Research

Adventures in (Real) Space
 

Some twenty years ago, Chelikowsky, Saad, and co-workers suggested solving the Kohn-Sham equations of density functional theory using a high-order finite difference approach on a real-space grid. For much of that time, our group has been a major partner in developing and applying this approach. It has now blossomed into a mature, massively parallel software suite, which we call PARSEC - the pseudopotential algorithm for real-space electronic structure calculations. This approach has many advantages. First and foremost, it produces Hamiltonian matrices that are very sparse. Therefore, the Hamiltonian is never computed or stored explicitly, but rather only its action on a wave function vector is computed. As a direct consequence, massively parallel calculations scale extremely well. Put in simpler language, when performing a parallel computation on a number of processors (from several to many thousands and more), for a large problem the computation time will decrease almost linearly with the increase in processor number. This, together with advances in diagonalization algorithms, allows us to attack problems with thousands of electrons.

The approach has other advantages as well:

  • With respect to localized basis sets, it provides an approach without an explicit basis so that convergence is trivial (just decrease the grid spacing), and all those pesky basis set issues are avoided. This also means that no recurring basis set-up and no spurious forces are associated with atom movement and that localized and delocalized electrons are treated on the same footing.
  • With respect to planewave approaches, we can treat periodic and non-periodic systems equally. This means that "super-cells", which introduce spurious periodicity, are not employed. Consequently, problems "inherited" from the super-cell, e.g., difficulties with treating monopolar or dipolar systems (e.g, in the study of charged defects or polar surfaces, respectively) are not encountered.
  • A real-space grid is also a natural arena for solving the optimized effective potential equation, and is therefore an important tool in our studies of orbital-dependent functionals.
  • The code is well-structured and physically transparent. This makes the implementation of new ideas (relatively) easy!
  • Last but not at all least, the approach serves as a basis for all-electron real-space calculations. In recent years, we have developed two such codes:

DARSEC – the diatomic algorithm for real-space electronic structure calculations: This program is a “cousin” of PARSEC, which employs a prolate-spheroidal grid to allow for all-electron solutions of atoms and diatomic molecules.

CARMA – the concurrent all-electron real-space multigrid algorithm: This program uses a locally-refined multi-grid approach to obtain an all-electron solution for an arbitrary molecular system.

Some of our recent articles in this research direction are:
 

An overview of the PARSEC approach:

  • L. Kronik, A. Makmal, M. Tiago, M. M. G. Alemany, X. Huang, Y. Saad, and J. R. Chelikowsky, "PARSEC - the pseudopotential algorithm for real-space electronic structure calculations: recent advances and novel applications to nanostructures", Phys. Stat. Solidi. (b) (Feature Article) 243, 1063 (2006).

Generalizations to periodicity, spin-orbit coupling, non-collinear magnetism, and transport:

  • D. Naveh, L. Kronik, M. L. Tiago, and J. R. Chelikowsky, "Real-Space Pseudopotential method for Spin-Orbit Coupling within Density Functional Theory", Phys. Rev. B 76, 153407 (2007).
  • A. Natan, A. Benjamini, D. Naveh, L. Kronik, M. L. Tiago, S. P. Beckman, and J. R. Chelikowsky, "Real-space pseudopotential method for first principles calculations of general periodic and partially periodic systems", Phys. Rev. B 78, 075109 (2008).
  • D. Naveh and L. Kronik, "Real-Space Pseudopotential method for Noncollinear Magnetism within Density Functional Theory", Solid State Comm. 149, 177 (2009).
  • B. Feldman, T. Seideman, O. Hod, L. Kronik, “A real-space method for highly parallelizable electronic transport calculations”, Phys. Rev. B 90, 035445 (2014).

