# Heats of Formation by Density Functional Theory Calculations

• N. L. Allinger
Part of the NATO Science Series book series (ASIC, volume 535)

## Abstract

The idea that the heat of formation of an organic molecule may be calculated by the additivity of bond energies goes back for a long time, and the method was reasonably successful. It is limited in a major way if molecules contain strain, because the bond additivities do not in themselves include such strain. However, if the strain is independently determined, it can be added into the calculation. This was done by hand methods years ago by simply assigning a strain energy to a five-membered ring, a different strain energy to a four-membered ring and so on. The method works to a reasonable extent, but the strain energies of all five-membered rings have to be equal, for example, for this method to work. Sometimes this condition is satisfied, but it does not work in general.

We can determine the strain energies in molecules by either quantum mechanical methods, or by molecular mechanical methods. Either way, we can sum this together with ordinary bond energy terms and calculate the heats of formation of molecules. The question is, how general is this, and how accurate?

We have carried out these methods in some detail for saturated hydrocarbons, and are extending the methods like various functionalized derivatives of hydrocarbons. The results at the hydrocarbon level are instructive, and indicate what is expected to follow.

For a substantial number of hydrocarbons which have experimentally known heats of formation (approximately 30 compounds), the calculations almost always give the heats of formation to within certain error limits. These error limits depend upon the exact method used. If the Hartree-Fock method at the 6-31G* basis level is used, the rms error is about 0.8 kcal/mol. if the molecular mechanics or DFT method is used, the error is about 0.4 kcal/mol. The reported experimental errors are about 0.4 kcal/mol. Hence the conclusion is that for saturated hydrocarbons, we can calculate either by molecular mechanics (MM4), or by ab initio-DFT methods, the heats of formation to within experimental accuracy, on average.

## Keywords

Saturated Hydrocarbon Experimental Accuracy Large Ring Functionalized Molecule American Petroleum Institute
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## Authors and Affiliations

• N. L. Allinger
• 1
1. 1.Department of Chemistry Computational Center for Molecular Structure and DesignUniversity of GeorgiaAthensUSA