Special Issue "In Memory of Walter Kohn—Advances in Density Functional Theory"

A special issue of Computation (ISSN 2079-3197). This special issue belongs to the section "Computational Chemistry".

Deadline for manuscript submissions: closed (20 August 2018)

Special Issue Editors

Guest Editor
Prof Dr. Levente Vitos

Department of Materials Science and Engineering, Royal Institute of Technology (KTH), Brinellvägen 23, SE-10044 Stockholm, Sweden
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Interests: density functional theory (DFT); semi-local approximations; electronic structure methods; Exact Muffin-Tin Orbitals method (EMTO); mechanical properties; magnetic properties; metal surfaces; defects; steels; high entropy alloys; magnetocaloric materials
Guest Editor
Dr. Stephan Schönecker

Department of Materials Science and Engineering, Royal Institute of Technology (KTH), Brinellvägen 23, SE-10044 Stockholm, Sweden
Website | E-Mail
Interests: density functional theory (DFT); electronic structure of solids and interfaces; strain engineering; ab initio treatment of magnetism, lattice vibrations, and superconductivity; steels; high entropy alloys
Guest Editor
Prof. Dr. Karlheinz Schwarz

Theoretical Chemistry Group, Material Chemisty, TU Wien, Technical University Vienna, A-1060 Vienna, Austria
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Phone: +43 1 58801 165301
Fax: +43 1 58801 165982
Interests: density functional theory (DFT); electronic structure of solids and surfaces; chemical bonding; spectra; high performance computing; Wien2k code

Special Issue Information

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                                                           In Memoriam Walter Kohn (1923--2016)

Dear Colleagues,

This Special Issue will consist of selected excellent papers from the “17th International Conference on Density Functional Theory and Its Application” (DFT2017), which will be held in Tällberg (Dalarna), Sweden, from 21 to 25 August 2017. This international conference is dedicated to Walter Kohn in memory of his essential contributions to this field. Contributers will be invited to submit and present papers in a wide variety of areas from concepts to applications. Topics of selected papers will include various method developments and applications to molecules, solids, surfaces and biomolecules. Related submissions outside the conference are also very welcome.

This Special Issue is dedicated to demonstrating recent advances in studying the electronic structure for a variety of systems in their ground state or excited state, from regular to highly correlated systems. Papers may report on original research, discuss methodological aspects, review the current state-of-the-art, or offer perspectives on future prospects.

These papers will be subjected to peer review and are published so as to widely disseminate new research results, including developments and applications.

The authors of papers submitted to the DFT2017 conference (http://www.dft2017.conf.kth.se) will be given the opportunity to submit extended versions of their works in this Special Issue, provided they fulfil the specific journal requirements found at https://www.mdpi.com/journal/computation/instructions.

Prof. Dr. Levente Vitos
Dr. Stephan Schönecker
Prof. Dr. Karlheinz Schwarz
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Computation is an international peer-reviewed open access quarterly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 350 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Density functional theory and the choice of functionals

  • Time-dependent DFT

  • Strongly correlated systems

  • applications of the DFT to solids, molecules and biosystems

  • Ground state, reactions and excited states

Published Papers (10 papers)

