Accidential Accuracy

 Why chocolate makes you fat but TNT doesn't

TNB: an explosive that is
closely related to TNT

Yesterday we carried out some (as we thought) very approximate calculations for a little 2 hrs quantum chemistry workshop that we will give during the annual meeting of my graduate school next week.

I thought it would be fun to calculate and compare detonation energy of an explosive to the energy content of "chocolate", which basically is sugar and fat 50:50. In doing so, one will find that you could never get fat from TNT because it actually contains only a small fraction of the chemical energy that is stored in chocolate.

a mono sugar: Glucose
(sucrose is too big)

Since we only have two hours for the whole workshop we've chosen to employ an approximate level of theory from the density functional theory (DFT) corner called B3LYP with a small SVP basis on model compounds. Furthermore, we decided to ignore all entropic, thermal and environmental influences to keep it simple. For the detonation of TNB we used a simplified reaction equation yielding only CO, N2 and H2 which circumvents the calculation of electronically complex (radical) nitroxides and such. At this level of theory, all calculations take about 1 hour on a modern laptop computer.

a fat model: Octanoic acid
(real triglycerides are to big)

The trickiest part to get right is the energy of liquid water, which is needed since we have physiological conditions. Here, we extrapolated from a few calculations (one water, one water using a solvent model (PCM), two water + PCM, four water+PCM, eight water+PCM) to to energy of liquid water.

Despite the crude model and level of theory we hoped to achieve at least qualitative agreement with the experiment, but then something not completely unexpected happened.

For comparison (taken from wikipedia)
- The experimental detonation energy of TNB is 3.8-3.9 kJ/g
- The physiological energy content of sugar is 17 kJ/g
- that of fat is 39 kJ/g.

Now look at the B3LYP/SVP results:

results of the B3LYP/SVP thermochemistry calculations

I think the explanation for this astounding accuracy is again a fortuitous cancellation of errors: The intermolecular interactions we neglect on the left side of the equation are obviously of the same or very similar size as the entropic and thermal corrections we neglect on the right side of the equation.

After all, its just spooky how well error cancellation can work out, in particular for DFT/B3LYP. This is not always a good thing! In my last post on nitrobenzene for example, you can read how error-cancellation can be quite problematic.