Formalism
Orbitaldependent functionals
Optimallytuned rangeseparated hybrid functionals
Local hybrid functionals
Ensemblegeneralized functionals
Simulated photoelectron spectroscopy
Dispersion corrections
Simulated doping
Orbitaldependent functionals
First principles electronic structure calculations, based only on the periodic table and the laws of quantum mechanics, have made large strides in recent decades and have become the foundation for the understanding of a huge variety of physical and chemical systems.
Much of this progress has been due to density functional theory (DFT), which has emerged as the workhorse approach for realworld materials (as opposed to model systems). DFT is an approach to the manyelectron problem in which the electron density, rather than the manyelectron wave function, plays a central role. It has become the method of choice for electronic structure calculations across an unusually wide variety of fields, from organic chemistry to condensed matter physics. There are two main reasons for the spectacular success of DFT:

First and foremost, DFT offers the only currently known practical way for first principles calculations of systems with many thousands of electrons.

Second, it enhances our understanding by relying on relatively simple, accessible quantities that are easily visualized even for very large systems.
DFT has progressed from a formal approach to a practical one by virtue of the KohnSham equations. These constitute a mapping of the original Nelectron Schrödinger equation into an effective set of N oneelectron Schrödingerlike equations, where all nonclassical electron interactions (i.e., exchange and correlation) are subsumed into an additive oneelectron potential, known as the exchangecorrelation potential. The latter is the functional derivative of the exchangecorrelation energy, which is a functional of the density. This mapping is exact in principle, but always approximate in practice. Progress therefore hinges critically on our ability to obtain more accurate approximations for exchangecorrelation functionals that are applicable across a wide range of systems.
We believe that research into orbitaldependent density functionals is one of the most promising arenas in modern density functional theory. In such functionals, the exchangecorrelation energy is expressed explicitly in terms of KohnSham orbitals and is only an implicit functional of the density. This allows maximal freedom in functional construction and offers a real hope for alleviating some of the most serious difficulties associated with present day treatments of exchange and correlation within DFT. Furthermore, orbitaldependent functionals can be employed fully within the original KohnSham framework, in which case the exchangecorrelation potential is derived using the optimized effective potential equation. However, they can also be employed using the generalized KohnSham framework, in which case one obtains a nonlocal potential that corresponds to mapping the original manyelectron problem into one of partially interacting electrons. A leading example of those, although not always recognized as such, is the socalled hybrid functionals, where a fraction of exact exchange is “mixed in” with a fraction of explicitly densitydependent exchange. While the KohnSham mapping is unique, there are many generalized KohnSham maps. This additional flexibility allows one to choose the best mapping for a given task.
Our group is actively engaged in constructing, testing, benchmarking, and applying to complex systems several important classes of orbitaldependent functionals.

For a comprehensive review article on the topic, see:
 S. Kümmel and L. Kronik, "Orbitaldependent density functionals: theory and applications", Rev. Mod. Phys. 80, 3 (2008).
Optimallytuned rangeseparated hybrid functionals
In recent years we have been developing and employing functionals based on the concept of optimaltuning of a rangeseparated hybrid functional. In this approach, one separates the electronrepulsion into short and longrange components, treating the shortrange so as to achieve a good balance between exchange and correlation, using semilocal approximations (possibly with shortrange exactexchange), but emphasizing exactexchange in the longrange so as to obtain the correct asymptotic potential. Optimaltuning means that the rangeseparation parameter (roughly, the crossover point from short to long range) is an adjustable, systemdependent parameter (rather than a universal one). This parameter is obtained nonempirically based on the satisfaction of physical constraints, typically the ionization potential theorem and related properties. This allowed us to solve several related problems that plagued density functional theory, including the infamous gap problem (for finite systems) and the chargetransfer excitation problem.

For a perspectives article on this line of research, see
 L. Kronik, T. Stein, S. RefaelyAbramson, R. Baer, “Excitation Gaps of FiniteSized Systems from OptimallyTuned RangeSeparated Hybrid Functionals”, J. Chem. Theo. Comp. (Perspectives Article) 8, 1515 (2012).
Recent highlights of this line of research include:

Solving the chargetransfer excitation problem, in all its forms:

Full charge transfer:
 T. Stein, L. Kronik, and R. Baer, "Reliable Prediction of Charge Transfer Excitations in Molecular Complexes Using TimeDependent Density Functional Theory", J. Am. Chem. Soc. (Communications), 131, 2818 (2009).