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Research

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Open AccessArticle Shannon Entropy in Atoms: A Test for the Assessment of Density Functionals in Kohn-Sham Theory
Computation 2018, 6(2), 36; https://doi.org/10.3390/computation6020036
Received: 10 March 2018 / Revised: 7 April 2018 / Accepted: 22 April 2018 / Published: 3 May 2018
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Abstract
Electron density is used to compute Shannon entropy. The deviation from the Hartree–Fock (HF) of this quantity has been observed to be related to correlation energy. Thus, Shannon entropy is here proposed as a valid quantity to assess the quality of an energy
[...] Read more.
Electron density is used to compute Shannon entropy. The deviation from the Hartree–Fock (HF) of this quantity has been observed to be related to correlation energy. Thus, Shannon entropy is here proposed as a valid quantity to assess the quality of an energy density functional developed within Kohn–Sham theory. To this purpose, results from eight different functionals, representative of Jacob’s ladder, are compared with accurate results obtained from diffusion quantum Monte Carlo (DMC) computations. For three series of atomic ions, our results show that the revTPSS and the PBE0 functionals are the best, whereas those based on local density approximation give the largest discrepancy from DMC Shannon entropy. Full article
(This article belongs to the Special Issue In Memory of Walter Kohn—Advances in Density Functional Theory)
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Open AccessArticle Asymptotic Behavior of Exact Exchange for Slabs: Beyond the Leading Order
Computation 2018, 6(2), 35; https://doi.org/10.3390/computation6020035
Received: 26 February 2018 / Revised: 19 April 2018 / Accepted: 21 April 2018 / Published: 29 April 2018
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Abstract
Far outside the surface of slabs, the exact exchange (EXX) potential vx falls off as 1/z , if z denotes the direction perpendicular to the surface and the slab is localized around z=0 . Similarly, the EXX
[...] Read more.
Far outside the surface of slabs, the exact exchange (EXX) potential v x falls off as 1 / z , if z denotes the direction perpendicular to the surface and the slab is localized around z = 0 . Similarly, the EXX energy density e x behaves as n / ( 2 z ) , where n is the electron density. Here, an alternative proof of these relations is given, in which the Coulomb singularity in the EXX energy is treated in a particularly careful fashion. This new approach allows the derivation of the next-to-leading order contributions to the asymptotic v x and e x . It turns out that in both cases, the corrections are proportional to 1 / z 2 in general. Full article
(This article belongs to the Special Issue In Memory of Walter Kohn—Advances in Density Functional Theory)
Open AccessFeature PaperArticle Dissipation Effects in Schrödinger and Quantal Density Functional Theories of Electrons in an Electromagnetic Field
Computation 2018, 6(1), 25; https://doi.org/10.3390/computation6010025
Received: 19 January 2018 / Revised: 23 February 2018 / Accepted: 25 February 2018 / Published: 6 March 2018
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Abstract
Dissipative effects arise in an electronic system when it interacts with a time-dependent environment. Here, the Schrödinger theory of electrons in an electromagnetic field including dissipative effects is described from a new perspective. Dissipation is accounted for via the effective Hamiltonian approach in
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Dissipative effects arise in an electronic system when it interacts with a time-dependent environment. Here, the Schrödinger theory of electrons in an electromagnetic field including dissipative effects is described from a new perspective. Dissipation is accounted for via the effective Hamiltonian approach in which the electron mass is time-dependent. The perspective is that of the individual electron: the corresponding equation of motion for the electron or time-dependent differential virial theorem—the ‘Quantal Newtonian’ second law—is derived. According to the law, each electron experiences an external field comprised of a binding electric field, the Lorentz field, and the electromagnetic field. In addition, there is an internal field whose components are representative of electron correlations due to the Pauli exclusion principle and Coulomb repulsion, kinetic effects, and density. There is also an internal contribution due to the magnetic field. The response of the electron is governed by the current density field in which a damping coefficient appears. The law leads to further insights into Schrödinger theory, and in particular the intrinsic self-consistent nature of the Schrödinger equation. It is proved that in the presence of dissipative effects, the basic variables (gauge-invariant properties, knowledge of which determines the Hamiltonian) are the density and physical current density. Finally, a local effective potential theory of dissipative systems—quantal density functional theory (QDFT)—is developed. This constitutes the mapping from the interacting dissipative electronic system to one of noninteracting fermions possessing the same dissipation and basic variables. Attributes of QDFT are the separation of the electron correlations due to the Pauli exclusion principle and Coulomb repulsion, and the determination of the correlation contributions to the kinetic energy. Hence, Schrödinger theory in conjunction with QDFT leads to additional insights into the dissipative system. Full article
