Nathan E. Rahat and Eli Kraisler, 

Plateaus in the potentials of density-functional theory: Analytical derivation and useful approximations, 

J. Chem. Theory Comput. 21, 3476 (2025)

Publisher's version                 arXiv version                 

We derive an analytical expression for the plateau in the Kohn-Sham potential of DFT, which forms around the center of the system, upon electron addition. The resulting formula is the first analytical expression of its kind. The derivation is performed using the orbital-free DFT framework, analyzing both the Kohn-Sham-Pauli and the Pauli potentials.

Alon Hayman*, Nevo Levy*, Yuli Goshen, Malachi Fraenkel, Eli Kraisler^@ and Tamar Stein^@, 

Spin migration in density functional theory: Energy, potential, and density perspectives, 

J. Chem. Phys. 162, 114301 (2025)     (Editor's Pick)

Publisher's version                 arXiv version

We study the behavior of the energy, the frontier orbitals, the Kohn-Sham potentials and the electron density, with respect to fractional spin, in different atomic systems. We analyze seven standard functionals and find two main scenarios of energy deviation from the expected behavior. We clearly recognize a jump in the frontier orbital energies upon spin variation and the related plateau in the KS potential, due to the spin-migration derivative discontinuity.

Eli Kraisler, 

How the piecewise-linearity requirement for the density affects quantities in the Kohn−Sham system, 

J. Chem. Theory Comput. 21, 155 (2025)

Publisher's version                 arXiv version                  

Piecewise-linearity of the energy is well-known and is widely used to both assess the performance of a given approximation, to generalize, to correct or fine-tune it.  Improvement in the prediction of the IP and the band gap is also well-established. But what about piecewise-linearity of the density? This aspect received so far much less attention. 

In this paper I suggest to express Kohn-Sham (KS) quantities using the two-point Taylor expansion (2pTE)  in the electron number, N, and find how the expansion coefficients are restricted by the piecewise-linearity requirement. I focus on the total electron density, the KS sub-densities, and the HOMO orbital density. A numerical investigation accompanies exact analytical results, aiming at future removal of density-driven errors in DFT.

Yuli Goshen and Eli Kraisler, 

Ensemble ground state of a many-electron system with fractional electron number and spin: Piecewise-linearity and flat-plane condition generalized,

J. Phys. Chem. Lett. 15, 2337 (2025)

Publisher's version                 arXiv version                  

In this Letter, we provide an exact description of the zero-temperature ensemble ground state of a general, finite, many-electron system and characterize the dependence of the energy and the spin-densities on the electron number (N_tot) and spin (M_tot); both can be fractional. We generalize the well-known piecewise-linearity principle and the flat-plane condition and determine which pure states contribute to the ground-state ensemble and which do not. We find a new derivative discontinuity, which manifests for spin variation at a constant N_tot, as a jump in the Kohn–Sham potential. Furthermore, we identify a previously unknown degeneracy of the ground state, such that the total energy and density are unique, but the spin-densities are not.

Eli Kraisler and Leeor Kronik,

Fundamental gaps with approximate density functionals: The derivative discontinuity revealed from ensemble considerations,

J. Chem. Phys. 140, 18A540 (2014)

Publisher's version              arXiv version

The fundamental gap is a central quantity in the electronic structure of matter, both in molecular and crystalline systems. The fundamental gap is not generally equal to the Kohn-Sham gap of density functional theory (DFT), even in principle. The two gaps differ by the derivative discontinuity, namely, an abrupt change in slope of the exchange-correlation energy as a function of electron number, expected across an integer-electron point. Popular approximate functionals are thought to be devoid of a derivative discontinuity, strongly compromising their performance for prediction of spectroscopic properties. In this paper we show that, in fact, all exchange-correlation functionals possess a derivative discontinuity, which arises naturally from the application of ensemble considerations within DFT, without any empiricism. This derivative discontinuity can be expressed in closed form using only quantities obtained in the course of a standard DFT calculation of the neutral system. For small, finite systems, addition of this derivative discontinuity indeed results in a greatly improved prediction for the fundamental gap, even when based on the most simple approximate exchange-correlation density functional – the local density approximation (LDA). For solids, the same scheme is exact in principle, but results in a zero derivative discontinuity correction when applied to common functionals, such as LDA or PBE. We show what is the reason for that: It is the combination of two factors: (1) the locality of the xc functional, i.e., the fact that the xc kernel is proportional to a delta function and/or its derivatives; (2) the extreme nonlocality of the Bloch functions in a periodic solid.

