Regensburg 2010 – scientific programme

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MM: Fachverband Metall- und Materialphysik

MM 26: Poster Session

MM 26.9: Poster

Tuesday, March 23, 2010, 14:45–16:30, Poster C

Stable and unique solutions for the OEP equation in the LCAO formalism — •julio juan fernandez¹, Christian Kollmar², and Michael Filatov¹ — ¹Institute for Advanced Materials, Groningen 9747 AG The Netherlands — ²Institut fur Physicalische und Theoretische Chemie, Bonn D53115 Germany

The treatment of orbital dependent functionals in Density Functional Theory (DFT) requires the use of the Optimized Effective Potential (OEP) technique for obtaining the local multiplicative potential. Using the exchange only (xOEP) functional this formalism leads to an equation that, in real space, possesses a unique and well defined solution for atoms and molecules. In a basis set (LCAO) scheme the method leads to a non unique solution of the equation due to the singularity of the matrix representation of the linear response operator. In this work we demonstrate that a good solution to this problem is to use an incomplete Cholesky decomposition of the linear response matrix. With the use of this technique numerically stable and unique solutions of the xOEP equations in the LCAO representation are obtained provided that the orbital basis set satisfies the condition of linear dependence of the products of occupied and virtual Kohn_sham orbitals. It is demonstrated that the obtained LCAO-xOEP solutions are independent on the criterion used to discriminate linearly dependent from linearly independent (ia) products.

The LCAO-xOEP solutions for atoms and molecules are obtained with the use of standard basis sets. The LCAO-xOEP energies are in excellent agreement with the numeric real space xOEP energies.