(This article belongs to the Special Issue In Memory of Walter Kohn—Advances in Density Functional Theory)
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Open AccessArticle Assessing Density-Functional Theory for Equation-Of-State
Computation 2018, 6(1), 13; https://doi.org/10.3390/computation6010013
Received: 19 January 2018 / Revised: 31 January 2018 / Accepted: 31 January 2018 / Published: 3 February 2018
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Abstract
The last decade has seen a continued development of better experimental techniques to measure equation-of-state (EOS) for various materials. These improvements of both static and shock-compression approaches have increased the accuracy of the EOS and challenged the complimentary theoretical modeling. The conventional modeling
[...] Read more.
The last decade has seen a continued development of better experimental techniques to measure equation-of-state (EOS) for various materials. These improvements of both static and shock-compression approaches have increased the accuracy of the EOS and challenged the complimentary theoretical modeling. The conventional modeling of EOS, at least at pressure and temperature conditions that are not too extreme, is founded on density-functional theory (DFT). Naturally, there is an increased interest in the accuracy of DFT as the measurements are becoming more refined and there is a particular interest in the robustness and validity of DFT at conditions where experimental data are not available. Here, we consider a broad and large set of 64 elemental solids from low atomic number Z up to the very high Z actinide metals. The intent is to compare DFT with experimental zero-temperature isotherms up to 1 Mbar (100 GPa) and draw conclusions regarding the theoretical (DFT) error and quantify a reasonable and defensible approach to define the theoretical uncertainty. We find that in all 64 cases the DFT error at high pressure is smaller than or equal to the DFT error at lower pressures which thus provides an upper bound to the error at high compression. Full article
(This article belongs to the Special Issue In Memory of Walter Kohn—Advances in Density Functional Theory)
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Open AccessArticle Solid-State Testing of a Van-Der-Waals-Corrected Exchange-Correlation Functional Based on the Semiclassical Atom Theory
Received: 27 December 2017 / Revised: 19 January 2018 / Accepted: 22 January 2018 / Published: 25 January 2018
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Abstract
We extend the SG4 generalized gradient approximation, developed for covalent and ionic solids with a nonlocal van der Waals functional. The resulting SG4-rVV10m functional is tested, considering two possible parameterizations, for various kinds of bulk solids including layered materials and molecular crystals as
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We extend the SG4 generalized gradient approximation, developed for covalent and ionic solids with a nonlocal van der Waals functional. The resulting SG4-rVV10m functional is tested, considering two possible parameterizations, for various kinds of bulk solids including layered materials and molecular crystals as well as regular bulk materials. The results are compared to those of similar methods, PBE + rVV10L and rVV10. In most cases, SG4-rVV10m yields a quite good description of systems (from iono-covalent to hydrogen-bond and dispersion interactions), being competitive with PBE + rVV10L and rVV10 for dispersion-dominated systems and slightly superior for iono-covalent ones. Thus, it shows a promising applicability for solid-state applications. In a few cases, however, overbinding is observed. This is analysed in terms of gradient contributions to the functional. Full article
(This article belongs to the Special Issue In Memory of Walter Kohn—Advances in Density Functional Theory)
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Open AccessFeature PaperArticle A Diagonally Updated Limited-Memory Quasi-Newton Method for the Weighted Density Approximation
Computation 2017, 5(4), 42; https://doi.org/10.3390/computation5040042
Received: 31 August 2017 / Revised: 22 September 2017 / Accepted: 23 September 2017 / Published: 26 September 2017
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Abstract
We propose a limited-memory quasi-Newton method using the bad Broyden update and apply it to the nonlinear equations that must be solved to determine the effective Fermi momentum in the weighted density approximation for the exchange energy density functional. This algorithm has advantages
[...] Read more.
We propose a limited-memory quasi-Newton method using the bad Broyden update and apply it to the nonlinear equations that must be solved to determine the effective Fermi momentum in the weighted density approximation for the exchange energy density functional. This algorithm has advantages for nonlinear systems of equations with diagonally dominant Jacobians, because it is easy to generalize the method to allow for periodic updates of the diagonal of the Jacobian. Systematic tests of the method for atoms show that one can determine the effective Fermi momentum at thousands of points in less than fifteen iterations. Full article
(This article belongs to the Special Issue In Memory of Walter Kohn—Advances in Density Functional Theory)
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Review

