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

摘要

We analyze the problem of determining the electronic ground state within O(N)schemes, focusing on methods in which the total energy is minimized withrespect to the density matrix. We note that in such methods a cruciallyimportant constraint is that the density matrix must be idempotent (i.e. itseigenvalues must all be zero or unity). Working within orthogonal tight-bindingtheory, we analyze two related methods for imposing this constraint: theiterative purification strategy of McWeeny, as modified by Palser andManolopoulos; and the minimization technique of Li, Nunes and Vanderbilt. Ouranalysis indicates that the two methods have complementary strengths andweaknesses, and leads us to propose that a hybrid of the two methods should bemore effective than either method by itself. This idea is tested by usingtight-binding theory to apply the proposed hybrid method to a set of condensedmatter systems of increasing difficulty, ranging from bulk crystalline C and Sito liquid Si, and the effectiveness of the method is confirmed. Theimplications of our findings for O(N) implementations of non-orthogonaltight-binding theory and density functional theory are discussed.