# How to calculate the enthalpy of reaction using Gaussian 09?

I'm having a hard time trying to understand what's the correct way to calculate the enthalpy of reaction given that I've already calculated the frequencies of my compounds in Gaussian. Below I show the reaction of interest:

As you can see in the figure, experimentally, this reaction leads to the formation of ionic species. As for my calculations, I have all four species optimized (all of them separated, I'm not working with complexes) with their respective frequencies.

As for the enthalpy, I'm using the following formula:

$$\Delta_\mathrm{R} H= \left[(\text{Iodide anion}) + (\text{cationic product})\right] - \left[(\ce{FeCpI(CO)2}) + (\text{phosphine reactant})\right]$$

All terms are the sum of the electronic energy and the thermal enthalpy as given by Gaussian.

Am I doing it correctly? Because I'm not sure, if I have to consider both products together or separated as I'm currently doing. Can you give me some light on this?

In principle your approach is correct. There are a few pitfalls though.

Quantum chemistry is usually not well equipped handling ions, especially anions, within reactions, hence the evaluation of these reaction energies will probably contain some errors. This is mostly due to the fact that you are technically calculating everything in the gas phase, and apply thermal corrections later. In well behaved systems, e.g. organic compounds without charges, that does not matter much. But even then we try to exploit error compensation with (for example) isodesmic reactions.

If you are treating the ions separately, you are neglecting all possible interactions between them, too. That might lead to additional errors. One way to approximate this is to calculate the ion pair together. That might not always lead to the correct result since solvents will also play a role here. Obviously you could also include these.

Another problem for your system is probably conformational space. Especially the phosphine is somewhat flexible and will adopt a few conformations (isolated as well as complexed). Here it is also important to find the global minimum, to evaluate the energies correctly.

It is advisable to look for similar systems in the literature and see what they have done. You may also find benchmark studies that will give you more information on how well your methodology performs for such systems. There is no general recipe for success; it always involves a lot of hands-on work. Eventually you will want to compare your calculated results to experimental ones to verify your findings.

• Thanks, @Martin! Your answer will surely help me a lot! Concerning the error contained in my calculations, what if I only want to see trends in the Enthalpy among different Phospines? More specifically, I'm varying the stereochemistry of them. I'm not really interested in obtaining accurate values. As for experimental results, I only have yields. – Benjamin233 Jul 30 '18 at 13:52
• @Benjamin233 Try calculating isodesmic reactions: $\ce{[Fe(phos)]+ + phos' <=> [Fe(phos')]+ + phos}$ where $\ce{phos}$ is your reference phosphine, something like $\ce{PMe3}$, and $\ce{phos'}$ is the one you'd like to investigate, and $\ce{[Fe(X)]+}$ is short for $\ce{[Fe(Cp)(CO)2(X)]+}$... That should give you the thermodynamical order of your target compounds. Here it is most important, that you have the global minimum of all structures. – Martin - マーチン Jul 30 '18 at 14:07
• I have five different phosphines, and each one has different stereochemistry, so I compared their relative energies to see which one is the most stable. So, what would be the difference between just comparing their energies and calculating isodesmic reactions? I actually did it and I could observe reasonable results, but which approach is more reliable? – Benjamin233 Aug 1 '18 at 23:44
• @Benjamin233 If you calculate relative energies of complexes which are stereoisomers, then then that is essentially the same as computing isodesmic reactions (you can show that by doing simple maths). You cannot compute relative energies of complexes which are not isomers, as they have no common point to be relative to; then isodesmic reactions are a way to use error cancellation. You can search this site for some examples. – Martin - マーチン Aug 2 '18 at 12:35
• @Benjamin233 This one. Ours. Chemistry. Or direct search link: isodesmic – Martin - マーチン Aug 2 '18 at 14:15