Some recent applications of PARSEC:

  • E. Kraisler and L. Kronik, “Fundamental gaps with approximate density functionals: the derivative discontinuity revealed from ensemble considerations”, J. Chem. Phys. 140, 18A540 (2014).
  • R. Viswanatha, D. Naveh, J. R. Chelikowsky, L. Kronik and D. D. Sarma, “Magnetic properties of Fe/Cu co-doped ZnO Nanocrystals”, J. Phys. Chem. Lett. 3, 2009 (2012).
  • F. Rissner, A. Natan, D. A. Egger, O. T. Hofmann. L. Kronik and E. Zojer, “Dimensionality effects in the electronic structure of organic semiconductors consisting of polar repeat units”, Org. Electr. 13, 3165 (2012).
  • F. Rissner, D. A. Egger, A. Natan, T. Körzdörfer, S. Kümmel, L. Kronik, and E. Zojer, “Collectively Induced Quantum-Confined Stark Effect in Monolayers of Molecules Consisting of Polar Repeating Units”, J. Am. Chem. Soc. 133, 18634 (2011).

An overview of the DARSEC approach:

  • A. Makmal, S. Kümmel, and L. Kronik, "Fully numerical all-electron solutions of the optimized effective potential equation for diatomic molecules", J. Chem. Theo. Comp. 5, 1731 (2009).

Some recent applications of DARSEC:

An overview of the CARMA approach:

 

​

Organic and Molecular Electronics

Organic−inorganic hybrids

Supra-molecular materials

Biogenic Materials
 

Organic and Molecular Electronics
 

Organic electronic materials are fascinating from both the basic and the applied science points of view, and bridge basic science and applied research, as well as physics and chemistry. Technologically, the electronic and optical properties of organic matter, including its interface with inorganic matter, are of tremendous importance for several emerging and nascent technologies. Chief among them is organic electronics, where electronic and opto-electronic devices (e.g., transistors, light-emitting diodes, and photovoltaic cells) rely on conjugated organic materials with semiconducting properties, rather than on traditional inorganic semiconductors. A related example is that of molecular electronics, where current conduction, rectification, information processing, and storage take place within a single molecule, and where the connection to inorganic leads is part and parcel of the device.

One obvious role of theory is to uncover the novel mechanisms for charge generation, transport, and transfer that allow the above-described devices to function. But even more interesting, from the theoretical point of view, is that organic electronic materials and organic/inorganic interfaces often possess a range of surprising electronic properties, whose identification and explanation is a significant challenge for both experiment and theory. To a large extent, this is because understanding these properties forces us to bridge two different ``world views'' - that of molecular orbital theory, which underlies much of organic chemistry, and that of delocalized electron waves, which underlies much of solid-state physics. One often encounters phenomena that are not well-described by either of the limiting textbook descriptions, and more elaborate theories need to be constructed.

In particular, we have been focusing on “collective phenomena”, namely, properties that the individual components comprising the interface (say a single molecule or an isolated inorganic substrate) do not exhibit, but the overall structure does. Perhaps the most striking example of such a collective effect is the possible emergence of magnetic phenomena at the interface between a non-magnetic metal and a closed-shell molecular layer. But there are many other examples, such as the emergence of qualitatively new electronic states at the interface, or highly delocalized excitons in organic materials. Furthermore, by no means is direct chemical interaction necessary for collective phenomena to occur. For example, long-range electrostatic effects can drastically affect the static polarization in, and electric fields outside of, a molecular monolayer. Consequently, properties of the molecular ensemble, as well as of its interface with the metal, can be very different from, and sometimes even opposite to, those of the isolated molecule.

Untangling the web of short-range chemical bonds, long-range electrostatic and dispersive interactions, and inter-molecular and molecule-substrate interplay presents significant challenges. This is all the more so given that one has not only to understand general mechanisms that may allow for collective behavior, but also to rationalize how these depend on system-specific properties such as bonding, order, and orientation, and understand when and how they may arise. Therefore, we mostly rely on first principles electronic structure theory, where electronic and optical properties are ideally deduced from nothing but the atomic species present and the laws of quantum physics.
 

