Isodesmic reaction

By definition, an isodesmic reaction is one in which the number of bonds and the bond types are the same on both sides of the reaction (Chesnut, 1996). An illustration of the use of isodesmic reactions is from the work of Cheng and Li (2003) in which they determined A H29S of n-tert-butyl methanes, where n = 1, 2, 3, and 4. We shall take the simplest example, calculation of AfH29i of er -butylmethane (2,2-dimethylpropane) itself. The isodesmic reaction is 

This enthalpy change is used to calculate the remaining unknown from the experimental values of Af//298 for methane and ethane 

If H29g is computed for a number of molecules related to one another by hydrogenation and isomerization reactions as in Fig. 3.10, and if Af//298 is known for any one of them, Af//298 can be calculated for all the rest (Rogers et al., 1998). In Fig. 3.10, the experimental value of the enthalpy of formation of acetone is well known, AfH29i = 52.23 0.14 (Wiberg et al., 1991), as are one or two of the other values, but most are not. Calculation of Af//298 for the remaining members in the scheme depends upon reactions with similar reactants and products 

Whatever the error there may be in an experimental measurement of Af//29g of the smaller molecules in an isodesmic reaction, it is multiplied by their stoichiometric coefficients in calculating A H29S of the target molecule. For example, whatever small error there may be in A Hm of ethane in the example cited above, it is multiplied by 16 in the calculation. 

The values lead to a computed value for AH of 60.64 kcal-moT for the reaction, and a predicted value of -94.64 kcal-moT for AHf for carbon dioxide. This value is in excellent agreement with the experimental value of -93.96 kcal-moT  

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  

This technique cannot be applied to reactions which do not happen to be isodesmic (for example, destruction of ozone by atomic chlorine). 

We will also compute the heat of formation for Sip4 using these reactions (studied at MP2/6-31 lG(d,p) // HF/6-31G(d))  

SiH4 + 4HF — 4H2 + Sip4 S1F2H2 + 2HF 2H2 + Sip4 SiH4 + 4F2 — Sip4 + 4HF 

Combining the calculated energy difference for the left- and right-hand sides with experimental values for CH4, CH2=CH2 and CH3CH3, the (absolute) stability of propene can be obtained reasonably accurately at a quite low levels of theory. This does, however, require that the experimental values for the chosen reference compounds are available (section 3.3). 

In addition to bond balance, we try to use working reactions with group balance for maximum cancellation of error. A number of work reactions in this study do not conserve group balance but they do conserve a majority of the groups and thus have better cancellation of errors than a conventional isodesmic reaction. Density Functional Theory calculations which included the corresponding ZPE and thermal corrections are performed for all species in reactions set, and the enthalpy change 29 of each reaction is calculated. 

The enthalpy of formation, A//°29s of the target species is determined from the calculated A 298 Hess s Law with the known enthalpies of the other reactants, (reference species) according to the following equation  

In a reaction set, the arithmetic mean is the final value obtained for A f°298 of a species. 

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Note that, for themiochemical purposes, there is no requirement that we can actually cany out the reaction. Systematic computational errors will, in some measure, cancel between the right and left sides of isodesmic reactions (10-20), giving an estimate of the GAMESS calculations at the STO-3G level lead... 

A second issue that arises in relation to isodesmic reaction enthalpies is why they should exist at all. If all we are doing is rearranging bonds, shouldn t the summed bond energies be the same on either side of the reaction Not really. A negative 6-3IG MP2 enthalpy of 5 kcal mol for the reaction... 

Use the experimental values of the enthalpies given in the section on isodesmic reactions along with the isodesmic reaction... 

Bodi MO theory and experimental measurements provide a basis for evaluation of the energetic effects of conjugation between a double bond and adjacent substituents. Table 1.16 gives some representative values. The theoretical values AE are for the isodesmic reaction... 

Table I.IS gives total bonding energies in kilocalories per mole for some simple molecules. The B3iyP results are comparable in accuracy to G1 and G2 results. Another comparison was done with a series of cyclic hydrocarbons as the test case. The calculations were done using an isodesmic reaction scheme. The results are given in Table 1.19. Density functional calculations have also been successfully extended to functionalized molecules. ...

Interesting stabilization and structural trends have been noted using MP2/6-31G calculations on the effect of substituents on imines. The data below give AE for the isodesmic reaction and show that stabilization tends to increase with Xbe 1 gi (>up electronegativity of the substituent. The X—N=CH2 bond angle decreases with Xbe-... 

Calculations are frequently done on the basis of isodesmic reactions in order to provide for maximum cancellation of errors in the total energies (see Section 1.3). The "experimental AH of the process can be obtained from the tabulated AHf values of the reactants and products. Table 4.2 compares the errors in AHf for some isodesmic reactions with those for the corresponding atomization reactions for G2 calculations on some... 

Calculations Using Atomization versus Isodesmic Reactions" ... 

Table 8.5 lists the enthalpies for a series of isodesmic reactions involving conversion of carbonyl derivatives to the methyl ketones. The A// of the reactions is given both from thermodynamic data and as calculated at the MP3/6—3H--I-G level. These... 

The isodesmic reaction approach (see Section 4.1) has also been applied to calculation of the resonance stabilization of benzene. 

Use the calculated energies for the molecules shown below to calculate isodesmic reaction energies for the equation ... 

The effect of substituents has been probed by MO calculations at the STO-3G level. An isodesmic reaction corresponding to transfer of a proton from a substituted <7-complex to an unsubstituted one will indicate the stabilizing or destabilizing effect of the substituent. The results are given in Table 10.1. 

An isodesmic reaction is one in which the total number of each type of bond is identical in the reactants and products. Here is a simple example ... 

In this reaction, there are twelve single bonds and one (C-O) double bond in both the reactants and products. Because of this conservation of the total number and types of bonds, very good results can be obtained relatively inexpensively for isodesmic reactions due to the cancellation of errors on the two sides of the reaction. In other words, comparing very similar systems enables us to take maximum advantage of cancellation of error. 

Isodesmic reactions may be studied in themselves. For example, energy differences may be compared between the reactants and products in order to predict AH. In addition, isodesmic reactions may be used to predict the heats of formation for compounds of interest by predicting AH for the reaction and then computing the desired heat of formation by removing the known heats of formation for the other compounds from this quantity. We will look at an example of each type in this section. 

In this example, we will use an isodesmic reaction to predict the heat of formation of... 

The types and number of bonds are the same for the products and reactants, so this is an isodesmic reaction. We can compute the heat of formation for CO2 in this way ... 

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. 

Although both predictions of AHflethane) are in reasonable agreement with experiment, they differ from one another by almost 5 kcal-mol. Such a large difference for a simple hydrocarbon system—the sort of species isodesmic reactions are purported to treat well—suggests caution when applying this technique. 

In all three reactions, MP2 theory overcompensates for electron correlation (as it often does). Of the methods used in the original study, only the MP3 level provides an adequate treatment of these reactions. Note, however, it is the special characteristics of isodesmic reactions that enables MP3 to do so well. 

Semi-empirical methods are sometimes suggested for studying isodesmic reactions. We performed this same study using the AMI method the results are given in the following table ... 

Sju could expand the discussion of the isodesmic reactions by considering additional similar reactions (e.g., X= NH2, SiH, PHj, CN, SH, CF3). You could also run the computations at the MP4 level to discuss the relative merits of the MP2, MP3 and MP4 levels of theory and to compare the B3LYP results to them. 

Solution These are the isodesmic reactions that we studied ... 

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