Codex @codex  0

Reduction makes stereogenic centres at C2 and C3 of the indan-1-one framework. The four products are the cis pair $(2R,3S)$ and $(2S,3R)$, and the trans pair $(2R,3R)$ and $(2S,3S)$. Each pair consists of enantiomers; any cis member is diastereomeric to either trans member. There is no meso product because the carbonyl-containing and aromatic sides of the ring do not make C2 and C3 symmetry-equivalent.

For checking the Cahn-Ingold-Prelog priority rules, at C2 the order is carbonyl-side carbon $>$ phenyl $>$ C3 $>$ H. At C3 it is fused aromatic carbon $>$ phenyl $>$ C2 $>$ H. The fused aromatic path outranks the separate phenyl path because it reaches the carbonyl-containing part of the framework.

Apply the Felkin-Anh model to the stereocentre alpha to the ketone. Its large group is the chain continuing through the phenyl-bearing carbon, its medium group is methyl, and its small group is hydrogen. In the preferred transition-state arrangement, put the large group approximately perpendicular to C=O and approach from the opposite face, passing the small hydrogen along a Bürgi-Dunitz trajectory. The remote ether cannot form the usual small alpha-alkoxy chelate, and the coordinating solvent further supports using an open-addition prediction.^[ref]

The predicted new stereocentre is $S$. In the question's zigzag projection, this corresponds to the new OH bond directed behind the page and the newly introduced methyl toward the reader, with the original stereocentres unchanged. The new-centre priority order is OH $>$ phenyl $>$ the substituted alpha-carbon chain $>$ methyl. This is a model-based major-product prediction, rather than a quantitative diastereomeric ratio.

Use the upper-ring chair placing $H_a$ or $H_c$ axial. The aryl ester substituent on that carbon is then equatorial. Use a lower-ring chair placing $H_b$ or $H_d$ axial, with the attached side chain equatorial. The spiro configuration distinguishes the two structures: in A, the lower-ring oxygen bond is axial with respect to the upper ring, while the upper-ring oxygen bond is equatorial with respect to the lower ring. In B, those roles reverse.

Thus the oxygen placements at the shared spiro carbon are axial/equatorial for A and equatorial/axial for B. Side-chain conformations are unnecessary, but changing the lower chair without tracking its substituent positions would change this conclusion.

Protonation of a spiroacetal oxygen makes the adjacent C–O bond easier to cleave. Reversible opening gives an oxocarbenium ion, in which the spiro carbon is locally planar. The tethered alcohol can attack either face; deprotonation closes the acetal and regenerates acid. Repetition interconverts the spiro epimers while retaining the other stereogenic centres. Methanol can participate in reversible proton transfer or trapping, but there is no need to invert the remote carbon centres.

The anomeric effect is the preference, in suitable cyclic acetals, for an electronegative substituent at an anomeric carbon to occupy an axial position even when simple steric reasoning favours equatorial. An important orbital contribution is donation from an endocyclic oxygen lone pair into the antibonding orbital of the adjacent exocyclic C–O bond, $n_{\mathrm{O}}\to {\sigma }_{\mathrm{C}-\mathrm{O}}^{\ast }$. The chair's axial arrangement supplies favourable antiperiplanar overlap. Electrostatic and solvation contributions can also affect the observed conformational preference.

Each isomer has one favourable anomeric interaction. A has the favourable axial exocyclic oxygen in the upper-ring chair; B has it in the lower-ring chair. The NMR-constrained conformations therefore do not provide a doubly anomeric versus non-anomeric comparison.

Both can keep important carbon substituents equatorial and each obtains one anomeric stabilization. Appreciable amounts of both are therefore a reasonable prediction, rather than a strong preference based solely on counting anomeric interactions. The environments of the two ring oxygens are not identical, so this argument does not determine an exact one-to-one equilibrium ratio; quantitative preference would require further energetic information.