Recent highlights of this line of research include:

  • Elucidating the nature of low-energy electronic and optical excitations in prototypical organic electronic materials, highlighting strongly delocalized excitons.
  • Identification of the role of an interface-induced density of states at an organic/inorganic interface in interface energetics and charge transport across the interface.
  • Understanding how collective effects at the metal/molecule interface affect molecular electronics.
    • D. Rakhmilevitch, S. Sarkar, O. Bitton, L. Kronik, and O. Tal, “Enhanced magnetoresistance in molecular junctions by geometrical optimization of spin-selective orbital hybridization”, Nano Lett., 16, 1741 (2016).
    • Y. Li, P. Zolotavin, P. Doak, L. Kronik, J. B. Neaton, and D. Natelson, “Interplay of bias-driven charging and the vibrational Stark effect in molecular junctions”, Nano Lett. 16, 1104 (2016).
       
    • R. Vardimon, T. Yelin, M. Klionsky, S. Sarkar, A. Biller, L. Kronik, O. Tal, “Probing the Orbital Origin of Conductance Oscillations in Atomic Chains”, Nano Lett. 14, 2988 (2014).
       
    • Y. Li, P. Doak, L. Kronik, J, B. Neaton, D. Natelson, “Voltage tuning of vibrational mode energies in single-molecule junctions”, PNAS 111, 1282 (2014).
       
    • T. Yelin, R. Vardimon, N. Kuritz, R. Korytár, A. Bagrets, F. Evers, L. Kronik and O. Tal, “Atomically wired molecular junctions: Connecting a single organic molecule by chains of metal atoms”, Nano. Lett. 13, 1956 (2013).
       
  • Understanding electrostatic, especially dipolar, properties of organic monolayers.
    • M. Eckshtain-Levi, E. Capua, S. Refaely-Abramson, 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).
       
    • F. Rissner, A. Natan, D. A. Egger, O. T. Hofmann. L. Kronik and E. Zojer, “Dimensionality effects in the electronic structure of organic semiconductors consisting of polar repeat units”, Org. Electr. 13, 3165 (2012).
       
    • F. Rissner, D. A. Egger, A. Natan, T. Körzdörfer, S. Kümmel, L. Kronik, and E. Zojer, “Collectively Induced Quantum-Confined Stark Effect in Monolayers of Molecules Consisting of Polar Repeating Units”, J. Am. Chem. Soc. 133, 18634 (2011).
       
    • A. Natan, L. Kronik, H. Haick, and R. Tung, "Electrostatic Properties of Ideal and Non-ideal Polar Organic Monolayers: Implications for Electronic Devices", Adv. Mater. 19, 4103 (2007).
       
  • Understanding molecular level reorganization and renormalization at metal interfaces.
    • D. A. Egger, Z.-F. Liu, J. B. Neaton, and L. Kronik, “Reliable Energy Level Alignment at Physisorbed Molecule-Metal Interfaces from Density Functional Theory”, Nano Lett. 15, 2448 (2015).
       
    • L. Kronik and Y. Morikawa, "Understanding the metal-molecule interface from first principles", in N. Koch, N. Ueno, and A. T. S. Wee, Ed., The Molecule-Metal Interface (Wiley-VCH, Weinheim, 2013),pp . 51-89.
       
    • E. Salomon, P. Amsalem, N. Marom, M. Vondracek, L. Kronik, N. Koch, and T. Angot, “Electronic structure of CoPc adsorbed on Ag(100): evidence for molecule-substrate interaction mediated by Co 3d orbitals", Phys. Rev. B 87, 075407 (2013).
       
    • A. Biller, I. Tamblyn, J. B. Neaton and L. Kronik, “Electronic level alignment at a metal-molecule interface from a short-range hybrid functional”, J. Chem. Phys. 135, 164706 (2011).
       

  • In addition, we have developed advanced methods for the accurate prediction of electronic and optical properties of organic molecules and solids. [Click here for more information].

