Research

Adventures in (Real) Space
 

Some thirty 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 is now expressed in a 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 tens of thousands and more), for a large problem the computation time will decrease almost linearly with the increase in processor number. This, together with advances various algorithmic advances, allows us to attack problems with tens of thousands of electrons.

The approach has other advantages as well:

  • With respect to localized basis sets, it is 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.
  • 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. Over the 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.

Recently, we have focused on improving the precision of energies and forces even at coarser grids, thereby accelerating the computation. Specifically, we showed that aliasing errors can be minimized through a scheme that we call finite difference interpolation. 

Recent articles in this research direction are:

  • D. Roller, A. M. Rappe, L. Kronik, and O. Hellman, “Improving the Precision of Forces in Real-Space Pseudopotential Density Functional Theory”, J. Chem. Phys. 61, 074113 (2024).
  • D. Roller, A. M. Rappe, L. Kronik, and O. Hellman, “Finite difference interpolation for reduction of grid-related errors in real-space pseudopotential density functional theory”, J. Chem. Theo. Comput. 19, 3889 (2023).

Biogenic and bio-inspired materials

Halide Perovskites

Two-dimensional materials

Molecular Spintronics

Porphyrins and phthalocyanines

 

Biogenic and bio-inspired 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 by various organisms for vision or for camouflage.

Bio-inspired materials generally attempt to learn from nature's achievements, by incorporating natural components or motifs in order to achieve ease of fabrication and/or desired functionality. These materials often exhibit unique mechanical, electrical, optical, or even magnetic properties, leading to novel applications.

In our work, we attempt to understand the unique order and structure in both biogenic and bio-inspired materials, and to discover novel properties and new structure-property relations. This is typically achieved by comparing first-principles calculations to the results of various microscopy and spectroscopy tools.
 

For an overview of organic crystals and their optical function in Biology, see:

  • L. Addadi, L. Kronik, L. Leiserowitz, D. Oron, and S. Weiner, “Organic Crystals and Optical Functions in Biology: Knowns and Unknowns”, Adv. Materials. 36, 2408060 (2024).

Some recent research achievements include:

Understanding polymorphism, structure, and nucleation of cholesterol·H2O, a pathological biological material, see: 

  • M. Shepelenko, A. Hirsch, N. Varsano, F. Beghi, L. Addadi, L. Kronik, and L. Leiserowitz, “Polymorphism, Structure, and Nucleation of Cholesterol·H2O at Aqueous Interfaces and Pathological Media: a Computational Perspective”, J. Am. Chem. Soc. 144, 5304 (2022).

Understanding high-refractive index birefringence in bio-inspired xanthine-derivative based materials, see: 

  • A. Niazov-Elkan, M. Shepelenko, L. Alus, M. Kazes, K. Rechav, G. Leitus, A.-E. Kossoy, Y. Feldman, L. Kronik, P. G. Vekilov, and D. Oron, “Surface-guided crystallization of xanthine derivatives for optical metamaterial applications”, Adv. Mater. 36, 2306996 (2024).

Discovering the crystal structure of biogenic xanthine crystals, see:

  • M. Ifliand, L. Houben, M. Shepelenko, Y. Feldman, A. E. Kossoy, O. Friedman, M. Hildebrand, L. Addadi, L. Leiserowitz, L. Kronik, “Discovering the crystal structure of biogenic xanthine crystals”, Cryst. Growth & Design 25, 7524-7536 (2025).

Showing that pH Variations Enable Guanine Crystal Formation within Iridosomes, see:

  • Z. Eyal, A. Gorelick-Ashkenazi, R. Deis, Y. Barzilay, Y. Broder, A. P. Kellum, N. Varsano, M. Hartstein, A. Sorrentino, I. Kaplan-Ashiri, K. Rechav, R. Metzler, L. Houben, L. Kronik, P. Rez, and D. Gur, “pH Variations Enable Guanine Crystal Formation within Iridosomes”, Nature Chem. Biol. (2025).