Tobias Schmidt, Eli Kraisler, Leeor Kronik and Stephan Kümmel,

One-electron self-interaction and the asymptotics of the Kohn–Sham potential: an impaired relation,

Phys. Chem. Chem. Phys. 16, 14357 (2014)

Publisher's version              arXiv version

One-electron self-interaction and an incorrect asymptotic behavior of the Kohn–Sham exchange-correlation potential are among the most prominent limitations of many present-day density functionals. However, a one-electron self-interaction-free energy does not necessarily lead to the correct long-range potential. This is shown here explicitly for local hybrid functionals: at large distance r, the potential approaches the limit of -g/r, where g alomst never has the desired value of 1. On the one hand, the latter asymptotic behavior is much better than the exponential decay of semi-local functionals. On the other hand, our result suggests that for the correct -1/r decay, one must consider functionals that are beyond the family of local hybrids. 

Furthermore, carefully studying the ratio of the von Weizsäcker kinetic energy density to the (positive) Kohn–Sham kinetic energy density, τ_W/τ, reveals that this ratio, which frequently serves as an iso-orbital indicator and is used to eliminate one-electron self-interaction effects, can fail to approach its expected value in the vicinity of orbital nodal planes. This perspective article suggests that the nature and consequences of one-electron self-interaction and some of the strategies for its correction need to be reconsidered.

Eli Kraisler and Leeor Kronik,

Piecewise-linearity of approximate density functionals revisited: Implications for frontier orbital energies,

Phys. Rev. Lett. 110, 126403 (2013)

Publisher's version              arXiv version

A known and well-established property of any many-electron system at zero temperature is that the total energy versus the number of electrons is a series of linear segments between integer points. However, common approximate density functionals produce total energies that do not exhibit this behavior. In this Letter, we show that, contrary to conventional wisdom, most of the required piecewise linearity of an arbitrary approximate density functional can be restored by careful consideration of the ensemble generalization of density-functional theory. The resulting formulation introduces the desired derivative discontinuity to any approximate functional, even one that is explicitly density dependent. All these advances are achieved while neither introducing empiricism nor changing the underlying functional form.

Uri Argaman, Guy Makov and Eli Kraisler,

Higher ionization energies of atoms in density-functional theory,

Phys. Rev. A 88, 042504 (2013)

Publisher's version              arXiv version

In this paper, we have calculated the total energies, spins and ionization energies for higher ions (i.e., second ion and higher) in atoms with 1 < Z < 29. We examined standard approximations of DFT, namely the local spin density approximation (LSDA) and Perdew-Burke-Ernzerhof general gradient approximation (PBE-GGA). This work is in some sense a continuation of of previous research published in Phys. Rev. A 80, 032115 (2009) and Phys. Rev. A 82, 042516 (2010).

For higher ions, we find the calculations are in close agreement with experiment, with an error of typically less than ca. 1%. No ensemble v-representable solutions, namely solutions with fractional occupations, occurred for high ions. Surprisingly, the error in this group of systems depends on the electronic configuration of the ion in both LSDA and PBE-GGA and is independent of both self-interaction and relativistic corrections. Larger errors are found for systems in which the spin-spin correlation is significant, which indicates the possible benefit from an orbital-dependent formulation of the correlation energy functional.

