The rem arkable progress in the architecture, speed and capacity of com puter hardw are continues to drive the development of quantum mechanical methods, thus allowing calculations on increasingly complex systems. Using high-end computers, accurate quantum mechanical all-electron studies are now possible for solids such as transition m etal compounds containing about fifty atoms per unit cell. Pseudo potential plane-wave methods are being applied to unit cells w ith 400 silicon atoms, and

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... c molecules consisting of over 100 atoms have become tractable using ab initio methods. Smaller, yet still useful calculations can be carried out on w orkstations. The combination of graphics workstations and high-performance supercomputers, integrated in tightly coupled heterogeneous networks, has allowed the design of software systems with unprecedented convenience and visualization capabilities. Despite this progress, however, there is still an urgent need for new quantum mechanical methods which converge system atically to the exact solution of Schrodinger's equation while m aintaining a reasonable scaling of the com putational effort w ith the system size.