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Computation
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Advances in Electronic Structure Theory: Method Development and Application
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Advances in Electronic Structure Theory: Method Development and Application

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

Deadline for manuscript submissions: closed (30 April 2017) | Viewed by 26848

Special Issue Editor

Dr. Jianmin Tao

E-Mail Website
Guest Editor
Department of Physics, Temple University, 1925 N. 12th Street, Philadelphia, PA 19122-1801, USA
Interests: density functional theory; time-dependent density functional theory; long-range van der Waals interaction; condensed matter theory; computational materials science

Special Issue Information

Dear Colleagues,

This is a Special Issue on computational methods and applications, entitled “Advances in Electronic Structure Theory: Method Development and Application”. It aims to solicit papers on all aspects of modern electronic structure theory, including wave function-based many-body methods, density functional theory, time-dependent density functional theory, long-range van der Waals interaction, as well as their applications to molecules and real materials. Both review articles and original papers are welcome. All the papers will be selected based on their merit of review and disseminated world-wide.

The topics of interest include:

  1. Fundamental issues in modern electronic structure theory.
  2. Development of wave function-based methods and computational study of molecules and materials.
  3. Development of density functional theory and application to molecules and materials.
  4. Development of time-dependent density functional theory and application to molecules and materials.
  5. Modeling of long-range van der Waals interaction and application of dispersion-corrected density functional theory to molecules and materials.

Dr. Jianmin Tao
Guest Editor

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 submissions that pass pre-check are 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 monthly 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 1800 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

  • Wave Function
  • DFT
  • TDDFT
  • van der Waals interaction
  • Electronic structure theory
  • quantum chemistry
  • computational materials science

Published Papers (6 papers)

