Isodesmic reaction schemes

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. ...

JANAF thermochemical tables [160a] estimate the heat of formation of FCO radicals to be —41 15 kcal mol". MacNeil and Thynne [171] determined the F—CO bond energy from electron impact ionization study of CFjO, arriving at a heat of formation of —42 kcal mol . Henrici et al. [172] suggested a value of —34 5 kcal mol from shock tube experiments. Bowers and Chau [173] estimated a value of -42 + 4 kcal mol . Using isogyric and isodesmic reaction schemes and ab initio methods, Francisco and Zhao [174] estimated the heat of formation of FCO as -42.9 0.8 kcal mol", consistent with the measurements of Bower and Chau. 

Standard enthalpies of formation, zW°29s are calculated using the B3LYP/6-311G(d,p) calculation level of density functional theory and isodesmic reaction schemes for cancellation of errors. The recommended a//°29s of each value is the average value of data obtained from several isodesmic reactions. Comparison of the thermodynamic properties between the peroxides and corresponding hydroperoxides shows uniformity in property trends. A set oxygenated hydrocarbon groups are determined that result in consistent prediction of thermodynamic properties for the substituted alkyl and vinyl peroxides and hydroperoxides. 

Standard enthalpies of formation for the oxygenated and non-oxygenated hydrocarbons compounds were calculated, using the isodesmic work reactions in Tables 4.2, 4.3 and 4.4. of the target species are estimated using two to five isodesmic reaction schemes for... 

Assuming that aromatic stabilization of 24a and 24b is of the same magnitude, and this is also true for the lone-pair repulsion in the pairs 24a/25a and 24b/25b, the energy, A , of the isodesmic reaction (1) corresponds to the contribution from greater aromatic stabilization of 25a with respect to 25b (Scheme 26). At the MP2/6-31G approximation, AE = 10.5 kJ mol (94JOC2799). Similar arguments applied to the isodesmic reaction (2) allow estimation of the energy contribution due to the repulsion of adjacent lone pairs in 25a. In MP2/6-31G approximation, A = -25.9 kJ mol ... 

Energy changes are for the isodesmic reaction shown in Scheme 13.33 h Calculated from the ab initio energies of R-[16]-OH and R-[17].33... 

The calculated values of AH for the isodesmic reactions shown in Scheme 13 (Table 4) suggest that the effects of a-carbonyl and a-thiocarbonyl substituents are controlled largely by the balance between two opposing interactions at the alkenes R-[17] ... 

When considering the stability of spin-delocalized radicals the use of isodesmic reaction Eq. 1 presents one further problem, which can be illustrated using the 1-methyl allyl radical 24. The description of this radical through resonance structures 24a and 24b indicates that 24 may formally be considered to either be a methyl-substituted allyl radical or a methylvinyl-substituted methyl radical. While this discussion is rather pointless for a delocalized, resonance-stabilized radical such as 24, there are indeed two options for the localized closed shell reference compound. When selecting 1-butene (25) as the closed shell parent, C - H abstraction at the C3 position leads to 24 with a radical stabilization energy of - 91.3 kj/mol, while C - H abstraction from the Cl position of trans-2-butene (26) generates the same radical with a RSE value of - 79.5 kj/mol (Scheme 6). The difference between these two values (12 kj/mol) reflects nothing else but the stability difference of the two parents 25 and 26. 

Ford and Herman have been able to correlate the calculated AMI stabilities of nitrenium ions vs. those of the corresponding arylmethyl carbo-cations, as defined by the isodesmic reactions of Scheme 69, through a simple relationship shown in equation (6)... 

SCHEME 12. Isodesmic reactions based on cyclobutyl derivatives 49-52. Reaction energies from MINDO/3 (first entry) and EHT calculations (second entry) in kcal mol173... 

To explore this possibility further, quantum chemical calculations were carried out for the isodesmic reactions of the model compounds 66 and 67 with dihydrogen to give the corresponding dihydrides (Scheme 17). These calculations showed that the reaction of 66 with H2 is about 14 kcalmol-1 less exothermic than that of 67. This difference may reflect aromatic resonance energy in the unsaturated molecule 66, reducing the enthalpy of the hydrogenation reaction. 

The related family of phosphonio-phospholides also belong to the five-membered aromatic heterocycles, as reviewed comprehensively in the recent work of Gudat [209] The aromaticity of the rings were concluded from stabilization in isodesmic reactions [210] and also from the structure of those rings characterized by X-ray diffraction, exhibiting equalized bond length distribution in the case of the cationic 59 [211] and also for the neutral zwitterionic 60 [212], and its r - and r 5-complexed forms [214] (Scheme 34)... 

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... 

The RSEs of the cyclic ethers demonstrate the usefulness of the GE scheme. Figure 3.5 plots the RSE against ring size for the cyclic ethers computed with the different schemes. As before, the isodesmic reaction fails by estimating positive... 

It has recently been argued " that the existing body of thermochemical data is inadequate to demonstrate quantitatively the effects of cyclopropyl conjugation that has been claimed for many systems. New measurements of the heats of vaporization of cyclopropyl cyanide and cyclopropylbenzene were made, and using these data and others in the literature the stabilities of a series of substituted cyclopropanes were compared to the corresponding 2-substituted propanes by the isodesmic reactions 1 and 2 shown in Scheme 1 ". ... 

Scheme 2. Isodesmic reactions used for calculations of the ring strain in cyclosiloxanes.

Isodesmic and homodesmotic reactions can use either experimental thermochemical data or energies obtained by MO or DFT calculations. There have been many specific reaction schemes and computational methods applied to calculation of stabilization energies. With the above homodesmotic sequence, calculations at the MP4(SDTQ)/6-31G((i,/ ) level give the following stabilization (AF) values. ... 

Figure 8. Plot of energies A q (Eq. [ 19]) of isodesmic reactions as a function of (Scheme 8). Data from Table 9.

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