scholarly journals Fractional Quantum Chemistry

2021 ◽  
Author(s):  
Mohammad Mostafanejad
Keyword(s):  
Quantum Chemistry ◽  
Density Functional ◽  
Arbitrary Order ◽  
Correlation Energy ◽  
Model Systems ◽  
Variable Order ◽  
Nonlocal Effects ◽  
Open Problems ◽  
Fractional Quantum ◽  
Fractional Schrödinger Equations

The realization of fractional quantum chemistry is presented. Adopting the integro-differential operators of the calculus of arbitrary-order, we develop a general framework for the description of quantum nonlocal effects in the complex electronic environments. After a brief overview of the historical and fundamental aspects of the calculus of arbitrary-order, various classes of fractional Schrödinger equations are discussed and pertinent controversies and open problems around their applications to model systems are detailed. We provide a unified approach toward fractional generalization of the quantum chemical models such as Hartree-Fock and Kohn-Sham density functional theory and develop fractional variants of the fundamental molecular integrals and correlation energy. Furthermore, we offer various strategies for modeling static and dynamic quantum nonlocal effects through constant- and variable-order fractional operators, respectively. Possible directions for future developments of fractional quantum chemistry are also outlined.

scholarly journals Improving Density Functional Prediction of Molecular Thermochemical Properties with a Machine-Learning-Corrected Generalized Gradient Approximation

2021 ◽  
Author(s):  
Jingchun Wang ◽  
DaDi Zhang ◽  
Rui-Xue Xu ◽  
ChiYung Yam ◽  
GuanHua Chen ◽  
...  
Keyword(s):  
Machine Learning ◽  
Density Functional ◽  
Correlation Energy ◽  
Model Systems ◽  
Kinetic Properties ◽  
Functional Prediction ◽  
Generalized Gradient ◽  
Exchange Correlation ◽  
The Past ◽  
Reduced Gradient

The past decade has seen an increasing interest in designing sophisticated density functional approximations (DFAs) by integrating the power of machine learning (ML) techniques. However, application of the ML-based DFAs is often confined to simple model systems. In this work, we construct an ML correction to the widely used Perdew-Burke-Ernzerhof (PBE) functional by establishing a semilocal mapping from the electron density and reduced gradient to the exchange-correlation energy density. The resulting ML-corrected PBE is immediately applicable to any real molecule, and yields significantly improved heats of formation while preserving the accuracy for other thermochemical and kinetic properties. This work highlights the prospect of combining the power of data-driven ML methods with physics-inspired derivations for reaching the heaven of chemical accuracy.

scholarly journals The Density Functional Theory and Beyond: Example and Applications

2021 ◽  
Author(s):  
Mohamed Barhoumi
Keyword(s):  
Density Functional Theory ◽  
Quantum Chemistry ◽  
Density Functional ◽  
Materials Science ◽  
Correlation Energy ◽  
Condensed Matter ◽  
Random Phase ◽  
Condensed Matter Physics ◽  
Functional Theory ◽  
The Density Functional Theory

Density Functional Theory is one of the most widely used methods in quantum calculations of the electronic structure of matter in both condensed matter physics and quantum chemistry. Despite the importance of the density functional theory to find the correlation-exchange energy, but this quantity remains inaccurate. So we have to go beyond DFT to correct this quantity. In this framework, the random phase approximation has gained importance far beyond its initial field of application, condensed matter physics, materials science, and quantum chemistry. RPA is an approach to accurately calculate the electron correlation energy.

scholarly journals Improving Density Functional Prediction of Molecular Thermochemical Properties with a Machine-Learning-Corrected Generalized Gradient Approximation

2021 ◽  
Author(s):  
Jingchun Wang ◽  
DaDi Zhang ◽  
Rui-Xue Xu ◽  
ChiYung Yam ◽  
GuanHua Chen ◽  
...  
Keyword(s):  
Machine Learning ◽  
Density Functional ◽  
Correlation Energy ◽  
Model Systems ◽  
Kinetic Properties ◽  
Functional Prediction ◽  
Generalized Gradient ◽  
Exchange Correlation ◽  
The Past ◽  
Reduced Gradient