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Research

2243 KiB  
Article
Theoretical Prediction of Electronic Structures and Phonon Dispersion of Ce2XN2 (X = S, Se, and Te) Ternary
by Mohammed Benali Kanoun and Souraya Goumri-Said
Computation 2017, 5(2), 29; https://doi.org/10.3390/computation5020029 - 13 Jun 2017
Cited by 2 | Viewed by 3416
Abstract
A systematic study of structural, electronic, vibrational properties of new ternary dicerium selenide dinitride, Ce2SeN2 and predicted compounds—Ce2SN2 and Ce2TeN2—is performed using first-principles calculations within Perdew–Burke–Ernzerhof functional with Hubbard correction. Our calculated results [...] Read more.
A systematic study of structural, electronic, vibrational properties of new ternary dicerium selenide dinitride, Ce2SeN2 and predicted compounds—Ce2SN2 and Ce2TeN2—is performed using first-principles calculations within Perdew–Burke–Ernzerhof functional with Hubbard correction. Our calculated results for structural parameters nicely agree to the experimental measurements. We predict that all ternary dicerium chalcogenide nitrides are thermodynamically stable. The predicted elastic constants and related mechanical properties demonstrate its profound mechanical stability as well. Moreover, our results show that Ce2XN2 are insulator materials. Trends of the structural parameters, electronic structures, and phonon dispersion are discussed in terms of the characteristics of the Ce (4f) states. Full article
(This article belongs to the Special Issue Advances in Electronic Structure Theory: Method Development and Application)
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283 KiB  
Article
Levy-Lieb-Based Monte Carlo Study of the Dimensionality Behaviour of the Electronic Kinetic Functional
by Seshaditya A., Luca M. Ghiringhelli and Luigi Delle Site
Computation 2017, 5(2), 30; https://doi.org/10.3390/computation5020030 - 10 Jun 2017
Cited by 1 | Viewed by 4323
Abstract
We consider a gas of interacting electrons in the limit of nearly uniform density and treat the one dimensional (1D), two dimensional (2D) and three dimensional (3D) cases. We focus on the determination of the correlation part of the kinetic functional by employing [...] Read more.
We consider a gas of interacting electrons in the limit of nearly uniform density and treat the one dimensional (1D), two dimensional (2D) and three dimensional (3D) cases. We focus on the determination of the correlation part of the kinetic functional by employing a Monte Carlo sampling technique of electrons in space based on an analytic derivation via the Levy-Lieb constrained search principle. Of particular interest is the question of the behaviour of the functional as one passes from 1D to 3D; according to the basic principles of Density Functional Theory (DFT) the form of the universal functional should be independent of the dimensionality. However, in practice the straightforward use of current approximate functionals in different dimensions is problematic. Here, we show that going from the 3D to the 2D case the functional form is consistent (concave function) but in 1D becomes convex; such a drastic difference is peculiar of 1D electron systems as it is for other quantities. Given the interesting behaviour of the functional, this study represents a basic first-principle approach to the problem and suggests further investigations using highly accurate (though expensive) many-electron computational techniques, such as Quantum Monte Carlo. Full article
(This article belongs to the Special Issue Advances in Electronic Structure Theory: Method Development and Application)
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318 KiB  
Article
Geometric Derivation of the Stress Tensor of the Homogeneous Electron Gas
by Jianmin Tao, Giovanni Vignale and Jian-Xin Zhu
Computation 2017, 5(2), 28; https://doi.org/10.3390/computation5020028 - 08 Jun 2017
Cited by 1 | Viewed by 3569
Abstract
The foundation of many approximations in time-dependent density functional theory (TDDFT) lies in the theory of the homogeneous electron gas. However, unlike the ground-state DFT, in which the exchange-correlation potential of the homogeneous electron gas is known exactly via the quantum Monte Carlo [...] Read more.
The foundation of many approximations in time-dependent density functional theory (TDDFT) lies in the theory of the homogeneous electron gas. However, unlike the ground-state DFT, in which the exchange-correlation potential of the homogeneous electron gas is known exactly via the quantum Monte Carlo calculation, the time-dependent or frequency-dependent dynamical potential of the homogeneous electron gas has not been known exactly, due to the absence of a similar variational principle for excited states. In this work, we present a simple geometric derivation of the time-dependent dynamical exchange-correlation potential for the homogeneous system. With this derivation, the dynamical potential can be expressed in terms of the stress tensor, offering an alternative to calculate the bulk and shear moduli, two key input quantities in TDDFT. Full article
(This article belongs to the Special Issue Advances in Electronic Structure Theory: Method Development and Application)
1641 KiB  
Article
Energetic Study of Clusters and Reaction Barrier Heights from Efficient Semilocal Density Functionals
by Guocai Tian, Yuxiang Mo and Jianmin Tao
Computation 2017, 5(2), 27; https://doi.org/10.3390/computation5020027 - 03 Jun 2017
Cited by 7 | Viewed by 4213
Abstract
The accurate first-principles prediction of the energetic properties of molecules and clusters from efficient semilocal density functionals is of broad interest. Here we study the performance of a non-empirical Tao-Mo (TM) density functional on binding energies and excitation energies of titanium dioxide and [...] Read more.
