Stephan Kümmel

Simple iterative construction of the optimized effective potential for orbital functionals, including exact exchange.

For exchange-correlation functionals that depend explicitly on the Kohn-Sham orbitals, the potential V(xcsigma)(r) must be obtained as the solution of the optimized effective potential (OEP) integral equation. This is very demanding and has limited the use of orbital functionals. We demonstrate that instead the OEP can be obtained iteratively by solving the partial differential equations for the orbital shifts that exactify the Krieger-Li-Iafrate approximation. Unoccupied orbitals do not need to be calculated. Accuracy and efficiency of the method are shown for atoms and clusters using the exact-exchange energy. Counterintuitive asymptotic limits of the exact OEP are presented.

Using optimally tuned range separated hybrid functionals in ground-state calculations: consequences and caveats.

Optimally tuned range separated hybrid functionals are a new class of implicitly defined functionals. Their important new aspect is that the range separation parameter in these functionals is determined individually for each system by iteratively tuning it until a fundamental, non-empirical condition is fulfilled. Such functionals have been demonstrated to be extremely successful in predicting electronic excitations. In this paper, we explore the use of the tuning approach for predicting ground state properties. This sheds light on one of its downsides - the violation of size consistency. By analyzing diatomic molecules, we reveal size consistency errors up to several electron volts and find that binding energies cannot be predicted reliably. Further consequences of the consistent ground-state use of the tuning approach are potential energy surfaces that are qualitatively in error and an incorrect prediction of spin states. We discuss these failures, their origins, and possibilities for overcoming them.

Optimized effective potential made simple: Orbital functionals, orbital shifts, and the exact Kohn-Sham exchange potential

The optimized effective potential (OEP) is the exact Kohn-Sham potential for explicitly orbital-dependent energy functionals, e.g., the exact exchange energy. We give a proof for the OEP equation which does not depend on the chain rule for functional derivatives and directly yields the equation in its simplest form: a certain first-order density shift must vanish. This condition explains why the highest-occupied orbital energies of Hartree-Fock and exact exchange OEP are so close. More importantly, we show that the exact OEP can be constructed iteratively from the first-order shifts of the Kohn-Sham orbitals and that these can be calculated easily. The exact exchange potential v x (r) for spherical atoms and three-dimensional sodium clusters is calculated. Its long-range asymptotic behavior is investigated, including the approach of c x (r) to a nonvanishing constant in particular spatial directions. We calculate total and orbital energies and static electric dipole polarizabilities for the sodium clusters employing the exact exchange functional. Exact OEP results are compared to the Krieger-Li-Iafrate and local density approximations.

Outer-valence Electron Spectra of Prototypical Aromatic Heterocycles from an Optimally Tuned Range-Separated Hybrid Functional.

Density functional theory with optimally tuned range-separated hybrid (OT-RSH) functionals has been recently suggested [Refaely-Abramson et al. Phys. Rev. Lett.2012, 109, 226405] as a nonempirical approach to predict the outer-valence electronic structure of molecules with the same accuracy as many-body perturbation theory. Here, we provide a quantitative evaluation of the OT-RSH approach by examining its performance in predicting the outer-valence electron spectra of several prototypical gas-phase molecules, from aromatic rings (benzene, pyridine, and pyrimidine) to more complex organic systems (terpyrimidinethiol and copper phthalocyanine). For a range up to several electronvolts away from the frontier orbital energies, we find that the outer-valence electronic structure obtained from the OT-RSH method agrees very well (typically within ∼0.1–0.2 eV) with both experimental photoemission and theoretical many-body perturbation theory data in the GW approximation. In particular, we find that with new strategies for an optimal choice of the short-range fraction of Fock exchange, the OT-RSH approach offers a balanced description of localized and delocalized states. We discuss in detail the sole exception found—a high-symmetry orbital, particular to small aromatic rings, which is relatively deep inside the valence state manifold. Overall, the OT-RSH method is an accurate DFT-based method for outer-valence electronic structure prediction for such systems and is of essentially the same level of accuracy as contemporary GW approaches, at a reduced computational cost.

Ionic and electronic structure of sodium clusters up toN=59

We determined the ionic and electronic structure of sodium clusters with even electron numbers and 2 to 59 atoms in axially averaged and three-dimensional density functional calculations. A local, phenomenological pseudopotential that reproduces important bulk and atomic properties and facilitates structure calculations has been developed. Photoabsorption spectra have been calculated for

Self-interaction correction and the optimized effective potential

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Thermal expansion in small metal clusters and its impact on the electric polarizability

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Coordination-driven magnetic-to-nonmagnetic transition in manganese-doped silicon clusters

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Electrical response of molecular systems: the power of self-interaction corrected kohn-sham theory.

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Two avenues to self-interaction correction within Kohn-Sham theory: unitary invariance is the shortcut

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