Partial charge transfer:
 T. Stein, L. Kronik, and R. Baer, "Prediction of chargetransfer excitations in coumarinbased dyes using a rangeseparated functional tuned from first principles", J. Chem. Phys. 131, 244119 (2009).

Chargetransfer like scenarios:
 N. Kuritz, T. Stein , R. Baer and L. Kronik, "Chargetransferlike π → π* excitations in timedependent density functional theory: a conundrum and its solution", J. of Chem. Theory and Comp. 7, 2408 (2011).

Solving the gap problem for finite systems:
 S. RefaelyAbramson, R. Baer and L. Kronik, "Fundamental and excitation gaps in molecules of relevance for organic photovoltaics from an optimally tuned rangeseparated hybrid functional”, Phys. Rev. B 84, 075144 (2011). Selected as “Editor’s suggestion”.
 T. Stein, H. Eisenberg, L. Kronik, and R. Baer, "Fundamental gaps of finite systems from the eigenvalues of a generalized KohnSham method", Phys. Rev. Lett.,105, 266802 (2010).

Generalization to molecular solids
 S. RefaelyAbramson, M. Jain, S. Sharifzadeh, J. B. Neaton, L. Kronik, “Solidstate excitonic effects predicted from optimallytuned timedependent rangeseparated hybrid density functional theory”, Phys. Rev. B (Rapid Comm.) 92, 081204(R) (2015).
 D. Lüftner, S. RefaelyAbramson, M. Pachler, R. Resel, M. G. Ramsey, L. Kronik, and P. Puschnig, “Experimental and theoretical electronic structure of quinacridone”, Phys. Rev. B 90, 075204 (2014).
 S. RefaelyAbramson, S. Sharifzadeh, M. Jain, R. Baer, J. B. Neaton, L. Kronik, “Gap renormalization of molecular crystals from density functional theory”, Phys. Rev. B (Rapid Comm.), 88, 081204 (2013).

Generalization and application to outervalence electronic structure
 L. Kronik and S. Kümmel, "Gasphase valenceelectron photoemission spectroscopy using density functional theory”, in Topics of Current Chemistry: First Principles Approaches to Spectroscopic Properties of Complex Materials, C. di Valentin, S. Botti, M. Coccoccioni, Editors (Springer, Berlin, 2014), Volume 347, pp. 137192.
 D. Lüftner, S. RefaelyAbramson, M. Pachler, R. Resel, M. G. Ramsey, L. Kronik, and P. Puschnig, “Experimental and theoretical electronic structure of quinacridone”, Phys. Rev. B 90, 075204 (2014).
 D. A. Egger, S. Weismann, S. RefaelyAbramson, S. Sharifzadeh, M. Dauth, R. Baer, S. Kümmel, J. B. Neaton, E. Zojer, L. Kronik, “Outervalence electron spectra of prototypical aromatic heterocycles from an optimallytuned rangeseparated hybrid functional”, J. Chem. Theo. Comp., 10, 1934 (2014).
 S. RefaelyAbramson, S. Sharifzadeh, N, Govind, J. Autschbach, J. B. Neaton, R. Baer and L. Kronik, “Quasiparticle spectra from a nonempirical optimallytuned rangeseparated hybrid density functional”, Phys. Rev. Lett. 109, 226405 (2012).

Applications to amino acids and peptide structures
 (invited paper) S. Sarkar and L. Kronik, “Ionization and (de)protonation energies of gasphase amino acids from an optimally tuned rangeseparated hybrid functional”, Mol. Phys. (Special Issue in Honor of Professor Andreas Savin), in press (2016).
 M. EckshtainLevi, E. Capua, S. RefaelyAbramson, S. Sarkar, Y. Gavrilov, S. Mathew, Y. Paltiel, Y. Levy, L. Kronik, and R. Naaman, “Cold Denaturation induces inversion of dipole and spin transfer in chiral peptide monolayers”, Nature Comm. 7, 10744 (2016).
 L. Sepunaru, S. RefaelyAbramson, R. Lovrinčić, Y. Gavrilov, P. Agrawal, Y. Levy, L. Kronik, I. Pecht, M. Sheves, and D. Cahen, “Electronic Transport via Homopeptides: The Role of Side Chains and Secondary Structure”, J. Am. Chem. Soc. 137, 9617 (2015). Highlighted in Phys.org.

