The sub-system functional scheme [1,2] is a recently proposed framework for constructing exchange-correlation density functionals for use in density-functional theory based calculations. The fundamental principle is to describe the physics in a real material by mapping onto model systems that exhibit the characteristic physics in each separate part of the real system. The LDA functional can be seen as a sub-system functional: in all parts of the real material the assumption is that the needed physics is well described by the uniform electron gas model system. It is well known that this assumption is less valid in certain cases but it holds for surprisingly large classes of materials. The AM05 [3,4] functional takes this a step further by distinguishing between two separate types of regions in a real material, one type that is assumed to be well described by the uniform electron gas, and the other type of region assumed to be well described by a surface model system. I will discuss fundamental concepts of the sub-system functional scheme, such as model systems and compatibility.

One important consequence of the sub-system functional scheme is that it is known what physics is included in a functional. From the performance of AM05 for solid-state systems, it is clear that including a surface reference system into the functional cures the over-binding problem of LDA [5,6]. As expected, including physics from a single surface is not enough for describing regions where van der Waals forces dominate the physics. I will present AM05 results and discuss where the model systems included are enough and when additional physics need to be included in a new functional.

Improvement of AM05 is possible by fine-tuning the details in the construction. But a new major step in accuracy improvement is only expected if new physics is integrated in a functional via an additional model system. I will discuss what type of physics would be needed and what model systems could be used for this next step beyond AM05.

Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.

[1] W. Kohn, A. E. Mattsson, Phys. Rev. Lett. 81 3487 (1998)
[2] R. Armiento, A. E. Mattsson, Phys. Rev. B 66 165117 (2002)
[3] R. Armiento, A. E. Mattsson, Phys. Rev. B 72 085108 (2005)
[4] A. E. Mattsson, R. Armiento, to appear in Phys. Rev. B (2009)
[5] A. E. Mattsson, R. Armiento, J. Paier, G. Kresse, J. M. Wills, T. R. Mattsson, J. Chem. Phys. 128 084714 (2008)
[6] P. Haas, F. Tran, P. Blaha, Phys. Rev. B 79, 085104 (2009); 79, 209902(E) (2009)