  Density functional theory offers a very accurate way of computing materials
properties from first principles. However, it is too expensive for modelling
large-scale molecular systems whose properties are, in contrast, computed using
interatomic potentials.
  The present paper considers, from a mathematical point of view, the problem
of constructing interatomic potentials that approximate a given
quantum-mechanical interaction model. In particular, a new class of
systematically improvable potentials is proposed, analyzed, and tested on an
existing quantum-mechanical database.