Understanding Guanine Crystallization by Particle Attachment, see:

 

Halide Perovskites

Halide perovskites (HaPs) are crystals with the structural formula ABX3, in which A is an organic or inorganic cation, B is a metal cation, and X is a halide anion. While known for a long time, in the last decade HaPs have emerged as extremely promising low cost yet high efficiency semiconducting materials for solar energy and other photovoltaic applications. It is thus of fundamental importance to reveal physical and chemical phenomena that govern the behavior of these materials. A preponderance of studies have suggested that in HaPs a variety of large structural dynamic effects, beyond small harmonic vibrations, arise already at room temperature. Our research focuses on the theoretical understanding and prediction of such effects, with an emphasis on their influence on defect properties.
 

Selected overviews 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).
  • Overview of unique optoelectronic properties of halide perovskites:
    • D. A. Egger, A. Bera, D. Cahen, G. Hodes, T. Kirchartz, L. Kronik, R. Lovrincic, A. M. Rappe, D. R. Reichman, and O. Yaffe, “What remains unexplained about the optoelectronic properties of halide perovskites?”, Adv. Mater. 30, 1800691 (2018).
  • A Broader Photoelectrochemistry Perspective of HaPs 
    • Z. Xu, R. A. Kerner, L. Kronik, B. P. Rand, “Beyond Ion Migration in Metal Halide Perovskites: Towards a Broader Photoelectrochemistry Perspective”, ACS Energy Lett. 9, 4645 (2024).

Selected research achievements include:

  • F. P. Delgado, F. Simões, L. Kronik, W. Kaiser, and D. A. Egger, “Machine-Learning Force Fields Reveal Shallow Electronic States on Dynamic Halide Perovskite Surfaces”, ACS Energy Lett. 10, 3367-3374 (2025).
  • R. A. Kerner, A. V. Cohen, Z. Xu, A. R. Kirmani, S. Y. Park, S. P. Harvey, J. P. Murphy, R. C. Cawthorn, N. C. Giebink, J. M. Luther, K. Zhu, J. J. Berry, L. Kronik, and B. P. Rand, “Electrochemical Doping of Halide Perovskites by Noble Metal Interstitial Cations”, Adv. Materials 35, 2302206 (2023).
  • D. Shin, F. Zu, A. V. Cohen, Y. Yi, L. Kronik, and N. Koch,”Mechanism and time-scales of reversible p-doping of methylammonium lead triiodide by oxygen”, Adv. Materials 33, 2100211 (2021).
  • A. V. Cohen, D. A. Egger, A. M. Rappe, and L. Kronik, “Breakdown of the static picture of defect energetics in halide perovskites: the case of the Br vacancy in CsPbBr3”, J. Phys. Chem. Lett. 10, 4490 (2019).
  • O. Yaffe, Y. Guo, L. Z. Tan, D. A. Egger, T. Hull, C. C. Stoumpos, F. Zheng, T. F. Heinz, L. Kronik, M. G. Kanatzidis, J. S Owen, A. M. Rappe, M. A. Pimenta, and L. E. Brus, “Local polar fluctuations in lead halide perovskite crystals”, Phys. Rev. Lett. 118, 136001 (2017).

 

Two-dimensional materials

Two-dimensional (2d) materials are crystalline solids that are only one or few atomic layers thick. These materials often exhibit unique mechanical, electronic, and optical properties. This has many potential applications and also raises basic science questions as to how these unique properties emerge.

Recent highlights of our work include:

Development and applications of anisotropic interlayer force fields for van homogeneous and heterogeneous 2d-layer interfaces:

  •  For a recent overview see:
  • For recent research articles see:
    • W. Jiang, R. Sofer, X. Gao, L. Kronik, O. Hod, M. Urbakh, and W. Ouyang, “Anisotropic Interlayer Force Field for Heterogeneous Interfaces of Graphene and h-BN with Transition Metal Dichalcogenides”, J. Phys. Chem. C. 129, 1417–1427 (2025).
    • W. Jiang, R. Sofer, X. Gao, A. Tkatchenko, L. Kronik, W. Ouyang, M. Urbakh, O. Hod, “Anisotropic Interlayer Force Field for Group-VI Transition Metal Dichalcogenides”, J. Phys.Chem. A 127 ,9820 (2023). Special Issue in honor of Prof. Gustavo Scuseria.

