The spatial directions of magnetization and the energy required to alter it are the essence of magnetic recording and permanent magnets, such as those in electric motors. Magnetooptics is the basis for many scientific probes, such as the surface magnetooptical Kerr effect, and for writable optical disk storage. In the case of magnetooptics, there is substantial evidence that the LSD approximation contains the required physics. Parameter-free calculations are quite successful in predicting the Kerr rotation of modestly complex intermetallic compounds.

In the case of magnetic alignment, there is encouraging evidence that these effects are within the reach of LSD-based calculations, although the importance of orbital magnetism to these effects is not well known. Additionally, extraction of the desired, but quantitatively small, total-energy differences from computational noise has proven to be very difficult. But there has been recent progress on this front, and continued progress represents a near-term opportunity.

Until recently, the analysis of rare-earth and actinide systems containing localized f electrons was thought to lie beyond the reach of LSD-based calculations. A relatively straightforward extension of the theory by Brooks, Johansson, and co-workers (M.S.F. Brooks, Physica 130 B:6, 1995; O. Eriksson, M.S.F. Brooks, B. Johansson, Physical Review B, Vol. 41, 7311, 1990) has proven very successful. While this advance permits the treatment of orbital magnetism and effects related to magnetic anisotropy, it does not extend to dynamical phenomena, such as the Kondo effect. The exploitation of this advance, in the context of hard magnets for example, is an opportunity for this field.

The cuprate high-T_c superconductors are perhaps the most dramatic illustration of the limitations of the LSD approximation. The transition-metal oxides are another highly visible example. Even here, however, calculations based on the LSD approximations have been quite useful. The guide they provide to the interpretation of angle-resolved photoemission has been particularly useful, both in NiO and the high-T_c materials. The use of these calculations to estimate parameter values for more phenomenological theories also has been valuable and represents an ongoing opportunity.

As the discussion above indicates, a theoretical extension of the LSD approximation remains an outstanding need as well as opportunity of the field. Nonetheless, the discussion also indicates that calculations based on the LSD approximation are often of considerable conceptual and practical utility. Exploitation of this theoretical framework as a guide to the design and development of new magnetic materials is particularly promising. The fact that prominent suppliers of materials design software will offer commercial software of this type is a measure of the practical opportunity. The fact that LSD-based calculations are parameter free means that the computation of chemical trends is often particularly reliable. Finally, the application of LSD-based theory to increasingly complex systems of technological interest ranks among the most straightforward ways to exploit anticipated increases in computational power.

Electron correlation effects play a critical role in certain classes of materials, such as magnets and superconductors. The ab initio treatment of electron correlation effects in real materials remains one of the most challenging tasks, both conceptually and numerically. Prototypical examples of strongly correlated systems include high-T_c superconductors, transition-metal oxides, f-electron systems, and superfluid ³He and ⁴He. It is widely accepted