Augmented Lagrangian method for order-N electronic structure

Molecular electronic ground-state theories, whether ab initio, or semiempir ical are most often formulated as a variational principle, where the electr onic ground-state energy, considered a linear or nonlinear functional of a reduced density matrix, obtains a constrained minimum. In this communicatio n, we present a Lagrangian analysis of the self-consistent-field electronic structure problem, which does not resort to the concept of orthogonal mole cular orbitals. We also develop a method of constrained minimization effici ently applicable to nonlinear energy functional minimization, as well as to linear models such as tight-binding. The method is able to treat large mol ecules with an effort that scales linearly with the system size. It has bui lt-in robustness and leads directly to the desired minimal solution. Perfor mance is demonstrated on linear alkane and polyene chains. (C) 2001 America n Institute of Physics.