ChemNews.Com VOL 10 NO 2

Thermochemical quantities provide an important tool for understanding chemical reactions. Two of the most helpful are the heat of reaction and the Gibbs free energy of reaction. Computing these quantities via electronic structure calculations can be an effective way of obtaining accurate predictions of the experimental values. In this article, we discuss how to use a few of the tools that the Gaussian program provides for making such calculations readily obtainable.

The Reaction

Electronic structure calculations have been used to study gas phase reactions for many years. More recently, it has become possible to compute information about reactions in solution as well.

In this article, we will focus on computing the heats and free energies for gas phase reactions. A negative heat of reaction indicates that heat will be evolved in a reaction at constant pressure. A negative Gibbs free energy indicates that it is possible for the reaction to proceed spontaneously.

Our example reaction will be the heat of combustion of methane:

CH₄(g) + 2O₂(g) --> CO₂(g) + 2H₂O(g)

The Model

The Gaussian program has a fairly large number of model chemistries which can be used for predicting the relative energies of compounds. A model chemistry is a predefined recipe for calculating molecular energies.

One of the nice features of model chemistries is that they are uniquely defined for a wide range of molecules, and there are no additional parameters or information to supply once the initial guess molecular geometries are furnished. This makes such models very easy to use.

We'll look at one in particular, CBS-QB3, since it generally yields results which are accurate to the same degree as many experiments: around 2 kcal/mol.

Ultimately, it is necessary to calculate the force constants for the molecules involved in the reaction. Generally, this entails optimizing the molecular geometry and running a frequency calculation.

Fortunately, the recipes for CBS-QB3 and many of the other model chemistries are built-into Gaussian, so these steps all happen automatically, and there is no need for users to do it as a series of separate jobs.

Calculations

CBS-QB3 calculations were run on each of the four compounds involved in the reaction, using input files similar to that shown for water in Figure 1.

The output from these calculations can be quite long. The energy summary near the end of the output, which is the part relevant for computing heats and free energies of reactions, is illustrated in Figure 2 for water. The line containing the enthalpy and the free energy is the most important for our purposes. Table 1 summarizes these results for all four molecules.

From here, computing the final values is easy: the heat of reaction is the enthalpies of the products minus the enthalpies of the reactants (1 Hartree = 627.5095 kcal/mol).

This result compares favorably with the experimental result (from the JANAF tables) of -191.75 kcal/mol.

Essentially the same computations go into determining the Gibbs free energy of reaction:

Again, this result compares well with experiment (-191.37 kcal/mol).

The simplicity of these final computations belie the complexity of the machinery that goes into the overall calculations. For example, calculating heats of reaction at a given temperature formally involves determining the heat of formation of each of the compounds in the reaction at that temperature, and then taking the difference between the sum of the products and the sum of the reactants.

Finding the heat of formation of a compound at a given temperature itself involves computing the heat of formation at 0°K using the experimental heats of formation of isolated gas phase atoms, and correcting the heat of formation to the desired temperature.

However, for a typical reaction, all the compounds will be at the same temperature, and there will be the same number of atoms of each element on each side of the reaction, so much of the complexity neatly cancels out, leaving a very simple procedure for calculating heats of reaction.

Potential Pitfalls

Even though the Gaussian program takes care of most of the work, there are a few points that anyone attempting to compute thermochemical values will want to be aware of.

• Electronic state: If the calculation is performed on the wrong electronic state of a molecule, then the final answers will be incorrect as well. For example, if the above calculations were performed on singlet oxygen rather than triplet oxygen, the results would be wrong.

• Geometry: It is possible to use a starting geometry which yields the wrong minimum. For example, it could be the wrong conformer of a molecule. Another possibility is that the geometry optimization method defined in model chemistry may not produce a geometry which is accurate.

  Typically, the geometry optimization method chosen for these models is a balance between speed and accuracy. Occasionally, the balance is upset, and the resulting geometry is inaccurate.

• Hindered rotors: Some molecules have hindered rotors or other low frequency modes. These modes can potentially contribute significant error to the thermochemical quantities which are being computed. The Gaussian program has tools to assist in reducing these errors, when they occur.

The tools in Gaussian can provide an enormous amount of information to chemists that would be hard to obtain any other way. Being aware of how to use these tools will help chemists extract that information easily.