The past decade has seen an increasing interest in designing sophisticated density functional approximations (DFAs) by integrating the power of machine learning (ML) techniques. However, application of the ML-based DFAs is often confined to simple model systems. In this work, we construct an ML correction to the widely used Perdew-Burke-Ernzerhof (PBE) functional by establishing a semilocal mapping from the electron density and reduced gradient to the exchange-correlation energy density. The resulting ML-corrected PBE is immediately applicable to any real molecule, and yields significantly improved heats of formation while preserving the accuracy for other thermochemical and kinetic properties. This work highlights the prospect of combining the power of data-driven ML methods with physics-inspired derivations for reaching the heaven of chemical accuracy.

Exchange-Correlation Energy Densities and Response Potentials: Connection Between Two Definitions and Analytical Model for the Strong-Coupling Limit of a Stretched Bond

2019 ◽  
Author(s):  
S. Giarrusso ◽  
Paola Gori-Giorgi
Keyword(s):  
Density Functional Theory ◽  
Strong Coupling ◽  
Density Functional ◽  
Correlation Energy ◽  
Order Term ◽  
Strong Coupling Limit ◽  
Local Form ◽  
Coupling Constant ◽  
Functional Theory ◽  
Exchange Correlation

We analyze in depth two widely used definitions (from the theory of conditional probablity amplitudes and from the adiabatic connection formalism) of the exchange-correlation energy density and of the response potential of Kohn-Sham density functional theory. We introduce a local form of the coupling-constant-dependent Hohenberg-Kohn functional, showing that the difference between the two definitions is due to a corresponding local first-order term in the coupling constant, which disappears globally (when integrated over all space), but not locally. We also design an analytic representation for the response potential in the strong-coupling limit of density functional theory for a model single stretched bond.<br>

Electronic Structure Benchmark Calculations of Inorganic and Biochemical Carboxylation Reactions

2018 ◽  
Author(s):  
Oscar A. Douglas-Gallardo ◽  
David A. Sáez ◽  
Stefan Vogt-Geisse ◽  
Esteban Vöhringer-Martinez
Keyword(s):  
Electronic Structure ◽  
Chemical Reactions ◽  
Density Functional ◽  
Correlation Energy ◽  
Electronic Energy ◽  
Basis Sets ◽  
Electronic Correlation ◽  
Correct Description ◽  
Carbon Dioxide Co2 ◽  
High Level

<div><div><div><p>Carboxylation reactions represent a very special class of chemical reactions that is characterized by the presence of a carbon dioxide (CO2) molecule as reactive species within its global chemical equation. These reactions work as fundamental gear to accomplish the CO2 fixation and thus to build up more complex molecules through different technological and biochemical processes. In this context, a correct description of the CO2 electronic structure turns out to be crucial to study the chemical and electronic properties associated with this kind of reactions. Here, a sys- tematic study of CO2 electronic structure and its contribution to different carboxylation reaction electronic energies has been carried out by means of several high-level ab-initio post-Hartree Fock (post-HF) and Density Functional Theory (DFT) calculations for a set of biochemistry and inorganic systems. We have found that for a correct description of the CO2 electronic correlation energy it is necessary to include post-CCSD(T) contributions (beyond the gold standard). These high-order excitations are required to properly describe the interactions of the four π-electrons as- sociated with the two degenerated π-molecular orbitals of the CO2 molecule. Likewise, our results show that in some reactions it is possible to obtain accurate reaction electronic energy values with computationally less demanding methods when the error in the electronic correlation energy com- pensates between reactants and products. Furthermore, the provided post-HF reference values allowed to validate different DFT exchange-correlation functionals combined with different basis sets for chemical reactions that are relevant in biochemical CO2 fixing enzymes.</p></div></div></div>

On the Structure of Lead(II) Complexes in Aqueous Solutions. I. Trinuclear Clusters

1995 ◽  
Vol 60 (4) ◽  
pp. 527-536 ◽  
Author(s):  
Martin Breza ◽  
Alena Manová
Keyword(s):  
Quantum Chemistry ◽  
Aqueous Solutions ◽  
Electronic Structures ◽  
Mndo Method ◽  
Model Systems ◽  
Trinuclear Clusters ◽  
The Stability ◽  
Semiempirical Mndo