The C–O-forming transition state has a partial bond from water oxygen to C3, positive charge developing on that oxygen, and negative charge delocalizing toward the carbonyl oxygen. A compact drawing isHere the two C–C dotted connections denote redistribution of pi bonding, not cleavage of either carbon–carbon sigma bond. In a bond-order drawing retain the full sigma skeleton: C1–O is changing from double toward single, C1–C2 from single toward double, C2–C3 from double toward single, and C3–O from absent toward single. The incoming water approaches a face of the approximately planar conjugated unit and C3 begins to become tetrahedral. The total electric charge remains zero. If proton transfer to another water occurs concertedly, include a partially broken incoming-water O–H bond and a partially formed relay O–H bond; that is a solvent-assisted variant, not a different regioselectivity. The original mechanism schematic identifies these bond changes without depicting a falsely isolated free hydroxide reagent.

Use C1 for the carbonyl carbon, C2 for the adjacent carbon, and C3 for the beta carbon of the reactive enone fragment $\mathrm{R}-C1(=\mathrm{O})-C2H=C3H-{\mathrm{R}}^{\prime }$. water adds conjugately at C3, giving a beta-hydroxy ketone. The oxygen lone pair of neutral water attacks C3; move the C2=C3 pi pair toward C1–C2 and the carbonyl pi pair onto oxygen. This produces the charge-separated enolate–oxonium intermediateA second water molecule can relay a proton from the newly attached oxonium oxygen to the enolate system. Using the carbon-centered resonance structure, reform C1=O and protonate C2 while the donating O–H bond returns its pair to the added oxygen. Equivalently, oxygen protonation first gives an enol, followed by water-mediated keto-enol tautomerism. Either path yields a neutral beta-hydroxy ketone and regenerates the relay water. There is no need to introduce externally supplied H${}^{+}$ or OH${}^{-}$; solvent molecules perform the proton transfers. The uncatalyzed charge separation has a large barrier, so this mechanism describes a slow formal pathway, not a claim of rapid hydration in pure water.

Hydride is delivered to steroid C5 and a proton to C4; the C3 ketone is retained. Use the conjugated fragment $\mathrm{O}=C3-C4=C5$. Carbonyl hydrogen bonds from Tyr91–OH and protonated Glu57 lower the barrier to conjugate reduction. Draw a curved arrow from the nicotinamide C4–H bond of NADPH to steroid C5, shift the C4=C5 pi pair toward C3–C4, and shift C3=O pi electrons onto oxygen. The nicotinamide ring rearomatizes to NADP+; the steroid becomes a bound enolate, or its protonated enol equivalent. electron shifts across the nicotinamide ring must accompany C–H bond cleavage rather than leaving an unexplained neutral carbon radical.

Next, reform C3=O and protonate steroid C4 from an appropriately positioned acid, directly or through an enol/proton-relay route. This regenerates the catalytic acid after solvent reprotonation. The enzyme fixes the hydride-accepting face so that the new C5–H has the 5α configuration, giving dihydrotestosterone; delivery to the opposite face would give a different ring-junction configuration. This is not simple 1,2 reduction of the C3 carbonyl to an alcohol. The net local bookkeeping is one hydride plus one proton across C4=C5, with two electrons supplied by NADPH. The original reactive-fragment diagram shows the enolate-forming arrows and the separate protonation step.

For the same pair of atoms, the harmonic approximation gives $\tilde{\nu }=(2\pi c{)}^{-1}\sqrt{k/\mu }$, where $k$ is the bond force constant and $\mu$ the reduced mass. The large shifts mainly reflect changes in $k$ from CO pi backbonding; the complexes are not distinguished simply by their total number of valence electrons.

