Realization of The DFT (Density Functional Theory) calculations with KLI (Krieger-Li-Iafrate) - approximation of OEP (Optimized Effective Potential) in.

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Realization of The DFT (Density Functional Theory) calculations with KLI (Krieger-Li-Iafrate) - approximation of OEP (Optimized Effective Potential) in Q96 (AllChem). Konstantin Popov Department of Mathematics, Syktyvkar Branch of Mathematics and Mechanics Institute, Ural Division, RAS

What is a problem ? The Quantum Many Particle Problem appears, when we examine atoms, molecules, clusters or solids as a charged particles systems. In Born-Oppenheimer approximation, the problem can be restricted to consideration only the electrons of the system. In this case we have to do with Fermi-system, in particular with finite Fermi- system.

The problem content. It is necessary to note that this problem must be recognized in a more comprehensive sense, then the simple determination of the system’s state. It’s goals are determination of the ground state energy, system’s structure, vibration spectrum, excitation spectrum, response function, energy gap in semiconductors or in superconductors and so on.

Preliminary restrictions We’ll try to follow the ab-initio approach based only on fundamental description of matter, like charge, mass, spin and so on in opposition to semi-empirical and model-based methods. In a frame of ab-initio calculations we can mark two approaches Hartree-Fock (HF) Theory and Density Functional Theory (DFT). The first one describes the system with the single particle variables. The second one based on using the spin- charge density as a fundamental variable. In this work we put our creative efforts to the DFT.

Four stages of DFT evolution Thomas-Fermi Theory ( )- established the direct mapping between electron density and potential. Landau Theory of Fermi liquids( ) - introduced the energy of the system as a functional of charge distribution. Hohenberg-Kohn-Shem Theory ( ) - proved one-to- one mapping of the density and potential. Derived the equations for single electron wave functions, which can be solved in a mode of self-consistent-field. Talman-Shadwick Theory (1976) and Its Krieger-Li-Iafrate approximation (1992) - exact expression for exchange potential.

The main formalism of DFT

Program Implementations This strategy was realized in most of the existing packages for that tip of calculations. Such as: Gaussian, GAMESS UK, DeFT, Q96, Abinit. In 1976 the procedure leading to exact expression for exchange-correlation energy functional was suggested by Talman and Shadwick (named OEP- Optimized Effective Potential). In 1992 a useable approximation of OEP was obtained by Krieger, Li and Iafrate (KLI approximation).

The relations for V OEP-KLI xc  (r)

Some motivations. Not to do everything by us, but join to the existing stream of development. Work only with Open Source projects. Try to work with pure DFT programs

Q (AllChem) A. Koster and M. Krack, Hanover University of FRG