The accurate first-principles prediction of the energetic properties of molecules and clusters from efficient semilocal density functionals is of broad interest. Here we study the performance of a non-empirical Tao-Mo (TM) density functional on binding energies and excitation energies of titanium dioxide and water clusters, as well as reaction barrier heights. To make a comparison, a combination of the TM exchange part with the TPSS (Tao–Perdew–Staroverov–Scuseria) correlation functional—called TMTPSS—is also included in this study. Our calculations show that the best binding energies of titanium dioxide are predicted by PBE0 (Perdew–Burke–Ernzerhof hybrid functional), TM, and TMTPSS with nearly the same accuracy, while B3LYP (Beck’s three-parameter exchange part with Lee-Yang-Parr correlation), TPSS, and PBE (Perdew–Burke–Ernzerhof) yield larger mean absolute errors. For excitation energies of titanium and water clusters, PBE0 and B3LYP are the most accurate functionals, outperforming the performance of semilocal functionals due to the nonlocality problem suffered by the latter. Nevertheless, TMTPSS and TM functionals are still good accurate semilocal methods, improving upon the commonly-used TPSS and PBE functionals. We also find that the best reaction barrier heights are predicted by PBE0 and B3LYP, thanks to the nonlocality incorporated into these two hybrid functionals, but TMTPSS and TM are obviously more accurate than SCAN (Strongly Constrained and Appropriately Normed), TPSS, and PBE, suggesting the good performance of TM and TMTPSS for physically different systems and properties. Full article
(This article belongs to the Special Issue Advances in Electronic Structure Theory: Method Development and Application)
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880 KiB  
Article
Schrödinger Theory of Electrons in Electromagnetic Fields: New Perspectives
by Viraht Sahni and Xiao-Yin Pan
Computation 2017, 5(1), 15; https://doi.org/10.3390/computation5010015 - 09 Mar 2017
Cited by 8 | Viewed by 5536
Abstract
The Schrödinger theory of electrons in an external electromagnetic field is described from the new perspective of the individual electron. The perspective is arrived at via the time-dependent “Quantal Newtonian” law (or differential virial theorem). (The time-independent law, a special case, provides a [...] Read more.
The Schrödinger theory of electrons in an external electromagnetic field is described from the new perspective of the individual electron. The perspective is arrived at via the time-dependent “Quantal Newtonian” law (or differential virial theorem). (The time-independent law, a special case, provides a similar description of stationary-state theory). These laws are in terms of “classical” fields whose sources are quantal expectations of Hermitian operators taken with respect to the wave function. The laws reveal the following physics: (a) in addition to the external field, each electron experiences an internal field whose components are representative of a specific property of the system such as the correlations due to the Pauli exclusion principle and Coulomb repulsion, the electron density, kinetic effects, and an internal magnetic field component. The response of the electron is described by the current density field; (b) the scalar potential energy of an electron is the work done in a conservative field. It is thus path-independent. The conservative field is the sum of the internal and Lorentz fields. Hence, the potential is inherently related to the properties of the system, and its constituent property-related components known. As the sources of the fields are functionals of the wave function, so are the respective fields, and, therefore, the scalar potential is a known functional of the wave function; (c) as such, the system Hamiltonian is a known functional of the wave function. This reveals the intrinsic self-consistent nature of the Schrödinger equation, thereby providing a path for the determination of the exact wave functions and energies of the system; (d) with the Schrödinger equation written in self-consistent form, the Hamiltonian now admits via the Lorentz field a new term that explicitly involves the external magnetic field. The new understandings are explicated for the stationary state case by application to two quantum dots in a magnetostatic field, one in a ground state and the other in an excited state. For the time-dependent case, the evolution of the same states of the quantum dots in both a magnetostatic and a time-dependent electric field is described. In each case, the satisfaction of the corresponding “Quantal Newtonian” law is demonstrated. Full article
(This article belongs to the Special Issue Advances in Electronic Structure Theory: Method Development and Application)
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739 KiB  
Article
Excitons in Solids from Time-Dependent Density-Functional Theory: Assessing the Tamm-Dancoff Approximation
by Young-Moo Byun and Carsten A. Ullrich
Computation 2017, 5(1), 9; https://doi.org/10.3390/computation5010009 - 29 Jan 2017
Cited by 12 | Viewed by 5181
Abstract
Excitonic effects in solids can be calculated using the Bethe-Salpeter equation (BSE) or the Casida equation of time-dependent density-functional theory (TDDFT). In both methods, the Tamm-Dancoff approximation (TDA), which decouples excitations and de-excitations, is widely used to reduce computational cost. Here, we study [...] Read more.
Excitonic effects in solids can be calculated using the Bethe-Salpeter equation (BSE) or the Casida equation of time-dependent density-functional theory (TDDFT). In both methods, the Tamm-Dancoff approximation (TDA), which decouples excitations and de-excitations, is widely used to reduce computational cost. Here, we study the effect of the TDA on exciton binding energies of solids obtained from the Casida equation using long-range-corrected (LRC) exchange-correlation kernels. We find that the TDA underestimates TDDFT-LRC exciton binding energies of semiconductors slightly, but those of insulators significantly (i.e., by more than 100%), and thus it is essential to solve the full Casida equation to describe strongly bound excitons. These findings are relevant in the ongoing search for accurate and efficient TDDFT approaches for excitons. Full article
(This article belongs to the Special Issue Advances in Electronic Structure Theory: Method Development and Application)
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