title: The trust-region self-consistent field method in Kohn-Sham density-functional theory.
abstract: The trust-region self-consistent field (TRSCF) method is extended to the optimization of the Kohn-Sham energy. In the TRSCF method, both the Roothaan-Hall step and the density-subspace minimization step are replaced by trust-region optimizations of local approximations to the Kohn-Sham energy, leading to a controlled, monotonic convergence towards the optimized energy. Previously the TRSCF method has been developed for optimization of the Hartree-Fock energy, which is a simple quadratic function in the density matrix. However, since the Kohn-Sham energy is a nonquadratic function of the density matrix, the local energy functions must be generalized for use with the Kohn-Sham model. Such a generalization, which contains the Hartree-Fock model as a special case, is presented here. For comparison, a rederivation of the popular direct inversion in the iterative subspace (DIIS) algorithm is performed, demonstrating that the DIIS method may be viewed as a quasi-Newton method, explaining its fast local convergence. In the global region the convergence behavior of DIIS is less predictable. The related energy DIIS technique is also discussed and shown to be inappropriate for the optimization of the Kohn-Sham energy.
authors.affiliation: Department of Chemistry, University of Arhus, DK-8000 Arhus C, Denmark. lea@chem.au.dk
authors.forename: Lea
authors.initials: L
authors.lastname: Thøgersen
authors.forename: Jeppe
authors.initials: J
authors.lastname: Olsen
authors.forename: Andreas
authors.initials: A
authors.lastname: Köhn
authors.forename: Poul
authors.initials: P
authors.lastname: Jørgensen
authors.forename: Paweł
authors.initials: P
authors.lastname: Sałek
authors.forename: Trygve
authors.initials: T
authors.lastname: Helgaker
mesh_terms: D000465:Algorithms; D002104:Cadmium / Q000737:chemistry; D002627:Chemistry, Physical / Q000379:methods*; D003198:Computer Simulation; D008956:Models, Chemical; D015233:Models, Statistical; D008962:Models, Theoretical; D012107:Research Design; D012984:Software; D013816:Thermodynamics; D015032:Zinc / Q000737:chemistry
chemical_list: D002104:Cadmium; D015032:Zinc