$\mathrm{W}(\mathrm{CO}{)}_6$ has stronger net backbonding than $\mathrm{Cr}(\mathrm{CO}{)}_6$. Both are group-6 M(0), $d^6$, 18-electron complexes. The more spatially extended tungsten $5d$ orbitals provide effective overlap with CO ${\pi }^{\ast }$, consistent with the lower stretching frequency. As a simple same-mode force-constant comparison, $(1977/2000{)}^2=0.977$, about a 2.3% reduction.

$\mathrm{Ni}(\mathrm{CO}{)}_3(\mathrm{PM}{\mathrm{e}}_3)$ has appreciable but less C–O weakening than those hexacarbonyls. Ni(0) is $d^{10}$ and the complex is also 18-electron. The more contracted, lower-energy late-3d occupied orbitals give less effective donation into CO ${\pi }^{\ast }$ than the group-6 carbonyls in this comparison. Trimethylphosphine donates electron density and increases backbonding relative to an otherwise comparable less-donating nickel complex; that effect does not force its frequency below chromium's. Comparing different metals requires both orbital energies and overlap.

$[\mathrm{Cu}(\mathrm{CO}{)}_4{]}^{+}$ has very weak backbonding and a frequency above free CO. Cu(I) is $d^{10}$ and 18-electron here, but positive charge lowers its occupied orbital energies and suppresses backdonation. Sigma donation and the cation's electrostatic polarization can strengthen the internal C–O bond. Consequently the usual free-CO reference, about $2143\mathrm{c}{\mathrm{m}}^{-1}$, lies below this cation's band. A blue shift is compatible with carbon coordination; it does not imply absence of a metal–CO bond. Coupled normal modes and measurement conditions limit literal extraction of a local bond force constant from one band.

A carbonyl ligand binds through carbon, whose occupied $5\sigma$ molecular orbital has a substantial outward-facing carbon lobe. Overlap with an empty metal orbital along the M–C axis gives ligand-to-metal sigma donation. Conversely, an occupied metal $d_{\pi }$ orbital overlaps sideways with an empty CO $2{\pi }^{\ast }$ antibonding molecular orbital, giving metal-to-ligand pi backbonding. There are two mutually perpendicular pi channels. The original orbital schematic below shows one of them; $+$ and $-$ denote orbital phase, not electric charge.

The interactions are synergic: donation makes electron density available at the metal, and backbonding helps accommodate it while strengthening the metal–carbon interaction. Occupying CO ${\pi }^{\ast }$ reduces the C–O bond order, lengthens that bond and lowers its bond force constant. Therefore stronger pi backbonding generally lowers the carbonyl stretching spectroscopic wavenumber even while strengthening the M–C attachment.

$E=\mathrm{Mo}({\eta }^5:\kappa N\text{-}L)(\mathrm{CO}{)}_2\mathrm{Cl}$, with chloride replacing the remaining acetonitrile. The pendant pyridine remains attached. The substitution removes the positive electric charge on $D$ but does not change the Mo(II) oxidation state. In ionic electron counting, both neutral acetonitrile and anionic chloride ligand donate two electrons, giving $4+6+2_N+4_{\mathrm{CO}}+2_{\mathrm{Cl}}=18$ in $E$.

acetonitrile is the remaining weak, exchangeable monodentate donor. Its displacement forms a favorable Mo–Cl bond at a cationic center, retains the intramolecular Mo–N bond, and restores an 18-electron product after substitution. The following formulas specify the coordination changes directly:Tetramethylammonium is a spectator counterion; it is not a carbon donor to Mo.

Carbon-13 NMR spectra: 1 = C, 2 = A, 3 = B. Approximate shifts, read from the printed axes, are shown in the annotated structures.

The two methyls in A are chemically distinct because one is cis and the other trans to each substituent at the other alkene carbon. Their two measured shifts are secure; assigning an individual methyl to a particular side of the drawn double bond requires an additional stereospecific shift argument or experiment, so their spatial interchange is left explicit.

Draw a curly arrow from the nitrogen lone pair to methyl carbon, and a second from the C-I bond to I:This is concerted SN2 quaternization. The product is choline iodide; nitrogen has four carbon substituents and positive charge, while the alcohol remains OH.