And finally some caveats
 A. Karolewski, L. Kronik, and S. Kümmel “Using optimallytuned range separated hybrid functionals in groundstate calculations: consequences and caveats”, J. Chem. Phys. 138, 204115 (2013).

Full charge transfer:
Local hybrid functionals
A different area of much interest to us is the development of novel local hybrid functionals, where the fraction of exact exchange is spatiallydependent, following variations in the density and orbitals. In particular, we are interested in using this to develop nonlocal correlation functionals compatible with exact exchange, that are free of oneelectron selfinteraction, respect constraints derived from uniform coordinate scaling, and exhibit the correct asymptotic behavior of the exchangecorrelation energy.

This approach is highlighted in:
 T. Schmidt, E. Kraisler, L. Kronik, S. Kümmel, “Oneelectron selfinteraction and the asymptotics of the KohnSham potential: an impaired relation”, Phys. Chem. Chem. Phys. 16, 14357 (2014).
 T. Schmidt, E. Kraisler, A. Makmal, L. Kronik, S. Kümmel, “A selfinteractionfree local hybrid functional: accurate binding energies visàvis accurate ionization potentials from KohnSham eigenvalues”, J. Chem. Phys. (Special issue on Density Functional Theory) 140, 18A510 (2014).
Ensemblegeneralized functionals
We have been heavily involved in the study of the derivative discontinuity – a quirky property of the exchangecorrelation potential, which makes it “jump” by a constant across an integer number of electrons. Traditionally, simple approximations to the exchangecorrelation functional were thought to be devoid of this derivative discontinuity, with severe implications to the computation of bandgaps from eigenvalues, where this must be taken into account. Recently, we have discovered that in fact with a simple ensemblegeneralization all functionals possess a derivative discontinuity and that this can be used to extract relatively accurate molecular gaps even from very simple functionals.
Recent highlights of this line of research include:

Demonstrating the existence and importance of the derivative discontinuity in the potential of a dissociating molecule:
 A. Makmal, S. Kümmel, and L. Kronik, "Dissociation of diatomic molecules and the exactexchange KohnSham potential: the case of LiF", Phys. Rev. A 83, 062512 (2011).

Revealing the derivative discontinuity from ensemble considerations, including implications for orbital energies and gaps:
 E. Kraisler and L. Kronik, “Fundamental gaps with approximate density functionals: the derivative discontinuity revealed from ensemble considerations”, J. Chem. Phys. 140, 18A540 (2014).
 T. Schmidt, E. Kraisler, L. Kronik, S. Kümmel, “Oneelectron selfinteraction and the asymptotics of the KohnSham potential: an impaired relation” Phys. Chem. Chem. Phys. 16, 14357 (2014).
 E. Kraisler and L. Kronik, “Piecewise linearity of approximate density functionals revisited: Implications for frontier orbital energies”, Phys. Rev. Lett. 110, 126403 (2013).
 E. Kraisler, T. Schmidt, S. Kümmel, and L. Kronik, “Effect of ensemble generalization on the highestoccupied KohnSham eigenvalue”, J. Chem. Phys. 143, 104105 (2015).
Simulated photoelectron spectroscopy
We have been exploring the pros and cons of using various functionals, including explicitly densitydependent ones, and different conventional and novel hybrid ones, as a tool for quantitative simulations of photoelectron spectroscopy.
Recent highlights of this line of research include:

For an overview article, see:
 L. Kronik and S. Kümmel, "Gasphase valenceelectron photoemission spectroscopy using density functional theory”, in Topics of Current Chemistry: First Principles Approaches to Spectroscopic Properties of Complex Materials, C. di Valentin, S. Botti, M. Coccoccioni, Editors (Springer, Berlin, 2014).

