Group Additivity Values for predicting the heats of formation of organic compounds were developed by Benson and Buss. Here is a simple method to obtain the heats of formation of some acyclic alkanes using some known heats of formation and a little algebra.

Consider the three constitutional isomers of pentane in Fig. 1: n-pentane 1, 2-methylbutane (isopentane) 2 and 2,2-dimethylpropane (neopentane) 3. As branching increases from 1 to 3, the heats of formation become more negative (stable) and heats of combustion decrease. Each isomer can be characterized by the types of carbon atoms present: primary (P, CH₃), secondary (S, CH₂), tertiary (T, CH) and quaternary (Q). For n-pentane one can write equation 1.

2P + 3S = -35.1 kcal/mol (1)

Isopentane can be written as shown in equation 2

3P + S + T = -36.7 kcal/mol (2)

and neopentane becomes

4P + Q = -44.4 kcal/mol (3)

Clearly, three equations are not sufficient to provide unique values for P, S, T and Q given that there are four unknowns. Ethane's heat of formation (ΔH_f^o = -20.0 kcal/mol) can be divided in half to obtain a value of -10.0 kcal/mol for P. Propane (ΔH_f^o = -25.0 kcal/mol) satisfies equation 4.

2P + S = -25.0 kcal/mol (4)

Examination of the heats of formation of the n-alkanes reveals an increase of -5.0 kcal/mol per incremental methylene group to which value S may be assigned. Subtraction of -15.0 kcal/mol (3 x -5.0 kcal/mol) from the heat of formation of n-pentane (ΔH_f^o = -35.1 kcal/mol) leaves -20.1 kcal/mol for the residual two methyl groups. Halving this value gives -10.0 kcal/mol per methyl group P. Alternatively, ethane's heat of formation (ΔH_f^o = -20.0 kcal/mol) can be divided in half to obtain a value of -10.0 kcal/mol for P. Given the values of P and S, the value of a methine carbon T is calculated to be -1.7 kcal/mol using 2-methylbutane or higher 2-methylalkanes as models. [Note: Use of 2-methylpropane as a model gives a higher value of T as -2.1 kcal/mol.] Similarly using equation 4, Q has a positive value of 0.2 kcal/mol. These values illustrate that maximizing methyl groups contributes to increasing the heat of formation, i.e., more stable, and decreasing the heat of combustion. While these values obtained for P, S, T and Q are satisfactory, thet have been tweaked for better global application: P = -10.05; S = -4.95; T = -1.70 and Q = +0.50 kcal/mol.

The GAVs have been modified over the years, in particular the value of "T" (T = -1.7 kcal/mol; J. L. Holmes and C. Aubry, J. Phys. Chem. A, 2011, 115, 10,576). The chart on the right uses the GAVs within the yellow area. The chart lists a series of acyclic, saturated alkanes with the number of carbons, the values for P, S, T and Q and the calculated heat of formation. Experimental values for heats of formation (gas phase) are taken from the NIST website. As may be seen, these GAV values in general estimate heats of formation that have an error of less than a kcal/mol with a tendency to overestimate, i.e., a positive difference. This empirical method works satisfactorally up through the hexanes. Because 2- and 3-methylpentane have the same P, S, T and Q values, the method cannot accurately predict the difference in ΔHfo. The same is necessarily true of the higher homologs of the hexanes as well. As the number of carbons increases, so does the opportunity for branching. Entries 18-20 and 24-27 (in red) for the heptanes and octanes respectively, all have estimated heats of formation greater than one kcal/mol. Accordingly, a correction for each gauche interactions is introduced (G = 0.8 kcal/mol). The number of gauche interactions (#G) for each non-terminal C-C bond in its most stable conformation is counted and summed. Entry #25, 2,3,3-trimethylpentane, affords a calculated value for the heat of formation that is 4.7 kcal/mol too high (negative). The illustration below shows the lowest energy conformations viewing along the C2-C3 and C4-C3 bonds, there is a total of four and two gauche interactions, respectively. These six interactions add +4.8 kcal/mol to the computed heat of formation of -56.4 kcal/mol giving an adjusted value of ΔHfo = -51.6 kcal/mo that is nearly identical to the experimental value, ΔHfo = -51.7 kcal/mol.