Organic−inorganic hybrids
 

Hybrid organic−inorganic perovskites (HOIPs) are crystals with the structural formula ABX3 where A, B, and X are organic and inorganic ions, respectively. While known for several decades, HOIPs have only in recent years emerged as extremely promising semiconducting materials for solar energy applications. In particular, power conversion efficiencies of HOIP-based solar cells have improved at a record speed and, after only little more than 6 years of photovoltaics research, surpassed the 20% threshold, which is an outstanding result for a solution-processable material. It is thus of fundamental importance to reveal physical and chemical phenomena that contribute to, or limit, these impressive photovoltaic efficiencies. To understand charge-transport and light-absorption properties of semiconducting materials, one often invokes a lattice of ions displaced from their static positions only by harmonic vibrations. However, a preponderance of recent studies suggests that this picture is not sufficient for HOIPs, where a variety of structurally dynamic effects, beyond small harmonic vibrations, arises already at room temperature. Our research focuses on the theoretical understanding and prediction of such effects.
 

Recent highlights include:

  • General overview:
    • T. M. Brenner, D. A. Egger, L. Kronik, G. Hodes, D. Cahen “Hybrid organic–inorganic perovskites: low-cost semiconductors with intriguing charge transport properties”, Nature Reviews Materials 1, 15007 (2016).
  • Overview of dynamic effects:
    • D. A. Egger, A. M. Rappe, and L. Kronik, “Hybrid Organic-Inorganic Perovskites on the Move”, Acct. Chem. Research (Special Issue on Lead-Halide Perovskites for Solar Energy Conversion), Acc. Chem. Res. 49, 573 (2016).
       
  • Discussion of opportunities and challenges:
    • J. Berry, T. Buonassisi, D. A. Egger, G. Hodes, L. Kronik, Y.-L. Loo, I. Lubomirsky, S. R. Marder, Y. Mastai, J. S. Miller, D. B. Mitzi, Y. Paz, A. M. Rappe, I. Riess, B. Rybtchinski, O. Stafsudd, V. Stevanovic, M. F. Toney, D. Zitoun, A. Kahn, D. Ginley, D. Cahen, “Hybrid Organic-Inorganic Perovskites (HOIPs): Opportunities and Challenges”, Adv. Mater. (Essay) 27, 5102 (2015).
       
  • Research articles:
    • S. Dastidar, D. A. Egger, L. Z. Tan, S. B. Cromer, A. D. Dillon, S. Liu, L. Kronik, A. M. Rappe, and A. T. Fafarman, “High Chloride Doping Levels Stabilize the Perovskite Phase of Cesium Lead Iodide”,Nano Lett. in press (2016).
       
    • T. M. Brenner, D. A. Egger, A. M. Rappe, L. Kronik, G. Hodes, and D. Cahen, “Are Mobilities in Hybrid Organic-Inorganic Halide Perovskites Actually ‘High’?”, J. Phys. Chem. Lett. 6, 4754 (2015).
       
    • D. A. Egger, L. Kronik, and A. M. Rappe, “Theory of Hydrogen Migration in Organic-Inorganic Halide Perovskites”, Angew. Chem. Int’l Ed. 54, 12437 (2015).
       
    • D. A. Egger and L. Kronik, “Role of Dispersive Interactions in Determining Structural Properties of Organic-Inorganic Halide Perovskites: Insights from First Principles Calculations”, J. Phys. Chem. Lett. 5, 2728 (2014).

Supra-molecular materials

Supra-molecular materials are defined as systems composed of molecules bound together by relatively weak intermolecular interactions, typically consisting of van der Waals (vdW) forces and/or hydrogen bonds. Supra-molecular materials in general, and molecular solids in particular, play an important role in many areas of science and technology, ranging from mechanics and electronics to biology and medicine.

Molecular crystals often exhibit collective properties (i.e., properties arising from the weak intermolecular interactions) that are not found in the individual building blocks. See, e.g., the “organic molecular electronics” section for examples. Such properties are typically hard to predict from textbook molecular models. Therefore, first-principles  calculations can be of great help in elucidating such phenomena.

Unfortunately, all standard approximations within density functional theory (DFT) fail to include long-range correlation expressions needed to account for weak interaction scenarios. Therefore, until recently DFT has scarcely left a footprint in the field of supra-molecular materials.

