# Berlin 2008 – wissenschaftliches Programm

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# SYEC: Symposium Exact-exchange and hybrid functionals meet quasiparticle energy calculations

## SYEC 4: Exact-exchange and hybrid functionals meet quasiparticle energy calculations IV

### SYEC 4.6: Vortrag

### Freitag, 29. Februar 2008, 11:30–11:45, A 151

**Duality of the KS and OEP potentials and implementation of OEP in a plane wave code** — •Nikitas Gidopoulos^{1}, Stewart Clark^{2}, and Keith Refson^{3} — ^{1}ISIS, STFC, Rutherford Appleton Laboratory, HSIC, Didcot, Oxon, OX11 0QX, U.K. — ^{2}Department of Physics, University of Durham, Science Labs, South Road, Durham DH1 3LE, U.K. — ^{3}CSE, STFC, Rutherford Appleton Laboratory, HSIC, Didcot, Oxon, OX11 0QX, U.K.

Traditionally, the Kohn-Sham (KS) system is defined as the virtual non-interacting system of electrons with the same ground state density as the interacting system of interest. It is shown that in fact the KS system can also be obtained as the optimal non-interacting system in a straightforward unconstrained energy minimization [1], i.e., an energy optimization that does not constrain the ground state density in any way. It also turns out that the KS and the Optimised Effective Potential (OEP) systems are closely related by the duality of the variational principles from which they originate. The new point of view allows the natural development of ab initio expressions for the correlation energy and potential in KS theory. Further, we implement the OEP method in the plane wave code CASTEP exploiting the Hylleraas variational principle, which allows us to construct a minimization algorithm in order to obtain efficiently the infinite orbital sums that are necessary to determine OEP. Applications to semiconductor gaps will be presented.

[1] N.I. Gidopoulos, arXiv:cond-mat/0603277