Isodesmic equation

An alternative method for computing heats (or free energies) of formation involves consideration of a balanced chemical equation, e.g., 

As a specific example, we might seek the heat of formation of 6-methylquinoline, the size of which is such that application of a methodology like G3 would be computationally rather intensive. However, consider the isodesmic reaction 

Note that the construction of an isodesmic equation is something of an art, depending on chemical intuition and available experimental data. In the above situation, if an experimental heat of formation for quinoline were not available, we might decide to resort to a reaction like 

While this reaction is still balanced, it is less ideal than Eq. (10.38). For instance, on the r.h.s. of Eq. (10.39), there are two aromatic C-H bonds where the carbon atom is bonded to a nitrogen, but on the Lh.s. there is only one. As a result, we might be forced to go to higher levels of theory to ameliorate any error this might introduce. In the extreme, one can imagine balanced reactions like 

The necessary experimental heats of formation are known to exquisite accuracy (or defined as zero, in the case of H2), and the calculations will be trivial for such small molecules, but accurately accounting for the enormous differences in the natures of the bonds on the two sides of Eq. (10.40) will require levels of electronic-structure theory nearly as high as those that would be necessary for a direct or parametric computation on 6-methylquinoline alone. The one virtue of Eq. (10.40), which is an example of a bond separation reaction , is that the total amount of unpaired electron spin on the two sides of the reaction is the same (in this case, zero) such a reaction is called isogyric . Note that atomization processes are 

---

Keywords DFT calculations Isodesmic equations Radicals ROMP2 calculations Thermodynamic stability... 

The reaction enthalpy and thus the RSE will be negative for all radicals, which are more stable than the methyl radical. Equation 1 describes nothing else but the difference in the bond dissociation energies (BDE) of CH3 - H and R - H, but avoids most of the technical complications involved in the determination of absolute BDEs. It can thus be expected that even moderately accurate theoretical methods give reasonable RSE values, while this is not so for the prediction of absolute BDEs. In principle, the isodesmic reaction described in Eq. 1 lends itself to all types of carbon-centered radicals. However, the error compensation responsible for the success of isodesmic equations becomes less effective with increasingly different electronic characteristics of the C - H bond in methane and the R - H bond. As a consequence the stability of a-radicals located at sp2 hybridized carbon atoms may best be described relative to the vinyl radical 3 and ethylene 4 ... 

Olefins are stabilized by alkyl substituents at the double bond. Every methyl group brings an additional stabilization of =4 kcal/mol [33], as illustrated by the isodesmic equation ... 

Aluminium alkyls, like all alkyls of electropositive elements, are destabilized by substitution at the a-carbon. A destabilization of =2.5 kcal/mol [33] can be estimated from the isodesmic equation ... 

Along the way it became clear that, perhaps surprisingly, HF energies could be chemically useful. Typically their utility was manifest for situations where the error associated with ignoring the correlation energy could be made unimportant by virtue of comparing two or more systems for which the errors could be made to cancel. The technique of using isodesmic equations, discussed in Section 10.6, represents one example of how such comparisons can successfully be made. 

However, if the theoretical target is instead the free energy change for the isodesmic equation... 

Friesner (2002) have reported average errors of about 150 mV for various organometallic species in different organic solutions. As already discussed for pA gS, still better accuracy in redox potentials can often be achieved through the use of isodesmic equations or functional-group-speciflc correction schemes (see, for example, Winget et al. 2000). 

In contrast, /1-silyl-substitution is predicted by the calculations to be far more stabilizing than /1-alkyl substitution. Thus, the isodesmic equation 3 predicts for 9 a stabilization by the /1-silyl group of 38 kcalmol-1, while the /1-methyl substitution in 10 gives only a stabilization of 28 kcalmol-1 [MP3/6-31G(d)//3-21G(d)]5. The stabilization by the silyl substituent is markedly orientation-dependent. Thus, the perpendicular conformation of the /1-silylethyl cation 9p is higher in energy by 29.6 kcalmol-1 compared with the bisected conformation 9 [MP3/6-31G(d)//3-21G(d)]5. The open /1-silyl-substituted vinyl cation 11 is lower in energy by 28.6 kcalmol-1 and 20.5 kcalmol-1 [MP3/6-31G(d)//3-21G(d)] compared with the vinyl cation (equation 4, R = H) and the 1-propenyl cation (equation 4, R = Me), respectively5. 

Using the isodesmic equations 9a-c Tsuno and coworkers calculated from the experimental gas phase basicities that the a-trimethylsilyl group stabilizes the styryl cation by 4.5 kcalmol-1 (equation 9a). Equations 9b and 9c which compare the effect of the a-trimethylsilyl group with those of the t-butyl- and the methyl substituent, respectively, are nearly thermoneutral, indicating the order Alkyl = SiMe3 > H of styryl cation stabilization ability18. 

Scheme 7.1 Isodesmic equation for the conversion of methane and propane into ethane (the abbreviation for the theoretical method, B3LYP/6-31 G(d), indicates the use of Becke s three-parameter hybrid exchange functional with the Lee-Yang-Parr correlation functional and a double-f Pople-type split valence basis set with one set of d-type polarization functions).

Now we turn from benzene to another cyclically delocalized molecule, oxirene or oxacyclopropene [172]. Is oxirene stabilized or destabilized by its 7t-electron system We can answer this question using an isodesmic equation, with B3LYP/ 6-31G energies/geometries as usual. Here we try to cancel out the strain in oxirene by having on each side of the equation about the same amount of ring strain (on each side two sp2C-0 bonds, etc) ... 

Finally, heats of reaction can be calculated by ab initio methods with the aid of isodesmic reactions (Section 5.5.2.2a), as indicated in Fig. 5.28 (actually, the scheme in Fig. 5.28 is not strictly isodesmic - for example, only on one side of the isodesmic equation is there an H-H bond). From this scheme... 

---