In recent years, we have been using pair-wise dispersive corrections, primarily those of Tkatchenko-Scheffler (for more information, see formalism section), to study such systems. We have shown that such corrections can be employed with any underlying exchange-correlation functional, which allows us to achieve an unprecedented balance of accuracy of different binding scenarios, ranging from the very strong to the very weak. This allows us to use DFT to understand novel effects in molecular materials, that include unusual structural properties, unique mechanical properties, and a quantitative account of electronic and optical properties.
 

Recent highlights of this line of research include:

  • An overview of recent achievements and remaining challenges.
    • L. Kronik and A. Tkatchenko, “Understanding molecular crystals with dispersion-inclusive density-functional theory: pair-wise corrections and beyond”, Acct. Chem. Research (Special Issue on DFT Elucidation of Materials Properties), Acc. Chem. Res, in press.
       
  • Theoretical prediction of a new polymorph of the guanine crystal, which is used for structural color determination in many organisms, followed by experimental confirmation of its dominance in biogenic guanine.
    • A. Hirsch, D. Gur, I. Polishchuk, D. Levy, B. Pokroy, A. J. Cruz-Cabeza, L. Addadi, L. Kronik, and L. Leiserowitz, “‘Guanigma’: the revised structure of biogenic anhydrous guanine”, Chem. Mater. 27, 8289 (2015).
       
  • Theoretical prediction, followed by experimental confirmation, of unusually large and highly anisotropic Young’s moduli in amino acid molecular crystals, resulting from the hydrogen-bonding network in these materials.
    • I. Azuri, E. Meirzadeh, D. Ehre, S. R. Cohen, A. M. Rappe, M. Lahav, I. Lubomirsky, and L. Kronik, “Unusually large Young's moduli of amino-acid molecular crystals”, Angew. Chem. Int’l Ed. 54, 13566 (2015).
       
  • Understanding of the unique stiffness of diphenylalanine-based peptide nanostructures – a bio-inspired supra-molecular structure.
    • I. Azuri, L. Adler-Abramovich, E. Gazit, O. Hod, L. Kronik, “Why are diphenylalanine-based peptide nanostructures so rigid? Insights from first principles calculations”, J. Am. Chem. Soc., 136, 963 (2014).
       
  • A complete understanding of the infra-red spectrum of brushite – a crystalline hydrated acidic form of calcium phosphate that occurs in both physiological and pathological biomineralization processes.
    • A. Hirsch, I. Azuri, L. Addadi, S. Weiner, K. Yang, S. Curtarolo, L. Kronik, “Infrared Absorption Spectrum of Brushite from First Principles”, Chem. Mater., 26, 2934 (2014).
       
  • Insights into the structure and formation of hemozoin – a molecular solid formed in the course of malaria.
    • N. Marom, A. Tkatchenko, S. Kapishnikov, L. Kronik and L. Leiserowitz, "Structure and Formation of Synthetic Hemozoin: Insights From First-Principles Calculations", Cryst. Growth & Design 11, 3332 (2011).
       
  • For an overview of the methodological developments that allow for these studies, Click here.

Biogenic Materials
 

Living organisms produce a wide range of materials, often revealing unique shapes, morphologies, structures, and functionality. Examples range from inorganic materials, such as calcium carbonates and phosphates used in, e.g., shells, bones, and teeth, to organic materials such as chitin, a polysaccharide used in the exoskeletons of arthropods, or a molecular solid of guanine, formed in the scales of some fish. In our work, we attempt to understand the unique order and structure in such materials, typically by comparing first-principles calculations to various spectroscopies.

Recent highlights include:

  • Understanding the relation between local order and infrared spectra of calcite.
    • R. Gueta, A. Natan, L. Addadi, S. Weiner, K. Refson, and L. Kronik, "Local atomic order and infrared spectra of biogenic calcite", Angew. Chemie Int'l Ed. 46, 291 (2007).
    • K. M. Poduska, L. Regev, E. Boaretto, L. Addadi, S. Weiner, L. Kronik, and S. C. Curtarolo, "Decoupling local disorder and optical effects in infrared spectra: differentiating between calcites with different origins", Adv. Mater. 23, 550 (2011).
       
