatives established this directing principle; it supports the mechanistic interpretation without itself measuring the selectivity of this acyclic substrate.^[ref]

The alcohol oxygen attacks sulfur of methanesulfonic anhydride. Cleavage of the anhydride S–O bond releases methanesulfonate, and the amine base removes the O–H proton, giving the corresponding mesylate. This activation preserves the substrate C–O bond while replacing the poor hydroxide leaving group by $\mathrm{OS}{\mathrm{O}}_2\mathrm{Me}$.

The base then removes a hydrogen from the adjacent methylene on the side toward the vinyl chloride. In a favorable antiperiplanar arrangement, C–H electrons form the new C=C bond while the C–OMs bond breaks. An E2 elimination creates the alkene between the former alcohol carbon and that methylene. It links the two neighboring unsaturated regions into the extended conjugated triene segment, while the pre-existing carbon skeleton and vinyl chloride are retained.The left-hand polyenoate portion is unchanged. The base is diisopropylethylamine; it accepts acid during mesylation and promotes elimination. The product's E/Z mixture concerns the newly formed alkene, and no single geometry needs to be assigned.

4-Fluorophenol probes acceptor strength because it donates its OH hydrogen. The qualitative order is C $>$ D $>$ B $>$ A: the electron-rich lactam oxygen is the strongest acceptor here, the secondary amine is next, pyridine nitrogen is intermediate, and aldehyde oxygen is weakest. Resonance donation from amide nitrogen increases the lactam oxygen's basicity relative to an ordinary aldehyde or ketone oxygen. The N-methylpyrrole site in A does not add an independent amine-like acceptor.

N-Methylpyrrolidin-2-one is a carbonyl acceptor without N–H, so it instead probes the solute's donor ability. B $>$ C $\gg$ A and D: B's phenolic OH is a strong donor, the lactam N–H of C is appreciable, A lacks a conventional donor, and D's neutral secondary-amine N–H is weak. The amine can be a good acceptor and a poor donor at the same time; the two properties are not opposites on one scale.

These are association equilibria in cyclohexane, where solvent competition for hydrogen bonds is weak. The quoted constants should be compared within each probe series, not treated as solvent-independent measures. At 298 K, as an illustrative common temperature, a tenfold increase in $K_a$ corresponds to a binding free-energy advantage $RT\ln 10\simeq 5.7\mathrm{kJ}\mathrm{mo}{\mathrm{l}}^{-1}$. This does not imply the experiment's temperature was specified, nor that every difference is the energy of one isolated hydrogen bond.

The reactive fragment is the C6 amidine-like portion of the purine ring; the N9–ribose attachment is retained. Write it locally as $N1=C6(\mathrm{N}{\mathrm{H}}_2)-$, with the rest of the fused ring understood. One productive acid catalysis route protonates N1, making C6 more electrophilic. water then adds at C6 while the C6=N1 pi electrons move onto N1. Subsequent proton transfers generate a carbinolamine and then a protonated amino leaving group:These are local bonding fragments: C6 retains its bond to the adjoining ring carbon at every step. In the addition step, an oxygen lone pair forms C6–O and the C6=N1 pi bond opens. During collapse, an oxygen lone pair reforms C6=O and the C6–N6 bond breaks toward the departing nitrogen. Solvent mediates each proton transfer; no direct unsupported transfer across a long distance is required.

water supplies the new C6 oxygen, and ammonia is expelled after protonation of the leaving group. Final deprotonation gives the lactam form of inosine. In acidic bulk solution the released ammonia is largely trapped as ammonium. The catalytic proton transfers regenerate acid around the substitution cycle; ammonium trapping separately affects the net proton balance. This is hydrolytic deamination, not cleavage of the glycosidic bond.

A chemically coherent mechanism combines zinc-activated water addition with a proton relay involving His238 and Glu217. In a simple route consistent with the displayed contacts, neutral His238 accepts a proton from zinc-bound water while protonated Glu217 donates to substrate N1. These transfers can be coupled to the bond-forming event rather than requiring accumulation of a free, doubly activated substrate. Zinc-bound hydroxide attacks C6; the C6=N1 pi electrons move onto N1, yielding the tetrahedral C6 intermediate bearing OH and NH${}_2$ while N1 bears H.

