Dimers and Monomers

FIGURE 11. Solid-state stmctures of donor-base-coordinated dimers and monomers 

TABLE 4. Donor-base-induced dimers and monomers of basic lithium organics 

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There is an equilibrium between the dimer and monomer, and molecular orbital study suggests that the heterochiral dimer is more stable than the homochiral isomer. The existence and behavior of the dimeric species were well confirmed by experiments such as cryoscopic molecular weight and NMR measurement. In the NMR study of a DAIB-catalyzed dialkylzinc addition reaction, noticeable changes were observed in the spectrum of the homochiral dimer on the addition of benzaldehyde, while the spectrum of the heterochiral complex remained the same. This may imply that the heterochiral complex is very stable and does not react, and the homochiral dimer leads to the reaction product. 

Nitrosobenzene crystallizes as the cis dimer, 24, whereas in the melt some cis dimer, more trans dimer, and monomer are present. On the other hand, o-... 

These observations showed that the reaction can be simplified by preformation of the indanone enolate in toluene/50% NaOH and subsequent addition of catalyst and CH3CI (Figure 12). This eliminates the "induction period and most importantly the high sensitivity of rate and ee to the catalyst/indanone ratio. Detailed kinetic measurements on this preformed enolate methylation in toluene/50% NaOH determined that the reaction is 0.55 order in catalyst. This is consistent with our finding that the catalyst goes into solution as a dimer which must dissociate prior to com-plexation with the indanone anion. If the rate has a first order dependence on the monomer, the amount of monomer is very small, and the equilibration between dimer and monomer is fast, then the order in catalyst is expected to be 0.5. The 0.5 order in catalyst is not due to the preformation of solid sodium indanone enolate but is a peculiarity of this type of chiral catalyst. Vlhen Aliquat 336 is used as catalyst in this identical system the order in catalyst is 1. Finally, in the absence of a phase transfer catalyst less than 2% methylation was observed in 95 hours. 

A further study of the aggregation state of PhLi in etheral solvents has resolved signals for the ipso carbon which firmly establish the tetramer and dimer structures in diethylether, and the dimer and monomer structures in THF. The effects of polar additives such as THF, DME, dioxolane, 2,5-dimethyltetrahydrofuran, TMEDA, PMDTA, HMTTA, HMPA, DMPU, and 12-crown-6 to solutions of PhLi in diethylether and/or THE have been studied by low-temperature multinuclear techniques. 

Recent NMR study suggested that PhLi exists as a mixture of tetramer and dimer in diethyl ether and that the addition of a stoichiometric amount of a coordinating solvent such as THF, dioxolane, DME or TMEDA induces complete conversion of the mixture to dimeric solvates. In a THF solution PhLi exists as a mixture of dimer and monomer. It was noted that the addition of 12-crown or HMPA increases the reactivity and decreases the selectivity of PhLi in THF. 

A fruitful approach to the problem of intermolecular interaction is perturbation theory. The wavefunctions of the two separate interacting molecules are perturbed when the overlap is nonzero, and standard treatment [49] yields separate contributions to the interaction energy, namely the Coulombic, polarization, dispersion, and repulsion terms. Basis-set superposition is no longer a problem because these energies are calculated directly from the perturbed wavefunction and not by difference between dimers and monomers. The separation into intuitive contributions is a special bonus, because these terms can be correlated with intuitive molecular... 

Relative fluorescence intensities and spectra at a series of pH values are shown in Fig. 12, and some pertinent parameters are summarized in Table IX. At a specific pH the fluorescence intensity as a function of wavelength has been expressed as relative to the intensity at the maximum at the same pH. The maximum intensities were different at different PH values. Nevertheless, the ratio of intensities of dimer and monomer, ID//M, being independent of polymer concentration, may be compared for all the samples and pH values. 

Cm, Xd> Xm arc concentrations and mole fractions, respectively, of dimer and monomer em° is the absorption coefficient of the monomer (found by extrapolating em to C=0 and Kx KC for Cd4. We found values of K for each of the alcohols at a series of temperatures from —10° to +45°C. A plot of log10 K vs. IjT is given in Fig. 4. There is considerable scatter, but the trend in each case is roughly linear, within the limits of error. From the slopes of the lines the heats of formation of the alcohol dimers were calculated and are listed in Table 1. 

