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Formation of a new benzene ring by joining carbon fragments, often followed by elimination and tautomerization that establish aromaticity.

Benzene has a planar ring of six carbon chemical atoms, each bearing one hydrogen. Its $\pi$ electron density is distributed over the ring; the alternating covalent bonds in one resonance structure do not describe alternating actual bond lengths. ^[ref]

Two benzene molecules associated by dispersion and electrostatic interactions. T-shaped and parallel-displaced geometries are important low-energy arrangements; a single permanent dipole–dipole model is inadequate.

A cage isomer of benzene with one carbon–carbon double bond, conventionally described as tricyclo[3.1.0.0(2,6)]hex-3-ene. Its ideal cage geometry belongs to the C2v molecular point group. Molecular symmetry depends on the full three-dimensional cage rather than the apparent symmetry of a planar skeletal projection.

Borazine is the alternating six-membered ${\mathrm{B}}_3{\mathrm{N}}_3{\mathrm{H}}_6$ ring. Planar boron and nitrogen centers permit N-to-B pi donation, but unequal orbital energies strongly polarize the bonding. It undergoes addition and hydrolysis much more readily than benzene; the structural analogy does not give benzene-like chemical inertness.

The dimethyl ester of benzene-1,2-dicarboxylic acid, with adjacent ester groups on a benzene ring.

The radius of gyration of a dilute linear polystyrene coil in a good solvent depends on its molar mass as $R_g=K{M}^{\nu }$, with a material- and solvent-dependent amplitude. A manufacturer-supplied light-scattering calibration for polystyrene in benzene or toluene near room temperature is the displayed relation, quoted over $M\simeq 2\times 10^5$ to $5\times 10^7\mathrm{g}\mathrm{mo}{\mathrm{l}}^{-1}$. The exponent is close to the Flory approximation $3/5$. Values outside the quoted mass range are extrapolations, not extra measured data. Using $c^{\ast }=M/[N_A(4\pi /3)R_g^3]$ then gives the polymer overlap concentration scaling $c^{\ast }\propto M^{1-3\nu }$. ^[ref]

A hydrogen bond acceptor supplies the electron-rich atom or group $Y$ interacting with the attached hydrogen of a hydrogen bond donor in $X-\mathrm{H}\cdots Y$. An oxygen lone pair in water is the familiar example. Acceptance describes the association, not necessarily acquisition of a proton. A single molecule, such as water or Ammonia, can offer both hydrogen bond donor and hydrogen bond acceptor sites. See Glasfeld: water and nitrogen-containing accepting sites.

A lone pair drawn in a Lewis structure is a useful clue, not a universal test. At an ordinary neutral amide nitrogen, the nominal lone pair participates in chemical resonance with the carbonyl group, so this nitrogen is ordinarily excluded from lists of hydrogen bond acceptors; the carbonyl group's oxygen remains an accepting site. Protonation changes the test again: ${\mathrm{NH}}_4^{+}$ has four N–H covalent bonds and no nitrogen lone pair, whereas Ammonia has three and one. These distinctions follow the actual chemical form, and accepting ability also depends on the partner and whether it can approach the site. See McMurry: amide resonance and protonation and Glasfeld: limitations of nitrogen accepting sites.

Conversely, an accepting group need not supply an atom-centred lone pair. The following phenol–benzene experiment probes an O–H donor interacting with the ring's distributed $\pi$ electron density.

Saggu, Levinson and Boxer (2011) used infrared spectroscopy to compare $200\mathrm{mmol}{\mathrm{L}}^{-1}$ phenol in different solvents. The O–H stretching peak was at $3611\mathrm{c}{\mathrm{m}}^{-1}$ in ${\mathrm{CCl}}_4$ and $3555.9\mathrm{c}{\mathrm{m}}^{-1}$ in benzene. To distinguish association from a general solvent effect, they diluted the ring-containing chemical solutions with ${\mathrm{CCl}}_4$: two peaks appeared, with the free peak nearly fixed while the associated peak depended on the partner. Replacing the O–H hydrogen with deuterium reproduced the ordering of shifts for different partners. Thus the perturbed O–H group identifies the hydrogen bond donor; the ring supplies the hydrogen bond acceptor. A peak shift alone does not specify a unique molecular geometry. ^[ref]

The roles make recognition between molecules intelligible: exposed hydrogen bond donors need compatible hydrogen bond acceptors in reachable positions. A count of sites is a starting description, not a prediction of binding strength. In water, forming a contact between two partners can also replace their existing hydrogen bonds to water; the Gibbs free energy of association concerns the whole change. See Glasfeld, pp. 15–16: competition with solvent interactions.

