CALCULATING LARGE SYSTEMS WITH PLANE-WAVES - IS IT A N-3 OR N-2 SCALING PROBLEM

It is commonly asserted that in performing large scale plane wave calc ulations with N plane waves, and indirect diagnolization, the N3 ortho gonalization step quickly becomes the limiting factor. Using a pre-con dition Lanczos subspace diagnolization algorithm we find that while th e orthogonalization will eventually become the dominate cpu restrictio n, this is not the limiting factor. Typically the limitation resides n ot with the cpu, but with the memory limitations of the functions scal es as N(atom)2. This scaling ''limitation'' is reached before the cpu time becomes the dominate factor. We illustrate this scaling with a Na vacancy calculation using up to 2000 atoms.