Exploring the Space of Kohn-Sham Potentials

Weitao Yang, Department of Chemistry, Duke University, Durham, NC 27708, USA
e-mail: weitao.yang@duke.edu

Jeudi 16 octobre 2000, 16^h00

The theory and computational methods for the Kohn-Sham non-interacting reference potentials will be presented. The main theme in our work is the formulation of several rigorous variational principles using the potential as the basic computational variable. The potential is expressed as a sum of a fixed potential and a linear combination of a basis set. Efficient computational approach for the optimization of the coefficients makes our approaches practical.
1) When the energy is expressed as a functional of Kohn-Sham orbitals, one needs the optimized effective potential (OEP) in density functional theory. Conventionally, the OEP is expressed as the solution of a three-dimensional integral equation, which is difficult to solve. To facilitate the accurate determination of OEP, a new method is developed. Accurate atomic and molecular calculations with gaussian basis sets will be presented. This efficient and accurate method for the exchange correlation potentials should play an important role in further development of density functional theory. Calculation with exact exchange and with exact exchange plus correlation will be presented. Extension of this method for performing density functional calculations with correct long-range potentials will be discussed.
(2) A direct optimization method is developed for the computation of the Kohn-Sham kinetic energy density functional and the exchange-correlation potential from a given electron density. The method is based on the construction of a variational functional of the one-electron potential. The analytic first and second derivatives of the variational functional are derived. This enables very efficient iterative optimization of the potential. The efficiency and accuracy of the method is shown in the numerical implementation for atomic and molecular calculations with gaussian basis set expansions both for molecular orbitals and for one-electron potentials. This method is also extended to general density functionals.
References:
Weitao Yang and Qin Wu, "A Direct Method for Optimized Effective Potentials in Density Functional Theory", Phys. Rev. Lett, 89, 143002 (2002).
Qin Wu, Paul W. Ayers and Weitao Yang, "Density Functional Theory Calculations with Correct Long Range Potentials ", J. Chem. Phys. 119, 2978 (2003).
Qin Wu and Weitao Yang, "Algebraic equation and iterative optimization for the optimized effective potential in density functional theory", J. Theo. Comp. Chem., accepted (2003).
Paula Mori-Sanchez, Qin Wu, and Weitao Yang, "Accurate Polymer Polarizabilities with Exact Exchange Density Functional Theory", J. Chem. Phys. Submitted (2003).
Qin Wu and Weitao Yang, "A direct optimization method for calculating density functionals and exchange correlation potentials from electron densities", J. Chem. Phys. 118, 2498--2509(2003).