Linear scaling implementation of molecular electronic self-consistent field theory.

A linear-scaling implementation of Hartree-Fock and Kohn-Sham self-consistent field SCF theories is presented and illustrated with applications to molecules consisting of more than 1000 atoms. The diagonalization bottleneck of traditional SCF methods is avoided by carrying out a minimization of the Roothaan-Hall RH energy function and solving the Newton equations using the preconditioned conjugate-gradient PCG method. For rapid PCG convergence, the L\uf6wdin orthogonal atomic orbital basis is used. The resulting linear-scaling trust-region Roothaan-Hall LS-TRRH method works by the introduction of a level-shift parameter in the RH Newton equations. A great advantage of the LS-TRRH method is that the optimal level shift can be determined at no extra cost, ensuring fast and robust convergence of both the SCF iterations and the level-shifted Newton equations. For density averaging, the authors use the trust-region density-subspace minimization TRDSM method, which, unlike the traditional direct inversion in the iterative subspace DIIS scheme, is firmly based on the principle of energy minimization. When combined with a linear-scaling evaluation of the Fock/Kohn-Sham matrix including a boxed fitting of the electron density, LS-TRRH and TRDSM methods constitute the linear-scaling trust-region SCF LS-TRSCF method. The LS-TRSCF method compares favorably with the traditional SCF/ DIIS scheme, converging smoothly and reliably in cases where the latter method fails. In one case where the LS-TRSCF method converges smoothly to a minimum, the SCF/DIIS method converges to a saddle point