Isodesmic model

Fig. 34 Analysis of the NMR aggregation studies in acetonitrile using the isodesmic (—) and modified isodesmic model (—)...

Resonance Energies from AMI, MNDO and PN3 Calculations with Energies for individual isodesmic model compounds (energies reported in kcal/mol for lowest energy conformers only) ... 

The isodesmic model has been very successfully used in many cases [6, 107,123,148,149]. However, steric or electronic effects may be responsible for significant departures from the isodesmic model. In particular, anticooperative [182] or cooperative [128,183-185] systems have been described. The case of cooperative systems, where the formation of long chains is favored over dimerization, is most interesting because the concentration dependence of the molar mass is stronger, so that the system is potentially more responsive than an isodesmic system [185]. 

Equilibrium polymerization is often described by a MSOA scheme such as given in Chapter 2, also known as the ladder model [27], the isodesmic model [28], or the free association model [29], where the equilibrium constants of the sequential back and forward reaction steps are presumed to be equal. (For a discussion of variants of this assumption, e.g., see [30].) Here, we give a statistical-mechanical prescription that is equivalent to it but that allows for a more straightforward generalization. 

Figures Universal polymerization curve of EPs. Plotted is the fraction polymerized material as a function of the dimensionless ratio hp T - Tp)/kBT with hp the net enthalpy gain of the formation of a single link, Tp the concentration-dependent polymerization temperature, and kg Boltzmann s constant. The line gives the theoretical prediction of the isodesmic model. The symbols Indicate experimental data on five chemically different ollgo(phenylene vlnyl)s In the solvent methyl cyclohexane at a concentration of 1M [38], By fitting to the data, values of hp are obtained from 24 to 70 kg T equivalent to 60 to 170 kJ mol". ...

The presumed supramolecular oligomers were subjected to concentration-dependent absorption spectroscopic analysis in solution. Fits of the extinction coefficients obtained as a function of concentration to an isodesmic model allowed association constants to be derived (cf. Table 12.1). On this basis, it was noted that... 

Table 12.1 Association constants for the supramolecular oligomers built up from TTE-C4Ps and DNP-C4PS, as inferred from fits of concentration-dependent absorption spectroscopic data to an isodesmic model [86]...

Concentration-dependent studies of the aggregates formed between 42 and each of the three DNP monomers were carried out using absorption spectroscopy. The data were then fit to an isodesmic model as above. The complexation constants derived from these analyses (cf. Fig. 12.36f) revealed association constants for the interaction with 42 in the order 49>47>48. This led to the suggestion that the length of the linker between the DNP moieties plays a role in modulating the binding events however, it does not fully explain these findings. More complex... 

As the next topic in this section, we want to calculate the average diffusion coefficient for systems in which aggregation occurs one molecule at a time. The simplest case is called the isodesmic model. It assumes that... 

Equations 6.2-26 and 6.2-32 show why the isodesmic model and micelle formation represent two extreme limits of solute aggregation. In the isodesmic case, aggregates of any size form with equal facility because all the steps are equal. In the micelle case, aggregates form only of that special micelle of n monomers the equilibrium constants are zero for all but that special size. 

Isodesmic reactions can be very useful for modeling systems and reactions. However, this approach is not without its limitations as well, which include the following ... 

Different isodesmic reactions will predict different values for the same heat of formation. Thus, this technique does not produce a uniquely defined value for the heat of formation it is not a model chemistry and cannot be systematically evaluated quantitatively. This effect is illustrated in the following example. 

The threshold concentration of monomer that must be exceeded for any observable polymer formation in a self-assembling system. In the context of Oosawa s condensation-equilibrium model for protein polymerization, the cooperativity of nucleation and the intrinsic thermodynamic instability of nuclei contribute to the sudden onset of polymer formation as the monomer concentration reaches and exceeds the critical concentration. Condensation-equilibrium processes that exhibit critical concentration behavior in vitro include F-actin formation from G-actin, microtubule self-assembly from tubulin, and fibril formation from amyloid P protein. Critical concentration behavior will also occur in indefinite isodesmic polymerization reactions that involve a stable template. One example is the elongation of microtubules from centrosomes, basal bodies, or axonemes. 

This chapter assesses the performance of quantum chemical models with regard to the calculation of reaction energies. Several different reaction classes are considered homolytic and heterolytic bond dissociation reactions, hydrogenation reactions, isomerization reactions and a variety of isodesmic reactions. The chapter concludes with a discussion of reaction energies in solution. 

The term " isodesmic was coined to designate a process in which the numbers of each kind of chemical bond are conserved, and only detailed bonding environments differed between reactants and products. The hope was that this would lead to significant cancellation of errors, and that even relatively simple models, in particular Hartree-Fock models, would provide an acceptable account of overall energetics. The comparisons which follow examine the extent to which such a conjecture is true. 

It is clear that proper description of the energetics of homolytic bond dissociation requires models that account for electron correlation. Are correlated models also needed for accurate descriptions of relative homolytic bond dissociation energies where the relevant reactions are expressed as isodesmic processes A single example suggests that they may not be. Table 6-15 compares calculated and measured CH bond dissociation energies in hydrocarbons, R-H, relative to the CH bond energy in methane as a standard ... 

Semi-empirical models are poor for relative base strength comparisons, paralleling their behavior for most other isodesmic reactions. They should not be used for this purpose. 

MNDO, AMI and PM3 models are unsatisfactory for assignment of ground-state conformer and for calculation of conformational energy differences in acyclic systems. While this could have been anticipated, given the poor performance of semi-empirical models for other isodesmic processes (see discussion in Chapter 6), it is nevertheless disappointing. In many cases, semi-empirical models either yield the... 

Both 3-21G and 6-31G models provide an excellent account of relative activation energies in these systems, paralleling their performance in accounting for the thermochemistry of isodesmic reactions (see Chapter 6). The STO-3G model is not successful, again consistent with its performance in isodesmic thermochemical comparisons. 

Density functional and MP2 models are needed to accurately account for the energetics of reactions where bonds are broken or formed and to describe absolute activation energies. Hartree-Fock models are unsatisfactory, but properly account for relative activation energies expressed in terms of isodesmic processes. MP2 models are also satisfactory here but density functional models sometimes lead to problems. 

Semi-empirical models are unsatisfactory in describing the energetics of all types of reactions, isodesmic processes included. 

Relative activation energies, when written in terms of isodesmic reactions, are also well described using Hartree-Fock models. MP2 models also provide satisfactory results but density functional models are problematic. 

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