Abstract:
We demonstrate that the time-dependent Krieger-Li-Iafrate approximation in combination with the exchange-only functional violates the `Zero-Force Theorem'. By analyzing the time-dependent dipole moment of Na5 and Na9+, we furthermore show that this can lead to an unphysical self-excitation of the system depending on the system properties and the excitation strength. Analytical aspects, especially the connection between the `Zero-Force Theorem' and the `Generalized-Translation Invariance' of the potential, are discussed.

Abstract:
Using the optimized effective potential method in conjunction with the semi-analytical approximation due to Krieger, Li and Iafrate, we have performed fully self-consistent exact exchange-only density-functional calculations for diatomic molecules with a fully numerical basis-set-free molecular code. The results are very similar to the ones obtained with the Hartree Fock approach. Furthermore we present results for ground states of positive atomic ions including correlation contributions in the approximation of Colle and Salvetti. It is found that the scheme performs significantly better than conventional Kohn-Sham calculations.

Abstract:
The role of the exchange-correlation potential and the exchange-correlation kernel in the calculation of excitation energues from time-dependent density functional theory is studied. Excitation energies of the He and Be atoms are calculated, both from the exact ground-state Kohn-Sham potential, and from two orbital-dependent approximations. These are exact exchange and self-interaction corrected local density approximation (SIC-LDA), both calculated using the Krieger-Li-Iafrate (KLI) approximation. For the exchange-correlation kernela, three adiabatic approximations were tested: The local density approximation, exact exchange, and SIC-LDA. The choice of the ground-state exchange-correlation potential has the largest impact on the absolute position of most excitation energies. In particular, orbital-dependent approximate potentials result in a uniform shift of the transition energies to the Rydberg states.

Abstract:
We have performed self-consistent calculations for first and second row atoms using a variant of density-functional theory, the optimized effective potential method, with an approximation due to Krieger, Li and Iafrate and a correlation-energy functional developed by Colle and Salvetti. The mean absolute deviation of first-row atomic ground-state energies from the exact non-relativistic values is 4.7 mH in our scheme, as compared to 4.5 mH in a recent configuration-interaction calculation. The proposed scheme is significantly more accurate than the conventional Kohn-Sham method while the numerical effort involved is about the same as for an ordinary Hartree-Fock calculation.

Abstract:
The Hartree-Fock exchange operator is an integral operator arising in the Hartree-Fock method and replaced by a multiplicative operator (a local potential) in Kohn-Sham density functional theory. This article presents a detailed analysis of the mathematical properties of various local approximations to the nonlocal Hartree-Fock exchange operator, including the Slater potential, the optimized effective potential (OEP), the Krieger-Li-Iafrate (KLI) and common energy-denominator approximations (CEDA) to the OEP, and the effective local potential (ELP). In particular, we show that the Slater, KLI, CEDA potentials and the ELP can all be defined as solutions to certain variational problems. We also provide a rigorous derivation of the integral OEP equation and establish the existence of a solution to a system of coupled nonlinear partial differential equations defining the Slater approximation to the Hartree-Fock equations.

Abstract:
For exchange-correlation functionals that depend explicitly on the Kohn-Sham orbitals, the potential $V_{\mathrm{xc}\sigma}(\re)$ 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 like exact exchange. We demonstrate that the OEP can be obtained iteratively by solving a system of partial differential equations instead of an integral equation. This amounts to calculating the orbital shifts that exactify the Krieger-Li-Iafrate (KLI) 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. Counter-intuitive asymptotic limits of the exact OEP, not accessible from previous constructions, are presented.

Abstract:
The optimized effective potential (OEP) method allows for calculation of the local, effective single particle potential of density functional theory for explicitly orbital-dependent approximations to the exchange-correlation energy functional. In the present work the OEP method is used together with the approximation due to Krieger, Li and Iafrate (KLI). We present the first application of this method to polymers. KLI calculations have been performed for the insulating polyethylene and the results have been compared to those from other orbital-dependent potentials. Various properties of the band structure are also calculated. The single-particle band gap strongly depends on the basis set with larger basis sets yielding narrow gaps. For the highest occupied orbital energy the difference is more pronounced. In order to get the right band gap in OEP the exchange contribution to the derivative discontinuity is calculated and added to the Kohn-Sham gap.

Abstract:
We devise an efficient practical method for computing the Kohn-Sham exchange-correlation potential corresponding to a Hartree-Fock electron density. This potential is almost indistinguishable from the exact-exchange optimized effective potential (OEP) and, when used as an approximation to the OEP, is vastly better than all existing models. Using our method one can obtain unambiguous, nearly exact OEPs for any finite one-electron basis set at the same low cost as the Krieger-Li-Iafrate and Becke-Johnson potentials. For all practical purposes, this solves the long-standing problem of black-box construction of OEPs in exact-exchange calculations.

Abstract:
Collisions of $^6$Li$_2$ molecules with free $^6$Li atoms reveal a striking deviation from universal predictions based on long-range van der Waals interactions. Li$_2$ closed-channel molecules are formed in the highest vibrational state near a narrow Feshbach resonance, and decay via two-body collisions with Li$_2$, Li, and Na. For Li$_2$+Li$_2$ and Li$_2$+Na, the decay rates agree with the universal predictions of the quantum Langevin model. In contrast, the rate for Li$_2$+Li is exceptionally small, with an upper bound ten times smaller than the universal prediction. This can be explained by the low density of available decay states in systems of light atoms [G. Qu\'em\'ener, J.-M. Launay, and P. Honvault, Phys. Rev. A \textbf{75}, 050701 (2007)], for which such collisions have not been studied before.

Abstract:
We present a density difference based analysis for a range of orbital--dependent Kohn--Sham functionals. Results for atoms, some members of the neon isoelectronic series and small molecules are reported and compared with ab initio wave-function calculations. Particular attention is paid to the quality of approximations to the exchange--only optimized effective potential (OEP) approach: we consider both the Localized Hartree Fock as well as the Krieger-Li-Iafrate methods. Analysis of density differences at the exchange--only level reveals the impact the approximations have on the resulting electronic densities. These differences are further quantified in terms of the ground state energies, frontier orbital energy differences and highest occupied orbital energies obtained. At the correlated level an OEP approach based on a perturbative second--order correlation energy expression is shown to deliver results comparable with those from traditional wave function approaches, making it suitable for use as a benchmark against which to compare standard density--functional approximations.