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Reversible association of two molecular units to form a dimer.

The strongest donor belongs to the acid, ${\alpha }_1=3.5$, and the strongest acceptor to the aminopyridine, ${\beta }_2=8.5$. The cocrystal pairs the strongest donor with the strongest acceptor, while the reciprocal amino-NH···carbonyl contact closes a complementary two-contact motif.

Using the simple favorable-contact score $\alpha \beta$, one heterodimer givesThe self-associated comparison, normalized to the same two molecules and two hydrogen bonds, is half an acid dimer plus half an aminopyridine dimer:ThusIn a model where bond free energy contains $-\alpha \beta$, this is a favorable energy change. No bonds have been artificially added to one side of the comparison: both alternatives contain two contacts per acid/aminopyridine pair.

The calculation rationalizes the hydrogen-bond preference. It is not a complete crystal free energy: packing, additional contacts, entropy and possible solvent effects also matter. Without a specified calibration, the numerical score should not be promoted to a measured cocrystallization free energy.

Two molecules of the aminopyridine form a self-complementary dimer through two N–H···N contacts. In each direction, one exocyclic amino hydrogen is the donor and the pyridine ring nitrogen of the other molecule is the acceptor.

Orient the two amino/pyridine-N edges toward one another, as in the second panel of the original homodimer drawing. Each molecule donates one NH and accepts at one ring N; the second amino H remains available for additional packing contacts. The chlorine substituent is retained but is not one of the two principal donor–acceptor sites.

Two molecules of the carboxylic acid form a cyclic carboxylic-acid dimer. Let Ar denote the meta-methylphenyl group. One molecule donates its OH hydrogen to the other's carbonyl oxygen, and the second donates back:
The two contacts close an eight-membered hydrogen-bonded ring, shown explicitly below.

Both molecules therefore act once as hydrogen-bond donor and once as hydrogen-bond acceptor, giving two O–H···O=C contacts. This is the conventional self-complementary dimer motif; the schematic is not a prediction of every weaker contact in an unprovided crystal structure.

Trialkylaluminium compounds commonly form dimers with two bridging alkyl groups and four terminal alkyl groups. Each electron-deficient bridge is a three-centre two-electron bond spanning Al–C–Al; the carbon–metal bond electrons are shared with the second aluminium center. A localized ordinary two-center bond to each Al would overcount the electrons.

For $[{\mathrm{R}}_2\mathrm{AlH}{]}_2$, hydride bridges are expected to be especially favorable, giving a four-membered Al–H–Al–H core with two terminal alkyl groups on each Al. The Al–H–Al links are again three-centre two-electron bonds. Hydride is small and can bridge without the steric cost of a bulky alkyl bridge. Aggregation still depends on substituent size, donor solvent and concentration; this is the natural dimeric model, not a statement that all dialkylaluminium hydrides are dimers under every condition.

Interpret the supplied free energies as standard reaction free energies and use $c^{\circ }=1\mathrm{mol}{\mathrm{L}}^{-1}$. The dimensionless equilibrium constants areUnder the ideal-solution approximation, $[C]=K_C[L]$ and $[D]=(K_D/c^{\circ })[L{]}^2$. Set $k_D=K_D/c^{\circ }$, with units ${\mathrm{M}}^{-1}$. Conservation counts two original molecules in each dimer:The physical, positive root can be written without subtractive cancellation asThe resulting concentrations are:

For example, the first row satisfies $[L]+[C]+2[D]=0.100\mathrm{M}$; using $[L]+[C]+[D]$ would incorrectly count dimers. At both concentrations almost all molecular units belong to dimers.

dimer formation is favored by sufficiently high concentration because it joins two molecules. Dilution favors the separated species, whereas $[C]/[L]=K_C$ is concentration-independent in this ideal model. More than half the molecular units are dimerized when $2[D]>[L]+[C]$, equivalently $c_0>(1+K_C{)}^2/k_D\simeq 7.36\times 10^{-7}\mathrm{M}$. The supplied free energies at one temperature do not determine a temperature trend without additional enthalpy information. At $1\mathrm{M}$, neglected nonideal activities could be significant; the table is the requested concentration-based model.

A hydrogen-bonding unit capable of forming a strongly associated, self-complementary dimer through a four-hydrogen-bond array.