Density matrices in O(N) electronic structure calculations: theory and applications

We analyze the problem of determining the electronic ground state within O( N) schemes, focusing on methods in which the total energy is minimized with respect to the density matrix. We note that in such methods a crucially im portant constraint is that the density matrix must be idempotent (i.e. its eigenvalues must all be zero or unity). Working within orthogonal tight-bin ding theory, we analyze two related methods for imposing this constraint: t he iterative purification strategy of McWeeny [Rev. Mod. Phys. 32 (1960) 33 5], as modified by Falser and Manolopoulos [Phys. Rev. B 58 (1998) 12704]; and the minimization technique of Li, Nunes and Vanderbilt [Phys. Rev. B 47 (1993) 10891]. Our analysis indicates that the two methods have complement ary strengths and weaknesses, and leads us to propose that a hybrid of the two methods should be more effective than either method by itself. This ide a is tested by using tight-binding theory to apply the proposed hybrid meth od to a set of condensed matter systems of increasing difficulty, ranging f rom bulk crystalline C and Si to liquid Si, and the effectiveness of the me thod is confirmed. The implications of our findings for O(N) implementation s of non-orthogonal tight-binding theory and density functional theory are discussed. (C) 1999 Elsevier Science B.V. All rights reserved.