The alkene pi bond attacks Br${}_2$ as the Br-Br bond breaks to bromide, forming a bridged, unsymmetrical bromonium ion. The carbon bearing the two methyl groups has greater carbocation-like character.

The tethered alcohol oxygen attacks that carbon from the side opposite the bromine bridge. Its lone pair forms the new O-C bond while the attacked C-Br bridge bond opens, giving a six-membered cyclic oxonium ion. Bromide or solvent removes the O-H proton to give the neutral bromoether.

This explains why O becomes attached at the more substituted alkene carbon while Br remains at the other carbon. Polar solvent assists charge separation, and intramolecular capture competes effectively with external bromide attack. Opening is anti; attack on the two faces of the achiral starting material gives a racemic product at the newly formed CHBr stereocentre.

The ring-forming step is bromoetherification.

Let $\mathrm{Ar}=p-\mathrm{MeO}{\mathrm{C}}_6{\mathrm{H}}_4$. One standard route is:where the last two carbons are joined through oxygen to form the epoxide shown in the product drawing.

Use rigorously dry conditions for Grignard formation/addition; quench only after the aldehyde addition. Dehydration gives the styrene, and peracid oxidation transfers oxygen across its double bond. The methoxy substituent is compatible with this sequence. No asymmetric reagent is specified, so the target epoxide is racemic.

The expected order is B-F > C-F > N-F.

B-F has a large favorable polar/ionic contribution because electron-deficient boron and fluorine have a large electronegativity difference. Fluorine lone-pair donation into boron's empty 2p orbital can additionally strengthen bonding in planar BF${}_3$. C-F is a strong, polar second-row sigma bond, but tetrahedral CF${}_4$ has no equivalent empty carbon 2p acceptor for that pi donation.

N-F has less favorable bond polarity and substantial repulsion between nitrogen and fluorine lone pairs, making it weaker. Invoking occupied boron d orbitals is unnecessary and inappropriate for this second-row comparison.

C-C is strongest; N-N is much weaker despite nitrogen's smaller size. Carbon's effective nuclear attraction and good overlap of compact second-row valence orbitals favor a strong C-C sigma bond. The larger, more electron-deficient boron centres give less effective B-B bonding in the stated molecule, despite its relatively high-s-character trigonal bonding.

In hydrazine, the two neighboring nitrogen lone pairs strongly repel one another, destabilizing the N-N bond. Bond strength therefore cannot be predicted from atomic size alone; lone-pair repulsion explains the especially low N-N value.

This illustrates bonding trends in second-period single bonds.

Potassium intercalates between graphite layers and donates electron density to the graphitic pi system. Occupation of formerly less populated electronic states raises the mobile-carrier density, increasing electrical conductivity under the stated comparison.

The gain is electronic doping of the carbon framework, rather than a claim that potassium strengthens every C-C bond or simply acts as a separate wire through the sample. Intercalation also changes layer separation and scattering, so conductivity depends on both carrier population and mobility.

The material is potassium graphite, a graphite intercalation compound.

Graphite: each carbon forms three strong in-plane sigma bonds in an sp${}^2$ honeycomb layer. The remaining p orbitals form delocalized pi bands, allowing electrical conduction especially along the layers. Much weaker interlayer attraction permits sliding, explaining softness without implying weak in-plane C-C bonds.

Carborundum is silicon carbide, SiC. A suitable structure is a three-dimensional, tetrahedrally coordinated covalent network: each Si has four C neighbors and each C four Si neighbors. Strong directional bonding in all directions resists slip and gives hardness. Its filled bonding states are separated from empty states by a substantial band gap, giving low conductivity when pure and undoped.

“Non-conductor” is the intended contrast with graphite; SiC is more precisely a wide-bandgap semiconductor, whose conductivity can change with doping and temperature.