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Insights from Natural Orbitals

A well-scaling natural orbital theory


How can we explain the observed properties of a material? How are those properties linked to the material's intricate atomistic details? Is it possible to custom-tailor a material by manipulating the atoms? Such questions arise in many areas of modern science, ranging from physics to chemistry, biology and materials science. A central role in the answer is played by the electrons. Electrons move between atoms and form a glue which holds the molecules or solids together.

The nature of this electronic sea is governed by the laws of quantum mechanics. It is the many-body wavefunction describing the state of the electrons which holds the information about most of the properties of a material. Unfortunately, this many-electron wavefunction is a very complex object, and it is impossible to store or handle the exact wavefunction even in today's most sophisticated computers. For this reason, scientists have long been developing alternative computational methods without attempting to store the exact wavefunction. Quantum chemists, for example, have devised powerful techniques to approximate the wavefunction. While very precise for small molecules, the complexity of such methods increases quickly with the number of electrons.

Another successful way to address the quantum many-electron problem is given by density-functional theory (DFT). Here one uses the density of electrons in space to describe a material. DFT has proven extremely useful and computationally tractable, but many issues remain regarding its precision, especially in cases where the electrons show strong correlations.

In a recent article published in the Proceedings of the National Academy of Sciences [1], ICTP's Ralph Gebauer together with Roberto Car from Princeton University and Morrel H. Cohen from Rutgers University have presented a new approach to this many-electron problem. The article, entitled "A well-scaling natural orbital theory" shows how one can focus on so-called "natural spin-orbitals" to describe the motion of individual electrons, solving for them together with their joint and individual probabilities of occurrence within the system. This approach avoids the description of the full many-body wavefunction, but is able to better account for strong electron correlation than traditional DFT. The approach retains the same scaling with system size as DFT or Hartree-Fock methods.