Ayelet Vilan, David Cahen and Eli Kraisler,

Rethinking transition voltage spectroscopy within a generic Taylor expansion view,

ACS Nano 7, 695 (2013)

Publisher's version            

Transition voltage spectroscopy (TVS) has become an accepted quantification tool for molecular transport characteristics, due to its simplicity and reproducibility. Alternatively, the Taylor expansion view, TyEx, of transport by tunneling suggests that conductance -voltage curves have approximately a generic parabolic shape, regardless of whether the tunneling model is derived from an average medium view (e.g., WKB) or from a scattering view (e.g., Landauer). Comparing TVS and TyEx approaches reveals that TVS is closely related to a bias-scaling factor, V₀, which is directly derived from the third coefficient of TyEx, namely, the second derivative of the conductance with respect to bias at 0 V. This interpretation of TVS leads to simple expressions that can be compared easily across primarily different tunneling models. Because the basic curve shape is mostly generic, the quality of model fitting is not informative on the actual tunneling model. However internal correlation between the conductance near 0 V and V₀ (TVS) provides genuine indication on fundamental tunneling features. Furthermore, we show that the prevailing concept that V₀ is proportional to the barrier height holds only in the case of resonant tunneling, while for off-resonant or deep tunneling, V₀ is proportional to the ratio of barrier height to barrier width.

Eli Kraisler, Guy Makov and Itzhak Kelson,

Ensemble v-representable ab initio density-functional calculation of energy and spin in atoms: A test of exchange-correlation approximations,

Phys. Rev. A 82, 042516 (2010)

Publisher's version              arXiv version

In this paper, we created a comprehensive and accurate database for DFT calculations for atomic systems. We present the total energies and the spin states for atoms and their first ions obtained with the local spin-density approximation (LSDA) and the Perdew-Burke Ernzerhof (PBE) generalized-gradient approximation (GGA). Contrary to common wisdom, there are many atoms and ions, which are not pure-state v-representable, in the Kohn-Sham system. For these, an ensemble v-representable solution with fractional occupations is provided, using a recently developed algorithm [E. Kraisler et al., Phys. Rev. A 80, 032115 (2009)].

Our main findings can be summarized as follows: (1) For many atoms, PBE-GGA only modestly improves LSDA. (2) The Kohn-Sham electronic configuration does not always equal the experimental configuration; they do not have to equal. Imposing the experimental configuration can prevent converging to the global minimum, e.g., in lanthanides. (3) The spin values fit the experiment for most atoms and are almost unaffected by the choice of the xc functional.

Eli Kraisler,

Density functional calculations in atomic systems,

M.Sc. thesis, Tel Aviv University (2010)

PDF version

Eli Kraisler, Guy Makov, Nathan Argaman and Itzhak Kelson,

Fractional occupation in Kohn-Sham density-functional theory and the treatment of non-pure-state v-representable densities,

Phys. Rev. A 80, 032115 (2009)

Publisher's version              arXiv version

Interestingly, within Kohn-Sham density-functional theory (KS-DFT), one can find many systems that are not non-interacting-pure-state v-representable (NI-PSVR), namely that the ground state of the Kohn-Sham system is not a pure state, but an ensemble. In this paper, we first prove that the use of densities which do not correspond to a ground state of their non-interacting reference system is forbidden. Second, we propose a numerical algorithm, which provides Kohn-Sham calculations considering only non-interacting-ensemble-v-representable (NI-EVR) densities and use the Fe atom as an illustration. Finally, we analyze the problem from the perspective of finite-temperature DFT, where we expose the physical significance of fractional occupations and resolve the question of why degenerate states can be unequally occupied.

מיכאל גוץ, גלינה גוץ, אלי קרייסלר, 

כא"מ מושרה בסליל כתוצאה מתנועת מגנט-מוט דרכו,

תהודה (2) 21, עמ' 24-29 (2000)

Michael Gots, Galina Gots and Eli Kraisler, 

Induced voltage in a coil as a result of a rod magnet motion through it

Tehuda 21 (2), 24-29 (2000)   [in Hebrew]

Publisher's version                 PDF version

This paper presents an experiment aimed at high school physics students. The phenomenon of the induced voltage formed in a coil as a result of a rod magnet moving through it is presented. The dependence of the voltage on a number of parameters, namely the number of turns in the coil, the direction of the turns, the radius of the coil, the speed of the magnet and the direction of its movement, is illustrated.  

(This is the first paper coauthored by E. Kraisler)