Using semiempirical MNDO method of quantum chemistry the optimal geometries and corresponding electronic structures of [Pb3(OH)n]6-n model systems as well as of their hydrated [Pb3(OH)n(H2O)8-n]6-n analogues (n = 4, 5) are investigated. The most stable trinuclear lead(II) complexes present in aqueous solutions correspond to cyclo-(μ3-OH)(μ2-OH)3Pb32+, Pb(μ-OH)2Pb(μ-OH)2Pb2+, cyclo-(μ3-OH)2(μ2-OH)3Pb3+, Pb(OH)(μ-OH)2Pb(μ-OH)Pb(OH)+ and Pb(OH)(μ-OH)2Pb(μ-OH)2Pb+ systems. The key role of OH bridges (by vanishing direct Pb-Pb bonds) on the stability of individual isomers is discussed.

Introduction to Relativistic Quantum Chemistry

2007 ◽  
Author(s):  
Kenneth G. Dyall ◽  
Knut Faegri
Keyword(s):  
Dirac Equation ◽  
Quantum Chemistry ◽  
Relativistic Theory ◽  
Density Functional ◽  
Relativistic Quantum ◽  
Relativistic Effects ◽  
Basis Sets ◽  
Spin Orbit ◽  
Approximate Methods ◽  
Nonrelativistic Theory

This book provides an introduction to the essentials of relativistic effects in quantum chemistry, and a reference work that collects all the major developments in this field. It is designed for the graduate student and the computational chemist with a good background in nonrelativistic theory. In addition to explaining the necessary theory in detail, at a level that the non-expert and the student should readily be able to follow, the book discusses the implementation of the theory and practicalities of its use in calculations. After a brief introduction to classical relativity and electromagnetism, the Dirac equation is presented, and its symmetry, atomic solutions, and interpretation are explored. Four-component molecular methods are then developed: self-consistent field theory and the use of basis sets, double-group and time-reversal symmetry, correlation methods, molecular properties, and an overview of relativistic density functional theory. The emphases in this section are on the basics of relativistic theory and how relativistic theory differs from nonrelativistic theory. Approximate methods are treated next, starting with spin separation in the Dirac equation, and proceeding to the Foldy-Wouthuysen, Douglas-Kroll, and related transformations, Breit-Pauli and direct perturbation theory, regular approximations, matrix approximations, and pseudopotential and model potential methods. For each of these approximations, one-electron operators and many-electron methods are developed, spin-free and spin-orbit operators are presented, and the calculation of electric and magnetic properties is discussed. The treatment of spin-orbit effects with correlation rounds off the presentation of approximate methods. The book concludes with a discussion of the qualitative changes in the picture of structure and bonding that arise from the inclusion of relativity.

scholarly journals Band degeneracy enhanced thermoelectric performance in layered oxyselenides by first-principles calculations

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Ning Wang ◽  
Menglu Li ◽  
Haiyan Xiao ◽  
Zhibin Gao ◽  
Zijiang Liu ◽  
...  
Keyword(s):  
Density Functional ◽  
Transport Theory ◽  
Relaxation Times ◽  
Wide Band ◽  
Type Systems ◽  
Model Systems ◽  
Boltzmann Transport ◽  
Seebeck Coefficients ◽  
Boltzmann Transport Theory ◽  
P Type

AbstractBand degeneracy is effective in optimizing the power factors of thermoelectric (TE) materials by enhancing the Seebeck coefficients. In this study, we demonstrate this effect in model systems of layered oxyselenide family by the density functional theory (DFT) combined with semi-classical Boltzmann transport theory. TE transport performance of layered LaCuOSe and BiCuOSe are fully compared. The results show that due to the larger electrical conductivities caused by longer electron relaxation times, the n-type systems show better TE performance than p-type systems for both LaCuOSe and BiCuOSe. Besides, the conduction band degeneracy of LaCuOSe leads to a larger Seebeck coefficient and a higher optimal carrier concentration than n-type BiCuOSe, and thus a higher power factor. The optimal figure of merit (ZT) value of 1.46 for n-type LaCuOSe is 22% larger than that of 1.2 for n-type BiCuOSe. This study highlights the potential of wide band gap material LaCuOSe for highly efficient TE applications, and demonstrates that inducing band degeneracy by cations substitution is an effective way to enhance the TE performance of layered oxyselenides.