Understanding cumulative polarization in multi-layered interfacial ferroelectrics:

  • ​​​​​​​ W. Cao, S. Deb, M. Vizner Stern, N. Raab, M. Urbakh, O. Hod, L. Kronik, M. Ben Shalom, “Polarization Saturation in Multi-layered Interfacial Ferroelectrics”, Adv. Mater. 36, 2400750 (2024).
  •  S. S. Atri, W. Cao, B. Alon, N. Roy, M. Vizner Stern, V. Falko, M. Goldstein, L. Kronik, M. Urbakh, O. Hod, M. Ben Shalom, “Spontaneous Electric Polarization in Graphene Polytypes”, Adv. Phys. Research 3, 2300095 (2024).
  • S. Deb, W. Cao, N. Raab, K. Watanabe, T. Taniguchi, M. Goldstein, L. Kronik, M. Urbakh, O. Hod, and M. Ben Shalom, “Cumulative Polarization in Conductive Interfacial Ferroelectrics”, Nature 612, 465 (2022).
     

Unique structure-property relations in 2d materials:

  • ​​​​​​​A. Champagne, M. Camarasa-Gómez, F. Ricci, L. Kronik, and J. B. Neaton, “Strongly-bound excitons and anisotropic linear absorption in monolayer graphullerene”, Nano Lett. 24, 7033 (2024).
  • Y.-C. Leem, Z. Fang, C. Lee, N.-Y. Kim, W. Liu, S.-P. Cho, C. Kim, Y. Wang, Z. Ji, L. Kronik, A. M. Rappe, S.-Y. Yim, R. Agarwal, “Optically-triggered emergent mesostructures in monolayer WS2”, Nano Lett. 24, 5395 (2024).
     

Methods for accurate prediction of electronic and optical properties in 2d materials:

  • ​​​​​​​F. Florio, M. Camarasa-Gómez, G. Ohad, D. Naveh, L. Kronik, and A. Ramasubramaniam, “Resolving contradictory estimates of bandgaps of bulk PdSe2: A Wannier-localized optimally-tuned screened range-separated hybrid density functional theory study”, Appl. Phys. Lett. 126, 143101 (2025).
  • M. Camarasa-Gómez, S. E. Gant, G. Ohad, J. B. Neaton, A. Ramasubramaniam, L. Kronik, “Electronic and Optical Excitations in van der Waals Materials from a Non-Empirical Wannier-Localized Optimally-Tuned Screened Range-Separated Hybrid Functional”, npj Comp.Mater. 10, 288 (2024).
  • M. Camarasa-Gómez, A. Ramasubramaniam, J. B. Neaton, L. Kronik, “Transferable screened range-separated hybrid functionals for electronic and optical properties of van der Waals materials”, Phys. Rev. Materials 7, 104001 (2023).

 

Molecular Spintronics

Spintronics is a field of electronics that uses the fundamental property of an electron spin, in addition to its charge, in order to store and/or process and/or transmit information. Molecular electronics is a field of electronics that uses single molecules as building blocks for electronic components like transistors, diodes, and wires. Molecular spintronics joins these two fields in that it used single molecules as building blocks for spintronic devices and phenomena.

Our research in molecular spintronics focuses mainly on understanding chirality-induced spin selectivity, an umbrella term that defines a wide range of phenomena in which the chirality of molecular species imparts significant spin selectivity to various electron processes.