  • Assignment of the infrared spectrum of brushite, a crystalline hydrated acidic form of calcium phosphate that occurs in both physiological and pathological biomineralization processes.
    • A. Hirsch, I. Azuri, L. Addadi, S. Weiner, K. Yang, S. Curtarolo, L. Kronik, “Infrared Absorption Spectrum of Brushite from First Principles”, Chem. Mater. 26, 2934 (2014).
       
  • Theoretical prediction of a new polymorph of the guanine crystal, which is used for structural color determination in many organisms, followed by experimental confirmation of its dominance in biogenic guanine.
    • A. Hirsch, D. Gur, I. Polishchuk, D. Levy, B. Pokroy, A. J. Cruz-Cabeza, L. Addadi, L. Kronik, and L. Leiserowitz, “‘Guanigma’: the revised structure of biogenic anhydrous guanine”, Chem. Mater. 27, 8289 (2015).

Orbital-dependent functionals

Optimally-tuned range-separated hybrid functionals

Local hybrid functionals

Ensemble-generalized functionals

Simulated photoelectron spectroscopy

Dispersion corrections

Simulated doping

 

Orbital-dependent 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 work-horse approach for real-world materials (as opposed to model systems). DFT is an approach to the many-electron problem in which the electron density, rather than the many-electron 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 Kohn-Sham equations. These constitute a mapping of the original N-electron Schrödinger equation into an effective set of N one-electron Schrödinger-like equations, where all non-classical electron interactions (i.e., exchange and correlation) are subsumed into an additive one-electron potential, known as the exchange-correlation potential. The latter is the functional derivative of the exchange-correlation 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 exchange-correlation functionals that are applicable across a wide range of systems.

We believe that research into orbital-dependent density functionals is one of the most promising arenas in modern density functional theory. In such functionals, the exchange-correlation energy is expressed explicitly in terms of Kohn-Sham 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, orbital-dependent functionals can be employed fully within the original Kohn-Sham framework, in which case the exchange-correlation potential is derived using the optimized effective potential equation. However, they can also be employed using the generalized Kohn-Sham framework, in which case one obtains a non-local potential that corresponds to mapping the original many-electron problem into one of partially interacting electrons. A leading example of those, although not always recognized as such, is the so-called hybrid functionals, where a fraction of exact exchange is “mixed in” with a fraction of explicitly density-dependent exchange. While the Kohn-Sham mapping is unique, there are many generalized Kohn-Sham 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 orbital-dependent functionals.

  • For a comprehensive review article on the topic, see:

Optimally-tuned range-separated hybrid functionals

 

In recent years we have been developing and employing functionals based on the concept of optimal-tuning of a range-separated hybrid functional. In this approach, one separates the electron-repulsion into short- and long-range components, treating the short-range so as to achieve a good balance between exchange and correlation, using semi-local approximations (possibly with short-range exact-exchange), but emphasizing exact-exchange in the long-range so as to obtain the correct asymptotic potential. Optimal-tuning means that the range-separation parameter (roughly, the cross-over point from short to long range) is an adjustable, system-dependent parameter (rather than a universal one). This parameter is obtained non-empirically 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 charge-transfer excitation problem.

Recent highlights of this line of research include:

