The fundamentals of theoretical chemistry are straightforward. A molecule’s electrons and atomic nuclei interact via a Coulomb potential. Nuclei can usually be treated as stationary classical particles, and electrons can often be assumed to be nonrelativistic. Solving the Schrödinger equation thus yields a molecule’s electronic structure and energy, from which one can derive reaction energies, spectroscopic properties, and other aspects of chemical behavior.

But the many-electron Schrödinger equation is too difficult to solve exactly. Computational chemists must develop simplifications that sacrifice some accuracy for the sake of efficiency. One approach, suitable for especially large or dynamic systems, is to treat just part of the molecule quantum mechanically and to simulate the rest classically. For their pioneering work on those quantum–classical hybrid models, Martin Karplus, Michael Levitt, and Arieh Warshel were awarded the 2013 Nobel Prize in Chemistry, which will be covered in detail in the December issue of Physics Today...

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