Next, the exocyclic amino group receives a proton, through His238, Glu217 and/or intervening water as permitted by the changing geometry. The oxygen is deprotonated as it forms the C6 carbonyl, and the C6–N6 bond cleaves to release ammonia. These transfers can be coupled in the collapse step, avoiding expulsion of $\mathrm{N}{\mathrm{H}}_2^{-}$. Zinc stabilizes the reacting oxygen and the organized intermediate; the ring regains conjugation in the inosine product. Product dissociation, fresh water binding and proton exchange with solvent reset the catalytic groups.

The core result is zinc-assisted addition–elimination, with acid/base proton transfers and water supplying C6 oxygen. The contributions are metal ion catalysis, general base catalysis, general acid catalysis, electrostatic catalysis and proximity and orientation catalysis. The proposed route does not require covalent catalysis by a protein side chain: a substrate–water C–O bond is not an enzyme–substrate covalent linkage. Asp296 can retain a structural hydrogen-bonding role without acting as an indispensable acid/base.

The data establish the importance of His238 and Glu217 but do not uniquely assign the entire proton relay. In particular, an alternative has Glu217 first deprotonate water and then deliver that proton to N1, with His238 assisting hydroxide stabilization and later amino-group protonation. The primary observation that His238 substitution need not abolish analogue hydration cautions against calling its initial-base role proven.^[ref] pH-rate profiles, solvent isotope effects and time-resolved intermediate experiments would discriminate these refinements. The diagram is a proposed catalytic route, not a structure directly observed by the crystal experiment.

A suitable structure is a triangular Ti${}_3$ metal cluster with one 1,2-Bis(dimethylphosphino)ethane chelate and one terminal chloride at each titanium, and one bridging ligand $\mu$-Cl spanning each edge. Include a direct Ti–Ti single metal-metal bond along each edge. The last panel distinguishes these direct bonds from the chloride bridges.

The six chlorides have total formal charge $-6$, so equivalent centers are Ti(II), $d^2$. At each titanium the two phosphorus donors supply four electrons, the terminal chloride supplies two, and the two incident chloride bridges each donate a pair in ionic electron counting. Two incident Ti–Ti single bonds supply another two electrons:Each $d^2$ center can contribute one electron to each of its two edge bonds, making three bonds from six metal electrons overall. This is a 14-electron early-metal cluster, not an 18-electron complex. Forcing the 18-electron rule here would invent excessive bond orders. chloride bridges donate to more than one center, so summing local counts is not the same as counting distinct electrons of the whole cluster.

Use an ${\eta }^5$ cyclopentadienyl ligand and four terminal carbonyl ligands at each titanium, with a Ti–Ti single metal-metal bond. The middle panel shows this connectivity. Neutral electron counting assigns five electrons to each Cp and givesEquivalently, the two Cp anions require an average oxidation state Ti(I), hence $d^3$; ionic counting gives $3+6+8+1=18$. The formal Ti–Ti bond order is one. The large coordination envelope can make this bond weak and long; reaching 18 electrons is bookkeeping, rather than proof of a short, strong bond. There is no need to invent extra CO bridges or a higher Ti–Ti bond order.

Place four terminal trifluorophosphine donors on each cobalt and join the cobalt centers by a single metal-metal bond, as in the first panel. The P atoms bind to cobalt; the fluorines remain attached to phosphorus. Each neutral donor supplies two electrons. Neutral electron counting givesThe ionic description is Co(0), $d^9$, with eight electrons from the four donors and one from the Co–Co bond. A Co–Co single bond supplies the missing electron at each center. No bridging PF${}_3$ is required by this count.

The principal electronic variable is the net population of metal–metal bonding molecular orbitals relative to antibonding molecular orbitals. For otherwise comparable complexes, a larger bond order generally gives a shorter metal-metal bond; removing an antibonding electron can shorten a bond even though the total electron count falls. Different orbital symmetries also matter: sigma, pi and delta overlaps respond differently to distance and rotation of the metal fragments.

metal size, oxidation state and radial orbital extent set the underlying distance scale. Comparing a first-row metal with a larger heavier congener does not isolate bond order. Increasing positive charge often contracts the metal orbitals, but can also change electron occupancy, ligand binding and electrostatic interactions. The ligand field and donor/acceptor properties of the surrounding ligands in coordination chemistry determine which metal orbitals remain available for direct bonding and how much density instead participates in pi backbonding.