  • Solving the charge-transfer excitation problem, in all its forms:
    • Full charge transfer:
    • Partial charge transfer:
      • T. Stein, L. Kronik, and R. Baer, "Prediction of charge-transfer excitations in coumarin-based dyes using a range-separated functional tuned from first principles", J. Chem. Phys. 131, 244119 (2009).
    • Charge-transfer like scenarios:
    • Solving the gap problem for finite systems:
      • S. Refaely-Abramson, R. Baer and L. Kronik, "Fundamental and excitation gaps in molecules of relevance for organic photovoltaics from an optimally tuned range-separated 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 Kohn-Sham method", Phys. Rev. Lett.,105, 266802 (2010).
    • Generalization to molecular solids
      • S. Refaely-Abramson, M. Jain, S. Sharifzadeh, J. B. Neaton, L. Kronik, “Solid-state excitonic effects predicted from optimally-tuned time-dependent range-separated hybrid density functional theory”, Phys. Rev. B (Rapid Comm.) 92, 081204(R) (2015).
      • D. Lüftner, S. Refaely-Abramson, 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. Refaely-Abramson, 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 outer-valence electronic structure
    • Applications to amino acids and peptide structures
      • (invited paper) S. Sarkar and L. Kronik, “Ionization and (de-)protonation energies of gas-phase amino acids from an optimally tuned range-separated hybrid functional”, Mol. Phys. (Special Issue in Honor of Professor Andreas Savin), in press (2016).
      • M. Eckshtain-Levi, E. Capua, S. Refaely-Abramson, 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. Refaely-Abramson, R. Lovrinčić, Y. Gavrilov, P. Agrawal, Y. Levy, L. Kronik, I. Pecht, M. Sheves, and D. Cahen, “Electronic Transport via Homo-peptides: 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 optimally-tuned range separated hybrid functionals in ground-state calculations: consequences and caveats”, J. Chem. Phys. 138, 204115 (2013).

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 spatially-dependent, following variations in the density and orbitals. In particular, we are interested in using this to develop non-local correlation functionals compatible with exact exchange, that are free of one-electron self-interaction, respect constraints derived from uniform coordinate scaling, and exhibit the correct asymptotic behavior of the exchange-correlation energy.

Ensemble-generalized functionals

 

We have been heavily involved in the study of the derivative discontinuity – a quirky property of the exchange-correlation potential, which makes it “jump” by a constant across an integer number of electrons. Traditionally, simple approximations to the exchange-correlation 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 ensemble-generalization 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 exact-exchange Kohn-Sham 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, “One-electron self-interaction and the asymptotics of the Kohn-Sham 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 highest-occupied Kohn-Sham eigenvalue”, J. Chem. Phys. 143, 104105 (2015).

Simulated photoelectron spectroscopy

 

We have been exploring the pros and cons of using various functionals, including explicitly density-dependent 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, "Gas-phase valence-electron 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- Self-Interaction 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. Refaely-Abramson, S. Sharifzadeh, M. Dauth, R. Baer, S. Kümmel, J. B. Neaton, E. Zojer, L. Kronik, “Outer-valence electron spectra of prototypical aromatic heterocycles from an optimally-tuned range-separated hybrid functional”, J. Chem. Theo. Comp. 10, 1934 (2014).
  • For investigation of aromatic molecules and their derivatives, see:
    • D. Lüftner, S. Refaely-Abramson, 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. Refaely-Abramson, S. Sharifzadeh, N, Govind, J. Autschbach, J. B. Neaton, R. Baer and L. Kronik, “Quasiparticle spectra from a non-empirical optimally-tuned range-separated hybrid density functional”, Phys. Rev. Lett. 109, 226405 (2012).
    • T. Körzdörfer, S. Kümmel, N. Marom, and L. Kronik, "When to trust photoelectron spectra from Kohn-Sham 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 3,4,9,10-perylene tetracarboxylic-acid-dianhydride (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 pair-wise and beyond-pair-wise dispersion corrections both standard and optimally-tuned range-separated hybrid functionals, as a means of incorporating long-range 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 dispersion-inclusive density-functional theory: pair-wise 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 optimally-tuned range-separated hybrid functionals, see:
    • P. Agrawal, A. Tkatchenko, and L. Kronik, “Pair-wise and many-body dispersive interactions coupled to an optimally-tuned range-separated 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 first-principles simulations, because the typically low concentration of dopants renders an explicit treatment intractable. Furthermore, the width of the space-charge 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 SCR-related 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. Self-consistency 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 quantum-mechanically. The method, called CREST—the charge-reservoir 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, “Multi-scale 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 pseudo-atoms", Phys. Rev. B 87, 235305 (2013).