The Subsystem Functional Scheme: The Armiento-Mattsson 2005 (AM05) Functional and Beyond

The subsystem functional scheme (Kohn and Mattsson, Phys Rev Lett 1998, 81, 3487; Armiento and Mattsson Phys Rev B 2002, 66, 165117) 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 local density approximately (LDA) functional can be seen as a subsystem 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 very accurate for surprisingly large classes of materials. The Armiento Mattsson 2005 (AM05) (Armiento and Mattsson, Phys Rev B 2005, 72, 085108; Mattsson and Armiento, Phys Rev B 2009, 79, 155101) 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. AM05 gives a consistent improvement over LDA. One important consequence of the subsystem functional scheme is that it is known what physics is included in a functional. Based on the performance of AM05 for a number of different systems, we 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. We discuss what type of physics would be needed and what model systems could be used for this next step beyond AM05. (C) 2010 Wiley Periodicals, Inc. Int J Quantum Chem 110:2274-2282, 2010