Bond energy additivity rule

Turning now to the theorem first postulated by Fajans and elaborated much further by Sidgwick and Pauling according to which the heat of formation of organic compounds from free atoms can be represented as the sum of constant contributions characteristic of each chemical link, we note first that the validity of this theorem constitutes no evidence for the existence of a constant heat of formation of the bonds covered by its scope. Take two kinds of bonds formed, say, by carbon with the two different atoms X and Y. Whatever the variation may be in the energies of the C—X and C—Y bonds with the position of the C-atom, no deviation from the additivity rule would result, so long as the variations are equal for both kinds of bonds the additivity rule merely expresses the constancy of the substitution heat — AH, in the reaction... 

In addition we postulate the following three rules, which are justified by the qualitative consideration of the factors influencing bond energies. An outline of the derivation of the rules from the wave equation is given below. 

Alternatively, for many classes of compounds the heats of formation can be estimated through additivity of bond properties or group additivity rules [32], Let s take a simple example using the additivity of bond properties to estimate the heat of formation of some species A. Suppose we know (1) the heat of formation of a related compound ABR, where B is the atom to which A is bonded and R is the rest of the molecule, (2) the heat of formation of BR, and (3) that for a series of other molecules in which a A-B bond occurs the A-B bond-dissociation-energy is nearly constant, and we assign it the value B.D.E.(A-B) J. Now consider the endothermic reaction... 

Isomeric effect—The additivity rule for bond energies applies only to compounds in a homologous series and small changes in structure cause deviations in the heats of formation. If the additivity rule were correct, saturated hydrocarbons possessing the same number of carbon and hydrogen atoms would have identical heats of formation. This, however, is not correct as is shown in Table CIX, where the experimental data indicate that the heat of formation... 

Resonance energy— Where the deviations from the additivity rule are such that the actual energy of formation is greater than the calculated value, it is found possible to describe the molecule by more than one valence bond structure. Thus it is found that every resonating molecule is more stable than it would be if it had the valence bond structure assumed for it in calculating the bond energy. The difference between the calculated and observed values has been termed the resonance energy by Paulino. This quantity we shall denote by the symbol iis. 

By similar calculations using the energies of the G=0, G—O and O—H bonds, we find that for the group GOOH, = 20 kcals and for the group COOC, Er = 22 kcals. A greater deviation from the additivity rule occurs in acetic anhydride... 

If the Coulomb interaction between electrons of different pairs is ignored, each localized bond and lone pair contribute independently to the total energy, which implies a perfect additivity of bond energies. In the independent-particle model, the localized bond function can be visualized as a two-center molecular orbital occupied by two electrons. Nevertheless, it is possible to reproduce deviations from additivity rules within this scheme, for instance, by taking into account overlap (for a review, see e.g. 2>). 

AdE3 occurs when the carbanion and carbocation are not very stable The energy surface folds down the middle. The electrophile and nucleophile end up on opposite faces of the pi bond anti addition). Markovnikov s rule is followed. 

Despite the lack of strict additivity of bond energies, Pauling s Rule is extremely useful because it allows one to estimate the heats of formation of compounds that have not been studied, or have not even been prepared. Thus in the foregoing example, if we know the enthalpies of the C-C and C-H bonds from other data, we could estimate the total bond enthalpy of ethane, and then work back to get some other quantity of interest, such as ethane s enthalpy of formation. 

Of course, using the additive scheme rules out the possibility of calculating of the contribution of electron correlation component in bond energy. In fact, the difference between estimated from the Morse potential and experimental bond energies [40] decreases in HI, HBr, HC1, HF, H2 92.8 (31.4%), 81.8 (22.5 %), 59.5 (13.8 %), -25.8 (4.5 %), 30.4 (7.0 %) kJ/mol, respectively. Apparently, the accuracy of the calculation of bond energy in small molecules is usually low-level. Exceptions can be found with molecules containing atoms of inert gases. The enforced dissociation of NeOH was shown to be described by Morse-like potential... 

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