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mardi 12 avril — 14:00

Efficient Optimization of Orbital-Density-Dependent Energy Functionals

Peter Kluepfel, du Science Institute of the University of Iceland

par Pierre Pujol - 12 avril 2011

Orbital-Density-Dependent (ODD) energy functionals, e.g., self-interaction corrected DFT functionals [1], are a promising avenue towards a more accurate description of the electronic ground-state and dynamics.

An algorithm for the ground state minimization problem is presented, which is efficient, reliable and easy to implement. It combines the historic concepts of the construction of a unified Hamiltonian [2] with the more recent idea of a "double basis-set" approach [3]. The minimization problem is separated into a unitary invariant (generalized Kohn-Sham) eigenvalue problem and a non-unitary invariant optimization problem, i.e., the solution of the "localization condition" [4].

While elaborate methods exist for a fast and reliable solution of the eigenvalue problem, the solution of the "localization condition" turns out to be the performance limiting step in most applications of ODD functionals. Significant improvements can be found by a scheme explicitly conserving the orthonormality of the single-particle states, i.e., by a conjugate gradient optimization on a Stiefel manifold [5].

The new scheme allows for a careful review of the accuracy of self-interaction corrected LDA and GGA in ground state calculations of atomic, molecular and solid-state systems. Selected examples will illustrate the strengths and deficiencies of the Perdew-Zunger self-interaction correction (SIC).

The solution of the "localization condition" is also a bottleneck in applications of time-dependent SIC and major parts of the presented algorithm can readily be applied there.

References : [1] J. P. Perdew and A. Zunger, Phys. Rev. B 23, 5048 (1981).

[2] J. G. Harrison, R.A. Heaton and C. C. Lin, J. Phys. B 16, 2079 (1983).

[3] J. Messud, P. M. Dinh, P.-G. Reinhard and E. Suraud, Phys. Rev. Lett. 101, 096404 (2008).

[4] M. R. Pederson, R. A. Heaton, and C. C. Lin, J. Chem. Phys. 80, 1972 (1984).

[5] A. Edelman, T. A. Arias and S. T. Smith, SIAM J. Matrix Anal. Appl. 20, 303 (1998).