Localized orbital theory of electronic structure: A simple application

Galli and Parrinello introduced a formulation of electronic-structure theory based on the optimization of a set of orbital-like functions exactly equal in number to the number of electrons in the system, in contrast to conventional theories based on the occupied subspace of a larger variational Hilbert space. We have applied this formulation to a system sufficiently simple to permit study of its inner workings. We find that the unapproximated theory can be applied to delocalized, metallic systems, but the optimized functions, considered as a function of the strength of a localizing lattice potential, are not well localized for realistically weak (pseudo) potentials. Perhaps more importantly, we find that the formulation can be extremely numerically sensitive, rendering approximations made within the formulation potentially dangerous. © 1995 The American Physical Society.