The Group Increment Method

Values for the Heats of Formation of Simple Linear Alkanes (in kcal/mol) 

Once we have a CH2 group increment, it is simple to determine the group increment for a CH3 group in an alkane. We take AH° for -hexane, for example, subtract 4(-4.93 kcal/ mol) for the four CH2 s, and divide the remainder by 2, because there are two CHa s. When this is done and averaged over a number of alkanes, a value of-10.20 kcal/ mol is obtained for the CH3 group increment, designated as C-(H)3(C). We can now calculate a priori AH° for any linear alkane. For CHafCHa),- 2CH3, AH° is predicted to be exactly ( - 2)(-4.93 kcal/ mol) + 2(-10.20 kcal/mol). 

Sample calculation of using group increments, shown for isobutylbenzene. 

Now that we have established a definition of the stability of a compound—its heat of formation—we can return to the notion of strain. We introduced strain at the very outset of the chapter, defining it as an internal stress within a molecule due to some bonding or structural / conformational distortion. Now that we have a way to predict the stability of a molecule without any bonding distortions, we can give a very precise definition of strain energy. 

The group increments method suggests that we can predict AH ° for any organic molecule—a powerful tool, indeed. Let s consider some more examples. Table 2.5 shows calculated and experimental AH° values for simple cycloalkanes. The calculated AHf° for cyclo[u] is just w(-4.93 kcal/mol). For cyclohexane the result is quite good, but then things start to go downhill. The error for cyclopentane is considerable, while cyclobutane and cyclopropane are completely off. 

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As an example. Figure 2.4 shows how to calculate AH ° for isobutylbenzene. The process is straightforward, and it gives surprisingly good results. We will use the group increment method sporadically in later chapters, and soon we will introduce some additional features of the method. At this point, however, we state a few general observations, and a few... 

Hypothetical potential energy surface for cyclopropane isomerization based on the group increments method. 

A major difference with desired reactions is that the stoichiometry is often unknown, that is, the decomposition products are unknown. The reason is that decomposition reactions are often affected by the triggering conditions and thus often run along different reaction paths. This is a major difference compared to a total combustion, for example. The consequence is that the decomposition enthalpy cannot be predicted using standard enthalpies of formation AHjj taken from, for example, tables or estimated by group increment methods, such as Benson groups [3, 4] ... 

On the other hand, the volume contribution of structural groups already contains inbuilt information on the influence of the atomic surroundings. As a consequence the Van der Waals volume of the structural units can approximately be calculated as the sum of the Van der Waals volumes of the composing structural groups. Bondi (1964,1968) was the first to calculate the contributions of about 60 structural groups to Vw. Later Slonimskii et al. (1970) and Askadskii (1987) calculated about 100 values of atomic increments in different surroundings. Since the two approaches used the same method of calculation, and nearly equal basic data on the atomic radii, the calculated values for the structural units are approximately equal. In Table 4.2 also the group increments of Vw are shown, next to those of M. By means of these data the Van der Waals volumes of the Structural Units are easily calculated. 

The calculation of the liquid-fluid equilibria with the group contribution method has been presented elsewhere [4], The matrix of the parameters of group interaction (Table 1) contains values readjusted relative to the matrix obtained considering only liquid-fluid equilibria [4], These parameters are Ai5, A35, A45 and A59. The introduction of supplementary increments for the form of the molecules (a3 and P3.5) enables good results to be obtained for the calculation of solid-fluid equilibria and does not essentially modify the representation of liquid-fluid equilibria. The average relative deviation 5r(x) for the experimental data as a whole is 16 7% for the group contribution method and 13.3% for the model with E12 adjusted. The experimental data concern 40 isotherms (P,x) for 11 binary mixtures of solid aromatic hydrocarbon with supercritical C02. 

The heat of formation AH°f of 1 has been calculated by several groups (see Table 9). An experimental value is not available, but a value of 99kcalmol has been estimated from increments , and 97.3 kcal mol has been estimated <1997T13111> by applying the group additivity method <1996T14335>. 

If the two repeat units differ in size, they will also show a disparity in number of nearest neighbor contacts, or coordination number. We follow Staverman [24] and account for such differences assuming that ratios of coordination numbers can be identified with ratios of molecular surface areas. The latter can be estimated with Bondi s group increment method [25]. 

TABLE 2-383 Group Increments for the Ambrose Method Concluded)... 

An alternative to the measurement of the dimensions of the indentation by means of a microscope is the direct reading method, of which the Rockwell method is an example. The Rockwell hardness is based on indentation into the sample under the action of two consecutively applied loads - a minor load (initial) and a standardised major load (final). In order to eliminate zero error and possible surface effects due to roughness or scale, the initial or minor load is first applied and produce an initial indentation. The Rockwell hardness is based on the increment in the indentation depth produced by the major load over that produced by the minor load. Rockwell hardness scales are divided into a number of groups, each one of these corresponding to a specified penetrator and a specified value of the major load. The different combinations are designated by different subscripts used to express the Rockwell hardness number. Thus, when the test is performed with 150 kg load and a diamond cone indentor, the resulting hardness number is called the Rockwell C (Rc) hardness. If the applied load is 100 kg and the indentor used is a 1.58 mm diameter hardened steel ball, a Rockwell B (RB) hardness number is obtained. The facts that the dial has several scales and that different indentation tools can be filled, enable Rockwell machine to be used equally well for hard and soft materials and for small and thin specimens. Rockwell hardness number is dimensionless. The test is easy to carry out and rapidly accomplished. As a result it is used widely in industrial applications, particularly in quality situations. 

Tables 6.3-6.5 record data developed to undertake structural analysis in systems possessing chromophores that are conjugated or otherwise interact with each other. Chromophores within a molecule interact when linked directly to each other or when they are forced into proximity owing to structural constraints. Certain combinations of functional groups comprise chromophoric systems that exhibit characteristic absorption bands. In the era when UV-VIS was one of the principal spectral methods available to the organic chemist, sets of empirical rules were developed to extract as much information as possible from the spectra. The correlations referred to as Woodward s rules or the Woodward-Fieser rules, enable the absorption maxima of dienes (Table 6.3) and enones and dienones (Table 6.4) to be predicted. When this method is applied, wavelength increments correlated to structural features are added to the respective base values (absorption wavelength of parent compound). The data refer to spectra determined in methanol or ethanol. When other solvents are used, a numerical correction must be applied. These corrections are recorded in Table 6.5.

A well-known tool for the estimation of reactivity hazards of organic material is called CHETAH [5]. The method is based on pattern recognition techniques, based on experimental data, in order to infer the decomposition products that maximize the decomposition energy, and then performs thermochemical calculations based on the Benson group increments mentioned above. Thus, the calculations are valid for the gas phase, but this may be a drawback, since in fine chemistry most reactions are performed in the condensed phase. Corrections must be made, but in general they remain small and do not significantly affect the results. 

The transition of a protein or a single cooperative domain from the native to the denatured state is always accompanied by a significant increase of its partial heat capacity (see, for reviews, Sturtevant, 1977 Privalov, 1979). The denaturationaJ increment of heat capacity A JCP = C° Cp amounts to 25-50% of the partial heat capacity of the native protein and does not depend noticeably on the environmental conditions under which denaturation proceeds (Fig. 1) or on the method of denaturation. However, it is different foi different proteins and seems to correlate with the number of contacts between nonpolar groups in native proteins (Table I). On the other hand, the partial specific heat capacities of denatured states of different proteins appear to be rather similar (Tiktopulo et... 

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