Finally, the geometry can enforce or oppose the preferred separation. Bridging ligands impose bond-angle and bond-length constraints; bulky substituents produce steric hindrance; crystal packing can perturb the observed distance. A bond length is evidence for bonding only in its electronic and structural context. In particular, two bridges can hold metals close without proving a high direct bond order, while a sterically congested formal single bond can be unusually long.

The dimer has two unpaired electrons and a triplet ground state, $S=1$. Its approximately threefold-symmetric Fe${}_2$(CO)${}_3$ core supplies a pair of degenerate frontier molecular orbitals. The last two electrons occupy separate members with parallel spins, favored by exchange, rather than pairing in one. A useful qualitative picture is a sigma bond plus two perpendicular, singly occupied pi half-bonds: together these support a formal Fe–Fe double bond while retaining paramagnetism. The spin-only magnetic moment for $S=1$ is $\sqrt{8}{\mu }_B\simeq 2.83{\mu }_B$; real moments can include orbital and spin–orbit effects.

The formal 18-electron count does not require every molecular orbital to be doubly occupied. It is therefore compatible with an open-shell dimer. The primary structural/magnetic study establishes this unusual triplet state; an isolated-atom high-spin $d^7$ diagram would not describe the coupled metal–ligand system.^[ref]

The metal is Cr(II), $d^4$. A chloride ligand produces a relatively weak ligand field, so the octahedral center is a high-spin complex with $t_{2g}^3{e}_g^1$, $S=2$. The singly occupied $e_g$ pair is orbitally degenerate: $d_{z^2}$ and $d_{x^2-y^2}$ cannot retain identical occupancies once the distortion selects one. This is a strong setting for the Jahn-Teller effect.

On tetragonal elongation, the two axial Cr–Cl distances increase. Repulsion is reduced most for $d_{z^2}$, so it falls relative to $d_{x^2-y^2}$; $d_{xz},d_{yz}$ also fall relative to $d_{xy}$. The single $e_g$ electron occupies the lower $d_{z^2}$-derived level. The electronic stabilization offsets an elastic cost until a distorted equilibrium geometry is reached. The high-spin $d^4$ occupancy drives an elongated, rather than regular, octahedron. The three lower-set electrons remain one per orbital in this simple diagram; it is primarily the unequal $e_g$ occupancy that produces the strong distortion.

The all-carbonyl hydride, HCo(CO)${}_4$, is more acidic. Loss of ${\mathrm{H}}^{+}$ gives $[\mathrm{Co}(\mathrm{CO}{)}_4{]}^{-}$, whose negative charge is stabilized by pi backbonding into four carbonyl ligands. Replacing one CO by triphenyl phosphite reduces the net electron-withdrawing character of the ligand set relative to four carbonyls. The substituted hydride is more electron rich and its conjugate-base anion is less stabilized against protonation.Both conjugate bases have a conventional 18-electron count, so the difference is not a missing-electron argument. It is the relative stabilization of acid and base by the ligands in coordination chemistry. This concerns heterolytic deprotonation, not the homolytic Co–H bond-dissociation energy.

The filled alkene $\pi$ molecular orbital donates into a vacant metal acceptor orbital directed toward the center of the C=C bond. In the reverse direction, a filled metal $d$ orbital can overlap with the alkene ${\pi }^{\ast }$ antibonding molecular orbital. These are the donation and pi backbonding components of the Dewar-Chatt-Duncanson model, illustrated in the lower part of the bonding schematic. The alkene is an ${\eta }^2$ alkene ligand, attached through both carbons. Increasing backbonding weakens and lengthens C=C and can push the bonding toward a metallacyclopropane description.

Zr(IV) is $d^0$, so alkene-to-metal donation predominates. It has suitable empty orbitals but no occupied metal $d$ set to provide substantial conventional backbonding. An electron-deficient cationic zirconocene can consequently bind and activate an alkene largely through its Lewis acidity; it should not be drawn as a strongly backbonded late-metal alkene merely because its formal coordination mode is ${\eta }^2$.