For an overview, see:

  • F. Evers, A. Aharony, N. Bar-Gill, O. Entin-Wohlman, P. Hedegård, O. Hod, P. Jelinek, G. Kamieniarz, M. Lemeshko, K. Michaeli, V. Mujica, R. Naaman, Y. Paltiel, S. Refaely-Abramson, O. Tal, J. Thijssen, M. Thoss, J. M. van Ruitenbeek, L. Venkataraman, D. H. Waldeck, B. Yan, and L. Kronik, “Theory of Chirality Induced Spin Selectivity: Progress and Challenges”, Adv. Materials, 34 2106629 (2022).

For recent research highlights, see:

  • A. K. Mondal, N. Brown, S. Mishra, P. Makam, D. Wing, Y. Wiesenfeld, G. Leitus, L. J. W. Shimon, R. Carmieli, D. Ehre, G. Kamieniarz, J. Fransson, O. Hod, L. Kronik, E. Gazit, and R. Naaman, “Long-Range Spin-Selective Transport in Chiral Metal-Organic Crystals with Temperature-Activated Magnetization”, ACS Nano 14, 16624 (2020).
  • K. Banerjee-Ghosh, O. Ben Dor, F. Tassinari, E. Capua, S. Yochelis, A. Capua, S.-H. Yang, S. S. P. Parkin, S. Sarkar, L. Kronik, L. T. Baczewski, R. Naaman, and Y. Paltiel, “Separation of enantiomers by their enantiospecific interaction with achiral magnetic substrates”, Science 360, 1331 (2018). Highlighted by Chemical & Engineering News and Physics Today​​​​​​​.

 

Porphyrins and phthalocyanines

Porphyrins, phthalocyanines and their numerous analogues and derivatives are organic macrocycles of outstanding importance in a wide range of fields, from chemistry and materials science, through electronics and spintronics, to biology and medicine. Among many other things, they paint blood red (heme), leaves green (chlorophyll), and jeans blue (copper phthalocyanine). Our research is aimed at a fundamental understanding of their unique electronic structure and optical properties, especially but not only in the solid state, using advanced density functional theory approaches.

Some recent research achievements include:

  • Structure, bonding, and reactivity trends in subphthalocyanines:
  • Identification of a new polymorph of copper phthalocyanine:
    • I. Biran, L. Houben, H. Weismann, M. Hildebrand, L. Kronik, and B. Rybtchinski, “Real-space crystallography by low-dose focal-series TEM imaging of organic materials with near-atomic resolution”, Adv. Materials 34, 2202088 (2022).
       
  • Electronic and magnetic coupling in iron corroles:
    • ​​​​​​​A. Mizrahi, S. Bhowmik, A. Manna, W. Sinha, A. Kumar, M. Saphier, A. Mahammed, M. Patra, N. Fridman, I. Zilbermann, L. Kronik, and Z. Gross, “Electronic Coupling and Electrocatalysis in Redox Active Fused Iron Corrole”, Inorg. Chem. 61, 20725 (2022).​​​​​​​

Orbital-dependent density functionals

Optimally-tuned range-separated hybrid functionals

Ensemble-generalized functionals

 

 

Orbital-dependent density 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 be - and usually are - 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:
  • For work extending the scope and examining the properties of generalized Kohn-Sham theory, 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 and the charge-transfer excitation problem, for both molecules and solid-state systems.

Ensemble-generalized functionals

Usually, the reference fictitious electron gas of DFT, into which the original system is mapped, is a pure quantum mechanical state. However, there are important cases where use of a reference ensemble state, i.e., a statistical mixture of pure quantum states, is either desirable or outright necessary. Four scenarios where ensemble reference states arise are: (i) systems with degenerate ground states; (ii) systems possessing a fractional number of electrons; (iii) systems in an excited stationary state; (iv) systems at a finite temperature. Collectively, approaches dealing with any of the four scenarios (and related ones) are known as ensemble DFT (EDFT). Our work in this area focuses on developing a unified framework for the extension of standard approximate density functionals into novel ensemble density functionals, a process which we call “ensemblization”, and to use that to solve problems with which traditional DFT struggles.