Research

Jump to: Review

7 pages, 262 KiB

Open AccessArticle

Shannon Entropy in Atoms: A Test for the Assessment of Density Functionals in Kohn-Sham Theory

by Claudio Amovilli and Franca Maria Floris

Computation 2018, 6(2), 36; https://doi.org/10.3390/computation6020036 - 03 May 2018

Cited by 4 | Viewed by 3863

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)

► Show Figures

Figure 1

15 pages, 317 KiB

Open AccessArticle

Asymptotic Behavior of Exact Exchange for Slabs: Beyond the Leading Order

by Eberhard Engel

Computation 2018, 6(2), 35; https://doi.org/10.3390/computation6020035 - 29 Apr 2018

Cited by 3 | Viewed by 3262

Abstract

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 [...] 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)

18 pages, 375 KiB

Open AccessFeature PaperArticle

Dissipation Effects in Schrödinger and Quantal Density Functional Theories of Electrons in an Electromagnetic Field

by Xiao-Yin Pan and Viraht Sahni

Computation 2018, 6(1), 25; https://doi.org/10.3390/computation6010025 - 06 Mar 2018

Cited by 2 | Viewed by 3469

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 [...] Read more.

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)

► Show Figures

Figure 1

13 pages, 1919 KiB

Open AccessArticle

Assessing Density-Functional Theory for Equation-Of-State

by Per Söderlind and David A. Young

Computation 2018, 6(1), 13; https://doi.org/10.3390/computation6010013 - 03 Feb 2018

Cited by 17 | Viewed by 5516

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)

► Show Figures

Figure 1

18 pages, 1287 KiB

Open AccessArticle

Solid-State Testing of a Van-Der-Waals-Corrected Exchange-Correlation Functional Based on the Semiclassical Atom Theory

by Aleksandr V. Terentjev, Pietro Cortona, Lucian A. Constantin, José M. Pitarke, Fabio Della Sala and Eduardo Fabiano

Computation 2018, 6(1), 7; https://doi.org/10.3390/computation6010007 - 25 Jan 2018

Cited by 17 | Viewed by 4341

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 [...] Read more.

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)

► Show Figures

Figure 1

486 KiB

Open AccessFeature PaperArticle

A Diagonally Updated Limited-Memory Quasi-Newton Method for the Weighted Density Approximation

by Matthew Chan, Rogelio Cuevas-Saavedra, Debajit Chakraborty and Paul W. Ayers

Computation 2017, 5(4), 42; https://doi.org/10.3390/computation5040042 - 26 Sep 2017

Cited by 2 | Viewed by 3973

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)

► Show Figures

Figure 1

Review

Jump to: Research

19 pages, 5160 KiB

Open AccessReview

Kohn Anomaly and Phase Stability in Group VB Transition Metals

by Alexander Landa, Per Söderlind, Ivan I. Naumov, John E. Klepeis and Levente Vitos

Computation 2018, 6(2), 29; https://doi.org/10.3390/computation6020029 - 26 Mar 2018

Cited by 26 | Viewed by 9352

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 [...] Read more.

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)

► Show Figures

Figure 1

33 pages, 5867 KiB

Open AccessReview

Recent Progress in First-Principles Methods for Computing the Electronic Structure of Correlated Materials

by Fredrik Nilsson and Ferdi Aryasetiawan

Computation 2018, 6(1), 26; https://doi.org/10.3390/computation6010026 - 19 Mar 2018

Cited by 16 | Viewed by 6025

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 [...] Read more.

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)

► Show Figures

Figure 1

196 KiB

Open AccessFeature PaperReview

Challenges for Theory and Computation

by Karlheinz Schwarz

Computation 2017, 5(4), 49; https://doi.org/10.3390/computation5040049 - 04 Dec 2017

Cited by 1 | Viewed by 3203

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 [...] Read more.

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)

3206 KiB

Open AccessReview

Time-Dependent Density-Functional Theory and Excitons in Bulk and Two-Dimensional Semiconductors

by Volodymyr Turkowski, Naseem Ud Din and Talat S. Rahman

Computation 2017, 5(3), 39; https://doi.org/10.3390/computation5030039 - 25 Aug 2017

Cited by 22 | Viewed by 5837

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)

► Show Figures