Hence, the ratio of fluorescence efficiencies of dimer and monomer is given by... 

Ratio of Band Intensities of Dimer and Monomer for Normal and Delayed Fluorescence1,11... 

Equation (4r>) for the ratio of the delayed fluorescence efficiencies of dimer and monomer at low concentrations of ground state (c) can be written in the following form ... 

N21<, is the number of bound dimers in the volume v and N2 — N(N —1)/2 is the number of pairs (bound or free) in the volume v. Note that the right-hand side of this expression is roughly proportional to the reciprocal volume, /v. We may, therefore, write the expression to the left in terms of dimer and monomer densities, n2 = N2/V and nj = N/v, respectively [27],... 

Equilibration of carboxylic acid dimers and monomers in the sample solution depends on the extent to which the carboxy group is involved in hydrogen bonding with the solvent ... 

Depending on the fit, the number and strength of contacts, and other factors, a monomer-oligomer equilibrium will exist. For example, in the case of Concanavalin A the tetramer is in equilibrium with dimer and monomer under normal conditions. In the case of insulin the monomer, dimer, and hexamer are all in equilibrium. In hemoglobin the dimer and tetramer are in equilibrium. In the case of the adsorption of such proteins, one must not only know what is the aggregation state of the protein in solution, but must be able to deduce the adsorbed state. Do the molecules adsorb as dimers 21) Do they adsorb as dimers and then associate as tetramers or hexamers on the surface, etc. ... 

Table 4.3 Dimerization free energy in the gas phase (1 atm reference state), difference in hydration free energy between dimers and monomers and dimerization free energy in aqueous solution (1 M reference state) for selected complexes. The gas phase optimum geometry was used in all cases. All value are in kcal mol-1...

Fig. 19. Concentration dependence of the ellipticity at 222 nm of an- The lines are computer-generated, theoretical curves describing various monomer-to-nmer equilibria. The top panel shows the monomer-tetramer equilibrium, the middle panel shows monomer-trimer and monomer-hexamer equilbria, and the bottom panel shows monomer-dimer and monomer-octamer equilibria.

The heteropolyanion stabilizes protonated intermediates by coordination in solution and the pseudoliquid phase as well as on the surface, thus lowering the activation energy and accelerating reactions. Several protonated intermediates including the protonated ethanol dimer and monomer [18], the protonated pyridine dimer [12, 19], and protonated methanol [20] have been detected in the pseudoliquid phase directly by use of X-ray diffraction (XRD), IR or solid-state NMR. In solid-state H NMR, the chemical shift for the protonated ethanol dimer, (C2HsOH)2H+ is 9.5 ppm down-field from tetramethylsilane, which lies in the range of supcracids reported by Olah et al. [18]. This fact also supports the strong acidity of heteropolyacids. 

It is rare for a single complex to form as both dimers and monomers but just such a situation has been reported for copper(II) complexes of l,8-diamino-3,6-dia-zaoctane-4,5-dione (Fig. 7.5)[216l... 

In the presence of potential ligands for lithium, f-butyllithium was found to be a dimer in diethyl ether-<7 0, a mixture of dimers and monomers in TIIIw7 0 and entirely monomeric when complexed to PMDTA. All these results are derived from one bond 13C—6Li coupling patterns in 13C NMR spectra, needless to say with NMR determined at low temperature, >160 K, since the reagent rapidly deprotonates all these ligands at higher temperatures. 

Fig. 3.15. Analytical size-exclusion chromatography distinguishes between dimeric and monomeric chorismate mutases [97]. Wild-type MjCM (top trace) was found to be a mixture of dimer and higher-order aggregates. Most selected variants (e.g. traces A, B and C) were dimers or mixtures of dimers and monomers. Only oneof26 variants tested (mMjCM, bottom trace) eluted as a monomer. It had the six amino acid insert shown. Analytical ultracentrifugation confirmed that this protein is monomeric in solution.

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