Jump to: Research

Open AccessReview Kohn Anomaly and Phase Stability in Group VB Transition Metals
Computation 2018, 6(2), 29; https://doi.org/10.3390/computation6020029
Received: 28 February 2018 / Revised: 17 March 2018 / Accepted: 21 March 2018 / Published: 26 March 2018
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Abstract
In the periodic table, only a few pure metals exhibit lattice or magnetic instabilities associated with Fermi surface nesting, the classical examples being α-U and Cr. Whereas α-U displays a strong Kohn anomaly in the phonon spectrum that ultimately leads to the formation
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In the periodic table, only a few pure metals exhibit lattice or magnetic instabilities associated with Fermi surface nesting, the classical examples being α-U and Cr. Whereas α-U displays a strong Kohn anomaly in the phonon spectrum that ultimately leads to the formation of charge density waves (CDWs), Cr is known for its nesting-induced spin density waves (SDWs). Recently, it has become clear that a pronounced Kohn anomaly and the corresponding softening in the elastic constants is also the key factor that controls structural transformations and mechanical properties in compressed group VB metals—materials with relatively high superconducting critical temperatures. This article reviews the current understanding of the structural and mechanical behavior of these metals under pressure with an introduction to the concept of the Kohn anomaly and how it is related to the important concept of Peierls instability. We review both experimental and theoretical results showing different manifestations of the Kohn anomaly in the transverse acoustic phonon mode TA (ξ00) in V, Nb, and Ta. Specifically, in V the anomaly triggers a structural transition to a rhombohedral phase, whereas in Nb and Ta it leads to an anomalous reduction in yield strength. Full article
(This article belongs to the Special Issue In Memory of Walter Kohn—Advances in Density Functional Theory)
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Open AccessReview Recent Progress in First-Principles Methods for Computing the Electronic Structure of Correlated Materials
Computation 2018, 6(1), 26; https://doi.org/10.3390/computation6010026
Received: 27 February 2018 / Revised: 12 March 2018 / Accepted: 13 March 2018 / Published: 19 March 2018
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Abstract
Substantial progress has been achieved in the last couple of decades in computing the electronic structure of correlated materials from first principles. This progress has been driven by parallel development in theory and numerical algorithms. Theoretical development in combining ab initio approaches and
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Substantial progress has been achieved in the last couple of decades in computing the electronic structure of correlated materials from first principles. This progress has been driven by parallel development in theory and numerical algorithms. Theoretical development in combining ab initio approaches and many-body methods is particularly promising. A crucial role is also played by a systematic method for deriving a low-energy model, which bridges the gap between real and model systems. In this article, an overview is given tracing the development from the LDA+U to the latest progress in combining the G W method and (extended) dynamical mean-field theory ( G W +EDMFT). The emphasis is on conceptual and theoretical aspects rather than technical ones. Full article
(This article belongs to the Special Issue In Memory of Walter Kohn—Advances in Density Functional Theory)
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Open AccessFeature PaperReview Challenges for Theory and Computation
Computation 2017, 5(4), 49; https://doi.org/10.3390/computation5040049
Received: 21 November 2017 / Revised: 30 November 2017 / Accepted: 1 December 2017 / Published: 4 December 2017
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Abstract
The routinely made assumptions for simulating solid materials are briefly summarized, since they need to be critically assessed when new aspects become important, such as excited states, finite temperature, time-dependence, etc. The significantly higher computer power combined with improved experimental data open new
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The routinely made assumptions for simulating solid materials are briefly summarized, since they need to be critically assessed when new aspects become important, such as excited states, finite temperature, time-dependence, etc. The significantly higher computer power combined with improved experimental data open new areas for interdisciplinary research, for which new ideas and concepts are needed. Full article
(This article belongs to the Special Issue In Memory of Walter Kohn—Advances in Density Functional Theory)
Open AccessReview Time-Dependent Density-Functional Theory and Excitons in Bulk and Two-Dimensional Semiconductors
Computation 2017, 5(3), 39; https://doi.org/10.3390/computation5030039
Received: 21 July 2017 / Revised: 10 August 2017 / Accepted: 15 August 2017 / Published: 25 August 2017
Cited by 2 | PDF Full-text (3206 KB) | HTML Full-text | XML Full-text
Abstract
In this work, we summarize the recent progress made in constructing time-dependent density-functional theory (TDDFT) exchange-correlation (XC) kernels capable to describe excitonic effects in semiconductors and apply these kernels in two important cases: a “classic” bulk semiconductor, GaAs, with weakly-bound excitons and a
[...] Read more.
In this work, we summarize the recent progress made in constructing time-dependent density-functional theory (TDDFT) exchange-correlation (XC) kernels capable to describe excitonic effects in semiconductors and apply these kernels in two important cases: a “classic” bulk semiconductor, GaAs, with weakly-bound excitons and a novel two-dimensional material, MoS2, with very strongly-bound excitonic states. Namely, after a brief review of the standard many-body semiconductor Bloch and Bethe-Salpether equation (SBE and BSE) and a combined TDDFT+BSE approaches, we proceed with details of the proposed pure TDDFT XC kernels for excitons. We analyze the reasons for successes and failures of these kernels in describing the excitons in bulk GaAs and monolayer MoS2, and conclude with a discussion of possible alternative kernels capable of accurately describing the bound electron-hole states in both bulk and two-dimensional materials. Full article
(This article belongs to the Special Issue In Memory of Walter Kohn—Advances in Density Functional Theory)
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