Heat of formation alkanes

TABLE 11.2. MM4 Alkane Heat of Formation Parameters (kcal/mol)... 

The alkane heat of formation parameters have values more or less as we expect, but there are some peculiarities. Of course, they were obtained by a least-squares fitting of data points to experimental information, and this is the parameter set that gives the best fit. However, one wonders why the R< parameter is needed (it was not needed in early force fields when the statistical tteatment was omitted see later). And one might wonder why the TOR value is as large as it is, for example. 

In order to develop a quantitative interpretation of the effects contributing to heats of atomization, we will introduce other schemes that have been advocated for estimating heats of formation and heats of atomization. We will discuss two schemes and illustrate them with the example of alkanes. Laidler [11] modified a bond additivity scheme by using different bond contributions for C-H bonds, depending on whether hydrogen is bonded to a primary (F(C-H)p), secondary ( (C-H)g), or tertiary ( (C-H)t) carbon atom. Thus, in effect, Laidler also used four different kinds of structure elements to estimate heats of formation of alkanes, in agreement with the four different groups used by Benson. 

Inspection of the values for the structure elements and their contribution to the heats of formation again allows interpretation The B-terms correspond to the energies to break these bonds, and a sequence of three carbon atoms introduces stabihty into an alkane whereas the arrangement of three carbon atoms around a central carbon atom leads to the destabilization of an alkane. 

If the heat of fonnation parameters are derived on the basis of fitting to a large variety of compounds, a specific set of parameters is obtained. A slightly different set of parameters may be obtained if only certain strainless molecules are included in the parameterization. Typically molecules like straight chain alkanes and cyclohexane are defined as strainless. Using these strainless heat of formation parameters, a strain energy may be calculated as illustrated in Figure 2.14. 

In marked contrast to the n-alkanes, the cycloalkanes exhibit thermodynamic properties where such regularities are no longer present. Heats of formation (AH ) for a substantial number of cycloalkanes are available from heats of combustion. With the exception of cyclohexane, AH°f is always more positive than the quantity — 4.926n. The difference between the two quantities leads to a quantitative assessment of the important notion of ring strain. The AH -values and strain energy data listed in Table 1 were taken from Skinner and Pilcher (1963). Other references give different but usually comparable... 

This criterion was originally established for the fragmentation of alkanes by Stevenson [18] and was later demonstrated to be generally valid. [19,20] The rule can be rationalized on the basis of some ion thermochemical considerations (Fig. 6.4). Assuming no reverse activation barrier, the difference in thermodynamic stability as expressed in terms of the difference of heats of formation of the respective products determines the preferred dissociation pathway ... 

This amounts to a sizeable reduction of the information that has to be stored, while conserving a rather good accuracy in the data. With these four parameters unknown heats of formation of alkanes can be estimated by the additivity scheme with a similarly high accuracy. This approach has been extended to other series of compounds. 

The alkyl radical ionization potentials needed were calculated by the pseudo-ir-orbital method.20 It was found21 that these radical ionization potentials converge to a constant value at the pentyl radicals. For various structures the values were as follows n-pentyl, 8.60 e.v. sec-pentyl, 7.81 e.v. iso-pentyl, 8.48 e.v. teri-pentyl, 7.19 e.v. (see ref. 21 for details of these calculations). The molecular ionization potentials also converge to a constant value at about ten carbons. Whenever these constant values are reached the heats of formation of the ions in Table II vary only with the heat of formation of the associated alkane, and therefore decrease by 5 kcal. mole-1 for each successive carbon atom. 

Heats of formation assume resonance stabilizations 10.8 kcal mole-1 in ( CHaCN) 12.6 kcal mole-1 in (CH3CHCN) and in [(CH3)2CCN]. " Na = doubly bonded nitrogen in azo compounds. h This correction assumes that the barrier to rotation in the radical R is two-thirds the barrier in the corresponding alkane RH. See O Neal and Benson for further discussion of this point. AH° and to +2 cal mole-1 °K 1 for 5°. The following example shows how the table is used to calculate thermodynamic properties for the 2-butyl radical (12).41 H3C—ch—ch2—ch3 12 ... 

Despite these structural features, the adamantane ring system is not strain-free 142). Comparison of an estimated heat of formation for adamantane based on group increments derived from acyclic alkanes in completely skew-free conformations 142> with the experimentally determined value 143 indicates that adamantane is strained to the extent of 6.48 kcal/mole. 

Table 10. Comparison of calculated and observed heats of formation of alkanes and cycloalkanesa)...

In Tables 10 to 12 we show the heats of formation calculated by the various methods, together with their deviation from the experimentally observed values for alkanes and cycloalkanes, alkenes and cydoalkenes, and acetylenes and aromatic compounds. Table 13 shows a comparison of heats of formation of hydrocarbon radicals calculated by the MINDO methods. Finally, in Tables 14 and 15 we show the results of MINDO/1 calculations on a selection of oxygen- and nitrogen-containing compounds. 

It will be always desirable to conduct C-H transformations under catalytic control to minimize the energy required and to maximize the selectivity of the reaction. Controlling the selectivity 16] is of paramount importance, because energy boundary conditions for all C-H transformations of simple alkane molecules are unfavorable. Table 3 reports, as a qualitative measure, heat of formation data... 

Experimental thermochemical results were mainly required to extend the para-metrization of the current force fields to highly strained compounds. Heats of formation calculated with Allinger s MM2 force field for alkanes and its extension to alkylbenzenes proved to be in by far the best agreement with the experimental results A few examples which demonstrate the quality of this agreement are shown in Table 1. 

The same type of calculation can be continued for larger hydrocarbons. The enthalpy for any alkane can be obtained from rel. (2.2.30), and a similar correlation relation can be obtained from experimental heats of formation for alkenes (see Figure 2.2.6) ... 

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