For investigations of phthaolcyanines, see:
 N. Marom, O. Hod, G. E. Scuseria, and L. Kronik, "Electronic Structure of Copper Phthalocyanine: a Comparative Density Functional Theory Study", J. Chem. Phys. 128, 164107 (2008).
 (invited paper) N. Marom and L. Kronik, "Density Functional Theory of Transition Metal Phthalocyanines. I: Electronic Structure of NiPc and CoPc SelfInteraction Effects", Appl. Phys. A 95, 159 (2009). (Special Issue on Organic Materials for Electronic Applications).
 (invited paper) N. Marom and L. Kronik, "Density Functional Theory of Transition Metal Phthalocyanines. II: Electronic Structure of MnPc and FePc  Symmetry and Symmetry Breaking", Appl. Phys. A 95, 165 (2009). (Special Issue on Organic Materials for Electronic Applications)
 D. A. Egger, S. Weismann, S. RefaelyAbramson, S. Sharifzadeh, M. Dauth, R. Baer, S. Kümmel, J. B. Neaton, E. Zojer, L. Kronik, “Outervalence electron spectra of prototypical aromatic heterocycles from an optimallytuned rangeseparated hybrid functional”, J. Chem. Theo. Comp. 10, 1934 (2014).

For investigation of aromatic molecules and their derivatives, see:
 D. Lüftner, S. RefaelyAbramson, M. Pachler, R. Resel, M. G. Ramsey, L. Kronik, and P. Puschnig, “Experimental and theoretical electronic structure of quinacridone”, Phys. Rev. B 90, 075204 (2014).
 S. RefaelyAbramson, S. Sharifzadeh, N, Govind, J. Autschbach, J. B. Neaton, R. Baer and L. Kronik, “Quasiparticle spectra from a nonempirical optimallytuned rangeseparated hybrid density functional”, Phys. Rev. Lett. 109, 226405 (2012).
 T. Körzdörfer, S. Kümmel, N. Marom, and L. Kronik, "When to trust photoelectron spectra from KohnSham eigenvalues: the case of organic semiconductors", Phys. Rev. B (Rapid Comm.) 79, 201205 (2009).
 N. Dori, M. Menon, L. Kilian, M. Sokolowski, L. Kronik, and E. Umbach, "Valence Electronic Structure of Gas Phase 3,4,9,10perylene tetracarboxylicaciddianhydride (PTCDA): Experiment and Theory", Phys. Rev. B 73, 195208 (2006).
Dispersion corrections
Last but not at all least, we are interested in further developments and applications of pairwise and beyondpairwise dispersion corrections both standard and optimallytuned rangeseparated hybrid functionals, as a means of incorporating longrange correlation that is essential to the capture of weak interactions.
Recent highlights of this line of research include:

For an overview article, see:
 L. Kronik and A. Tkatchenko, “Understanding molecular crystals with dispersioninclusive densityfunctional theory: pairwise corrections and beyond”, Acct. Chem. Research (Special Issue on DFT Elucidation of Materials Properties), Acc. Chem. Res, in press.

For a combination of this approach with optimallytuned rangeseparated hybrid functionals, see:
 P. Agrawal, A. Tkatchenko, and L. Kronik, “Pairwise and manybody dispersive interactions coupled to an optimallytuned rangeseparated hybrid functional", J. Chem. Theo. Comp., 9, 3473 (2013).
Simulated doping
The inclusion of the global effects of semiconductor doping poses a unique challenge for firstprinciples simulations, because the typically low concentration of dopants renders an explicit treatment intractable. Furthermore, the width of the spacecharge region (SCR) at charged surfaces often exceeds realistic supercell dimensions. Recently, we developed a multiscale technique that fully addresses these difficulties. It is based on the introduction of a charged sheet, mimicking the SCRrelated field, along with free charge which mimics the bulk charge reservoir, such that the system is neutral overall. These augment a slab comprising “pseudoatoms” possessing a fractional nuclear charge matching the bulk doping concentration. Selfconsistency is reached by imposing charge conservation and Fermi level equilibration between the bulk, treated semiclassically, and the electronic states of the slab, which are treated quantummechanically. The method, called CREST—the chargereservoir electrostatic sheet technique—can be used with standard electronic structure codes.

For recent highlights of this approach see:
 O. Sinai, O. T. Hofmann, P. Rinke, M. Scheffler, G. Heimel, and L. Kronik, “Multiscale approach to the electronic structure of doped semiconductor surfaces”, Phys. Rev. B 91, 075311 (2015). Selected as “Editor’s suggestion”.
 O. Sinai and L. Kronik, ”Simulated doping of Si from first principles using pseudoatoms", Phys. Rev. B 87, 235305 (2013).