Molecules from scratch without the fiendish physics by Lisa Grossman.

From the post:

But because the equation increases in complexity as more electrons and protons are introduced, exact solutions only exist for the simplest systems: the hydrogen atom, composed of one electron and one proton, and the hydrogen molecule, which has two electrons and two protons.

This complexity rules out the possibility of exactly predicting the properties of large molecules that might be useful for engineering or medicine. “It’s out of the question to solve the Schrödinger equation to arbitrary precision for, say, aspirin,” says von Lilienfeld.

So he and his colleagues bypassed the fiendish equation entirely and turned instead to a computer-science technique.Machine learning is already widely used to find patterns in large data sets with complicated underlying rules, including stock market analysis, ecology and Amazon’s personalised book recommendations. An algorithm is fed examples (other shoppers who bought the book you’re looking at, for instance) and the computer uses them to predict an outcome (other books you might like). “In the same way, we learn from molecules and use them as previous examples to predict properties of new molecules,” says von Lilienfeld.

His team focused on a basic property: the energy tied up in all the bonds holding a molecule together, the atomisation energy. The team built a database of 7165 molecules with known atomisation energies and structures. The computer used 1000 of these to identify structural features that could predict the atomisation energies.

When the researchers tested the resulting algorithm on the remaining 6165 molecules, it produced atomisation energies within 1 per cent of the true value. That is comparable to the accuracy of mathematical approximations of the Schrödinger equation, which work but take longer to calculate as molecules get bigger (Physical Review Letters, DOI: 10.1103/PhysRevLett.108.058301). (emphasis added)

One way to look at this research is to say we have three avenues to discovering the properties of molecules:

- Formal logic – but would require far more knowledge than we have at the moment
- Schrödinger equation – but that may be intractable for some molecules
- Knowledge-based approach – May be less precise than 1 & 2 but works now.

A **knowledge-based approach** allows us to make progress now. Topic maps can be annotated with other methods, such as math or research results, up to and including formal logic.

The biggest different with topic maps is that the information you wish to record or act upon is not restricted ahead of time.