Filling the three bonding molecular orbitals with two electrons each givesThree isolated ethene-like $\pi$ bonds, evaluated with the same Hückel method parameters, have $E_{\mathrm{loc}}=3\{2(\alpha +\beta )\}=6\alpha +6\beta$. Thus the signed delocalization energy isEquivalently, the positive stabilization is $-2\beta =2|\beta |$.

Benzene has a planar cyclic conjugated system with six $\pi$ electrons, satisfying the $4n+2$ count with $n=1$. All three bonding $\pi$ molecular orbitals are filled and the antibonding levels are empty, giving the closed-shell stabilization associated with aromaticity. The conclusion uses the continuous cyclic overlap as well as the electron count.

Pyrazine belongs to $D_{2h}$, the D2h point group. With the printed axes, its three twofold axes are $x,y,z$; it also has an inversion centre and the three coordinate mirror planes. The nitrogen atoms occupy sites 1 and 4 on the $y$ axis. Interchanging carbon and nitrogen is not a molecular symmetry operation, so the sixfold benzene symmetry is lost.

The six $\pi$ electrons give the Hückel method energyThe appropriate localized reference contains two C=N $\pi$ bonds and one C=C $\pi$ bond. Three C=C bonds would incorrectly replace the nitrogen one-centre parameters. For one isolated C=N pair, the dimensionless matrix iswhose eigenvalues are $(1\pm \sqrt{5})/2$. Since $\beta <0$, the occupied bonding molecular orbital has energy $\alpha +(1+\sqrt{5})\beta /2$. Two doubly occupied C=N bonds and one doubly occupied C=C bond consequently giveTherefore the signed delocalization energy isThe positive stabilization is $1.82039|\beta |$, smaller than the benzene value $2|\beta |$ in the stated model but still stabilizing.

Pyrazine is aromatic: its planar cyclic conjugated system contains six $\pi$ electrons and has a filled set of three bonding $\pi$ molecular orbitals. Each ring nitrogen contributes one $p_z$ electron; its in-plane lone pair is outside this $\pi$ system. The heteroatoms change orbital energies and coefficients without interrupting cyclic conjugation or the $4n+2$ count. Aromaticity does not require the stabilization to equal benzene's.

The product is 1,4-dimethoxy-2,5-bis(2-methylbutan-2-yl)benzene. Each new substituent is $-\mathrm{C}(\mathrm{C}{\mathrm{H}}_3{)}_2\mathrm{C}{\mathrm{H}}_2\mathrm{C}{\mathrm{H}}_3$, a tert-amyl group, rather than the unrearranged secondary alkyl group of the alcohol. The two substituents are related by the symmetry of the ring.

The proton assignments are:

The integrals add to 30 H. The unusually shielded terminal ethyl methyl signal is compatible with an aryl-containing environment; its NMR quartet–NMR triplet partner and integral are the decisive assignment evidence. The molecular formula and degree of unsaturation, $\mathrm{DBE}=4$, fit a benzene ring with saturated side chains.

For a monocyclic, approximately planar, continuously conjugated pi system, Hückel's rule predicts aromatic closed-shell filling for $4n+2$ pi electrons, with $n=0,1,2,\dots$. Every atom on the circuit must have an appropriately oriented orbital; counting double bonds without checking pi conjugation is insufficient.

The two outer benzene rings are clearly aromatic; the central pyrone ring has a weaker, polarized six-pi aromatic contribution. Each outer ring has the familiar six-electron circuit. For the central ring, a useful charge-separated contributor moves the exocyclic carbonyl pi pair onto oxygen and donates one endocyclic oxygen lone pair into the ring. Its four fused carbon p centres contribute four electrons and the ring-oxygen lone pair supplies two: a six-pi, pyrylium-like circuit, with positive charge on the ring oxygen and negative charge on the carbonyl oxygen. This does not make three independent benzene rings of equal aromatic stabilization; localized carbonyl bonding and the fused benzene circuits remain important contributors.

The three oxygens play different roles. The endocyclic ether oxygen donates a p-type lone pair to pi conjugation. The carbonyl oxygen accepts pi density in the charge-separated contributor. The phenolic oxygen donates into the outer ring as a substituent. Its in-plane lone pair is not an extra pair to add to every ring's electron count. In particular, neither the external C=O pair nor both lone pairs on a ring oxygen should be counted as independent extra ring electrons. Structural studies of xanthone support a largely planar conjugated framework, while the division into strongly aromatic outer rings and a more polarized central ring is an electronic-structure interpretation.^[ref]

In water, separated benzene molecules require separate hydration environments around nonpolar surface. Bringing them together buries part of that surface and reorganizes the surrounding water. The resulting solvent contribution favours association relative to cyclohexane, where benzene was already well solvated by dispersion. This solvent-mediated contribution is the hydrophobic effect, not formation of a new covalent bond or a claim that benzene has become a conventional hydrogen-bond acceptor like oxygen.

