A simplified density matrix minimization for linear scaling self-consistent field theory

A simplified version of the Li, Nunes and Vanderbilt [Phys. Rev. B 47, 1089 1 (1993)] and Daw [Phys. Rev. B 47, 10895 (1993)] density matrix minimizati on is introduced that requires four fewer matrix multiplies per minimizatio n step relative to previous formulations. The simplified method also exhibi ts superior convergence properties, such that the bulk of the work may be s hifted to the quadratically convergent McWeeny purification, which brings t he density matrix to idempotency. Both orthogonal and nonorthogonal version s are derived. The AINV algorithm of Benzi, Meyer, and T (u) over circle ma [SIAM J. Sci. Comp. 17, 1135 (1996)] is introduced to linear scaling elect ronic structure theory, and found to be essential in transformations betwee n orthogonal and nonorthogonal representations. These methods have been dev eloped with an atom- blocked sparse matrix algebra that achieves sustained megafloating point operations per second rates as high as 50% of theoretica l, and implemented in the MondoSCF suite of linear scaling SCF programs. Fo r the first time, linear scaling Hartree-Fock theory is demonstrated with t hree- dimensional systems, including water clusters and estane polymers. Th e nonorthogonal minimization is shown to be uncompetitive with minimization in an orthonormal representation. An early onset of linear scaling is foun d for both minimal and double zeta basis sets, and crossovers with a highly optimized eigensolver are achieved. Calculations with up to 6000 basis fun ctions are reported. The scaling of errors with system size is investigated for various levels of approximation. (C) 1999 American Institute of Physic s. [S0021-9606(99)30702-9].