Convergence of density functional iterative procedures with a Newton-Raphson algorithm
Tóm tắt
State of the art first-principles calculations of electronic structures aim at finding the ground state electronic density distribution. The performance of such methodologies is determined by the effectiveness of the iterative solution of the nonlinear density functional Kohn-Sham equations. We first outline a solution strategy based on the Newton-Raphson method. A form of the algorithm is then applied to the simplest and earliest density functional model, i.e., the atomic Thomas-Fermi model. For the neutral atom, we demonstrate the effectiveness of a charge conserving Newton-Raphson iterative method for the computation, which is independent of the starting guess; it converges rapidly, even for a randomly selected normalized starting density.
Tài liệu tham khảo
Eyert, V.: A comparative study on methods for convergent acceleration of iterative vector sequences. J. Comput. Phys. 124, 271–285 (1996)
Kohn, W., Vashista, P.: Theory of the Inhomogeneous Electron Gas Ch. 2. Plenum Press, New York (1983)
Freeman, A.J., Wimmer, E.: Density functional theory as a major tool in computational materials science. Ann. Rev. Mater. Sci. 25, 7–36 (1995)
Hedin, L., Lundqvist, B.I.: Explicit local exchange correlation potentials. J. Phys. C 4 (14), 2064–2083 (1971)
Perdew, J.P., Chevay, J.A., Vosko, S.H., Jackson, K.A., Pederson, M.R., Singh, D.J., Fiolhais, C.: Atoms, molecules, solids, and surfaces. Phys. Rev. B 46(11), 6671–6687 (1992)
Prodan, E., Nordlander, P.: On the Kohn-Sham equations with periodic background potentials. J. Stat. Phys. 111, 967–992 (2003)
Kerkhoven, T., Saad, Y.: On acceleration methods for coupled nonlinear elliptic systems. Numer. Math. 60, 525–548 (1992)
Huang, Y., Hoffman, D.K., Kouri, D.J.: A minimal subspace residual method for large scale eigenvalue problems. J. Chem. Phys. 110, 8303–8308 (1999)
March, N.H.: Theory of the Inhomogeneous Electron Gas Ch. 1. Plenum Press, New York (1983)
Lieb, E.H.: Thomas-Fermi and related theories of atoms and molecules. Rev. Mod. Phys. 54, 603–641 (1981)