The supplied constants imply a thirtyfold enhancement. With matched standard states,at an illustrative 298 K. The water value is still slightly below $1{\mathrm{M}}^{-1}$, so enhancement relative to cyclohexane does not mean a negative standard association free energy for a 1 M standard state, nor does it imply that dilute benzene is all dimer. No universal “entropy only” explanation is needed: solvent enthalpy and entropy both contribute and depend on temperature.

Association in solution includes replacement of solute–solvent contacts, not just formation of the isolated dimer. cyclohexane solvates the benzene surface well through dispersion. Much of the London dispersion gained on bringing two benzene molecules together replaces comparable benzene–cyclohexane contacts, leaving only a modest net gain before the translational and orientational entropy penalty. cyclohexane cannot provide the complementary donor/acceptor interactions available when two waters hydrogen-bond, so water association gains a more distinctive interaction relative to its separated solvated monomers.

Using the same concentration standard state, $K^{\circ }=K_c{c}^{\circ }$ and $\Delta G_{\mathrm{assoc}}^{\circ }=-RT\ln K^{\circ }$. For illustration at 298 K and $c^{\circ }=1\mathrm{mol}{\mathrm{L}}^{-1}$, the ratio of the two supplied association constants corresponds toThus the water-molecule pair can associate more favourably in this solvent even though the stipulated isolated-pair binding energies are similar. Gas-phase potential energy alone omits both differential solvation and the entropy of association.

water achieves substantial binding through a localized O–H···O hydrogen bond; benzene achieves a comparable total through a larger set of weaker contacts. In the water dimer, one water is the hydrogen-bond donor and the other presents an oxygen lone pair region as acceptor. The interaction includes electrostatics, induction interaction, dispersion and short-range exchange repulsion; a hydrogen bond is not a separate fundamental force that can simply be added to all those terms again.

For benzene, draw a T-shaped edge-to-face pair or a slipped parallel pair. Its larger, more polarizable electron clouds provide appreciable London dispersion. Its quadrupolar charge distribution also makes the energy orientation dependent, despite each molecule having no permanent dipole by symmetry. An edge C–H approaching the other ring's pi region is therefore preferable to a model of two structureless, noninteracting dipole-free objects. Dispersion attracts while Pauli repulsion limits close overlap. Several distributed contacts can sum to the scale of one water–water hydrogen bond; counting only the number of conventional hydrogen bonds would miss them.

The comparison concerns the given gas-phase pair interaction energies, not an equality of every solvent-dependent association free energy. Correlated primary calculations explicitly identify both T-shaped and parallel-displaced benzene-dimer minima, rather than a uniquely preferred perfectly eclipsed sandwich.^[ref]

Number the ring with chlorine at C1 and the methylsulfonyl group at C4. The new nitro group is at C2, equivalently C6 by the starting ring's symmetry: the product is 1-chloro-2-nitro-4-(methylsulfonyl)benzene. Both substituents favour this site. Although chlorine deactivates the ring inductively, its lone pair donation stabilizes ortho/para Wheland intermediates. The sulfone is strongly electron withdrawing and meta directing; attack ortho or para to it produces especially unfavourable cationic contributors to resonance in chemistry. C2 is ortho to chlorine and meta to sulfone, whereas C3 has the opposite, less favourable relationship.

sulfuric acid protonates nitric acid, followed by loss of water to produce the nitronium ion. A ring pi bond attacks nitrogen, giving the Wheland intermediate with the new C–N bond. deprotonation at the attacked carbon restores aromaticity. This is electrophilic aromatic substitution: the aryl chloride and the sulfone both remain attached. The formula check is ${\mathrm{C}}_7{\mathrm{H}}_7\mathrm{Cl}{\mathrm{O}}_2\mathrm{S}+\mathrm{N}{\mathrm{O}}_2-\mathrm{H}={\mathrm{C}}_7{\mathrm{H}}_6\mathrm{ClN}{\mathrm{O}}_4\mathrm{S}$. It confirms replacement of one ring hydrogen rather than chlorine, but directing effects, rather than the formula alone, establish the position.