scholarly journals Applications of Distributed-Order Fractional Operators: A Review

Entropy ◽  
2021 ◽  
Vol 23 (1) ◽  
pp. 110
Author(s):  
Wei Ding ◽  
Sansit Patnaik ◽  
Sai Sidhardh ◽  
Fabio Semperlotti
Keyword(s):  
Fractional Calculus ◽  
Real World ◽  
Transport Processes ◽  
Model Systems ◽  
Variable Order ◽  
Fractional Operators ◽  
Research Activity ◽  
Road Map ◽  
Real World Applications ◽  
Distributed Order

Distributed-order fractional calculus (DOFC) is a rapidly emerging branch of the broader area of fractional calculus that has important and far-reaching applications for the modeling of complex systems. DOFC generalizes the intrinsic multiscale nature of constant and variable-order fractional operators opening significant opportunities to model systems whose behavior stems from the complex interplay and superposition of nonlocal and memory effects occurring over a multitude of scales. In recent years, a significant amount of studies focusing on mathematical aspects and real-world applications of DOFC have been produced. However, a systematic review of the available literature and of the state-of-the-art of DOFC as it pertains, specifically, to real-world applications is still lacking. This review article is intended to provide the reader a road map to understand the early development of DOFC and the progressive evolution and application to the modeling of complex real-world problems. The review starts by offering a brief introduction to the mathematics of DOFC, including analytical and numerical methods, and it continues providing an extensive overview of the applications of DOFC to fields like viscoelasticity, transport processes, and control theory that have seen most of the research activity to date.

scholarly journals Adsorption and Desorption Mechanisms of Rare Earth Elements (REEs) by Layered Double Hydroxide (LDH) Modified with Chelating Agents

2019 ◽  
Vol 9 (22) ◽  
pp. 4805 ◽  
Author(s):  
Shuang Zhang ◽  
Naoki Kano ◽  
Kenji Mishima ◽  
Hirokazu Okawa
Keyword(s):  
Rare Earth ◽  
Quantum Chemistry ◽  
Rare Earth Elements ◽  
Adsorption Capacity ◽  
Density Functional ◽  
Stable State ◽  
Experimental Result ◽  
Adsorption And Desorption ◽  
Adsorption Affinity ◽  
Quantum Chemistry Calculations

In order to obtain the adsorption mechanism and adsorption structures of Rare Earth Elements (REEs) ions adsorbed onto layered double hydroxides (LDH), the adsorption performance of LDH and ethylenediaminetetraacetic acid (EDTA) intercalated LDH for REEs was investigated by batch experiments and regeneration studies. In addition to adsorption capacity, the partition coefficient (PC) was also evaluated to assess their true performance metrics. The adsorption capacity of LDH increases from 24.9 μg·g−1 to 145 μg·g−1 for Eu, and from 20.8 μg·g−1 to 124 μg·g−1 for La by intercalating EDTA in this work; and PC increases from 45.5 μg·g−1·uM−1 to 834 μg·g−1·uM−1 for Eu, and from 33.6 μg·g−1·μM−1 to 405 μg·g−1·μM−1 for La. Comparison of the data indicates that the adsorption affinity of EDTA-intercalated LDH is better than that of precursor LDH no matter whether the concept of adsorption capacity or that of the PC was used. The prepared adsorbent was characterized by XRD, SEM-EDS and FT-IR techniques. Moreover, quantum chemistry calculations were also performed using the GAUSSIAN09 program package. In this calculation, the molecular locally stable state structures were optimized by density functional theory (DFT). Both the quantum chemistry calculations and the experimental data showed that REEs ions adsorbed by EDTA-intercalated LDH are more stable than those adsorbed by precursor LDH. Furthermore, the calculation results of adsorption and desorption rates show that adsorption rates are larger for Eu(III) than for La(III), which agrees with the experimental result that Eu(III) has a higher adsorption ability under the same conditions. The LDHs synthesized in this work have a high affinity for removing REEs ions.

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