Wednesday, July 31, 2013

would you do FMO-10 if you could?

The many-body expansion of the energy is a popular way to reduce the cost of computing the energy of an entire system too large to fit into your computer. The strategy is quite simple: chop your large system into several small pieces, do your quantum mechanics on each piece. In practice you can stop here (1-body), but often people to pair-corrections (2-body) to get good results and triples-corrections (3-body) if they want to be fancy. There are many implementations of this, including the eXplicit-POLarization method, the Fragment Molecular Orbtital method and the electrostatically-embedded many-body method, just to name a few.

My question is: would you do a 10-body calculation if you could?

Here is an argument against it, and it does not involve anything to do with accuracy, but rather computational cost.

The number of n-mers (1-mers, 2-mers, 3-mers and so on) increase quite drastically if one does not include approximations, but I can hear you ask: how bad is it?

For 16 water molecules, each water molecule is a 1-mer, the total number of calculations one would need to perform in order to calculate the n-body calculation is presented in the figure below


where we see that a 10-body calculation would require a total 58650 unique calculations whereas the 3-body calculation would require a "mere" 696.

Edit: For a discussion about timings, +Jan Jensen wrote a blog post on the subject.

That's at least an argument against dreaming of large n-body calculations unless you severely sit down and think about eliminating some of these calculations.
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