Inhalt des Dokuments
New Density Functionals
In many areas of application, Kohn-Sham density functional theory is indispensable, as it provides a unique combination of computational efficiency and accuracy. Nevertheless, the existing exchange-correlation functionals have clear accuracy limitations, in particular when it comes to universal applicability to different systems and different properties. For example, standard hybrid functionals like B3LYP, which include a spatially constant fraction of exact (Hartree-Fock-type) exchange, lack this universality. Relatively low fractions of exact exchange appear optimum for thermochemistry, larger amounts appear necessary to get good reaction barriers, magnetic properties and bonding in transition-metal systems or certain classes of excitations in TDDFT calculations. There is thus a need to construct improved functionals that still are computationally efficient yet more accurate than existing ones. We study several classes of "occupied-orbital-dependent" functionals in this context.
Development of local hybrid functionals with position-dependent exact-exchange admixture
- Figure 1: Principle of position-dependent exact-exchange admixture.
- © M. Kaupp
In so-called "local hybrid functionals"  (see also ), the exact-exchange admixture is done in a position-dependent rather than spatially uniform way (Figure 1). The position dependence is governed by a "local mixing function" (LMF). We have proposed two classes of LMFs that have provided for the first time accurate results for thermochemistry and reaction barriers [3,4,5]. The first and currently most successful class uses a scaled ratio t of von Weizsäcker kinetic energy density and noninteracting local kinetic energy density ("t-LMFs [3,5]), the second class depends on the dimensionless density gradient s (s-LMFs [4,5]). The two types of LMFs may also be combined to provide excellent accuracy for both thermochemistry and barriers, and at the same time the correct long-range asymptotic behavior. More recent developments include a) LMFs including spin-polarization as an additional variable , b) a combination of local hybrids with Grimme’s DFT-D3 dispersion correction terms , and c) a new generation of local hybrids based on a common LMF for both spin channels and improvements to the correlation functional of local hybrids involving range separation and self-interaction corrections to the short-range part . Another notable direction is the construction of LMFs within a first-principles framework, based on a local version of the adiabatic connection .
Self-consistent implementations are already available based on either the fully nonlocal exact-exchange potential  or with the LHF/CEDA approximation to the optimized effective potential (OEP) . The latter has been used to compute nuclear shielding constants within an uncoupled Kohn-Sham framework , whereas g-tensors have been implemented within a coupled-perturbed KS framework based on the former implementation . Our current efforts concentrate on a development version of the Turbomole package.
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 A thermochemically competitive local hybrid functional without gradient correction H. Bahmann, A. Rodenberg, A. V. Arbuznikov, M. Kaupp J. Chem. Phys. 2007, 126, 011103/1-4.
 Local hybrid exchange-correlation functionals based on the dimensionless density gradient A. V. Arbuznikov, M. Kaupp Chem. Phys. Lett. 2007, 440, 160-168.
 Local hybrid functionals: An assessment for thermochemical kinetics, M. Kaupp, H. Bahmann, A. V. Arbuznikov J. Chem. Phys. 2007, 127, 194102/1-12.
 Local hybrid functionals with an explicit dependence on spin polarization A. V. Arbuznikov, H. Bahmann, M. Kaupp J. Phys. Chem. A 2009, 113, 11891-11906.
 Evaluation of a combination of local hybrid functionals with DFT-D3 corrections for the calculation of thermochemical and kinetic data K. Theilacker, A. V. Arbuznikov, H. Bahmann, M. Kaupp J. Phys. Chem. A 2011, 115, 8990-8996.
 Importance of the correlation contribution for local hybrid functionals: range separation and self-interaction corrections A. V. Arbuznikov, M. Kaupp J. Chem. Phys. 2012, 136, 014111/1-13.
 What Can We Learn from the Adiabatic Connection Formalism about Local Hybrid Functionals? A. V. Arbuznikov, M. Kaupp J. Chem. Phys. 2008, 128, 214107/1-12.
 See, e.g. a) On occupied-orbital dependent exchange-correlation functionals. From local hybrids to Becke’s B05 model A. V. Arbuznikov, M. Kaupp Z. Phys. Chem. 2010, 224, 545-567; b) Advances in local hybrid exchange-correlation functionals: From thermochemistry to magnetic-resonance parameters and hyperpolarizabilities A. V. Arbuznikov, M. Kaupp Int. J. Quantum Chem. 2011, 111, 2625-2638, and references cited therein.
 From local hybrid functionals to "localized local-hybrid" potentials: Formalism and thermochemical tests A. V. Arbuznikov, M. Kaupp, H. Bahmann J. Chem. Phys. 2006, 124, 204102/1-15.
 Coupled-Perturbed Scheme for the Calculation of Electronic g-Tensors with Local Hybrid Functionals A. V. Arbuznikov, M. Kaupp J. Chem. Theory Comput. 2009, 5, 2985-2995.
 Nuclear shielding constants from localized local hybrid exchange-correlation potentials A. V. Arbuznikov, M. Kaupp Chem. Phys. Lett. 2007, 442, 496-503.
Work on Becke's real-space model of nondynamical correlation (B05)
Another attractive "occupied-orbital-dependent" functional is the B05 model by Becke et al.. Here nondynamical correlation is modelled in coordinate space. This functional is rather complicated, and a main challenge consisted in the self-consistent implementation. After some preliminary steps into this direction , this has been achieved recently [10a,15]. We have also used insight from the study of the B05 functional in designing our most recent local hybrids (see above [6,8]).
 Normalization of the effective exchange hole in Becke’s
nondynamical correlation model: Closed-form analytic
representation A. V. Arbuznikov , M. Kaupp J. Mol. Struct.,
Theochem 2006, 762, 151-153.
 On the self-consistent implementation of general occupied-orbital dependent exchange-correlation functionals with application to the B05 functional A. V. Arbuznikov, M. Kaupp J. Chem. Phys. 2009, 131, 084103/1-12.
ChairProf. Dr. M. Kaupp
- Dr. Alexey Arbuznikov 
- Dr. Hilke Bahmann