This review provides a perspective on the use of orbital-dependent functionals, which is currently considered one of the most promising avenues in modern density-functional theory. The focus here is on four major themes: the motivation for orbital-dependent functionals in terms of limitations of semilocal functionals; the optimized effective potential as a rigorous approach to incorporating orbital-dependent functionals within the Kohn-Sham framework; the rationale behind and advantages and limitations of four popular classes of orbital-dependent functionals; and the use of orbital-dependent functionals for predicting excited-state properties. For each of these issues, both formal and practical aspects are assessed.

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.

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.

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.

approximations (GGAs) and typical global hybrid functionals with 20%-25% of Fock exchange not only describe ground-state properties of organic materials reliably, but also predict non-charge-transfer excitations with reasonable accuracy (e.g., within 0.2 eV), the same approximations very seriously underestimate the energies of charge-transfer (CT) excitations, often by several eV. Thus, the total excitation spectrum is grossly misrepresented and not even qualitative insights can be gained, as the calculated ordering of excitations is far from the experimental reality. This problem has been identified many years ago. [2,3] It was considered a hallmark failure and very much limited the usefulness of TDDFT for guiding the design of energy relevant materials.In recent years, this problem has been overcome. At least three insights have been combined to achieve this breakthrough. First, it has been increasingly realized-as summarized in ref.[4]-that Generalized Kohn-Sham theory is not just a formal argument justifying the use of orbital-specific potentials as a poor man's approximation to Kohn-Sham theory, but leads to practical advantages that have a well founded theoretical basis. Second, combining Fock-exchange with (semi)local xc functional components not via a fixed mixing parameter as in global hybrids, but via range-separation that splits the Coulomb interaction into long-and short-range components [5] captures the physics of screening much better, and therefore is intrinsically better suited for describing CT. And third, it was realized that the range-separation parameter can be determined by a self-consistent procedure, [6] thus avoiding empirical fitting. This type of approach has been thoroughly tested for organic electronic materials, [7] it has been extended to molecules embedded in an environment, [8][9][10][11] to molecular solids, [12] and explicitly solvated systems. [13] It thus has proven to be reliably and broadly applicable. In this article, we put this breakthrough into perspective: we recap what the challenge was, summarize the decisive steps for overcoming it, and give an outlook on what can be expected of TDDFT for molecular electronics and energy relevant materials in the future.