Electron Density

Name: Electron Density | Concepts, Computation and DFT Applications
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Concepts, Computation and DFT Applications

Pratim Kumar Chattaraj Debdutta Chakraborty(Herausgeber*in)

Wiley (Verlag)

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Erschienen am 2. Juli 2024

608 Seiten

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Beschreibung

Discover theoretical, methodological, and applied perspectives on electron density studies and density functional theory

Electron density or the single particle density is a 3D function even for a many-electron system. Electron density contains all information regarding the ground state and also about some excited states of an atom or a molecule. All the properties can be written as functionals of electron density, and the energy attains its minimum value for the true density. It has been used as the basis for a quantum chemical computational method called Density Functional Theory, or DFT, which can be used to determine various properties of molecules. DFT brings out a drastic reduction in computational cost due to its reduced dimensionality. Thus, DFT is considered to be the workhorse for modern computational chemistry, physics as well as materials science.

Electron Density: Concepts, Computation and DFT Applications offers an introduction to the foundations and applications of electron density studies and analysis. Beginning with an overview of major methodological and conceptual issues in electron density, it analyzes DFT and its major successful applications. The result is a state-of-the-art reference for a vital tool in a range of experimental sciences.

Readers will also find:

A balance of fundamentals and applications to facilitate use by both theoretical and computational scientists
Detailed discussion of topics including the Levy-Perdew-Sahni equation, the Kohn Sham Inversion problem, and more
Analysis of DFT applications including the determination of structural, magnetic, and electronic properties

Electron Density: Concepts, Computation and DFT Applications is ideal for academic researchers in quantum, theoretical, and computational chemistry and physics.

Pratim Kumar Chattaraj, PhD, is a distinguished visiting Professor at Birla Institute of Technology Mesra, India. He was an Institute Chair Professor at Indian Institute of Technology Kharagpur, India. He is a Fellow of the World Academy of Sciences, Royal Society of Chemistry, and all three science academies of India, as well as a Sir J.C. Bose National Fellow.

Debdutta Chakraborty, PhD, is an Assistant Professor at Birla Institute of Technology Mesra, India.

Weitere Details

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Inhalt

Cover
Title Page
Copyright
Contents
List of Contributors
Preface
Chapter 1 Levy-Perdew-Sahni Equation and the Kohn-Sham Inversion Problem
1.1 Introduction
1.2 One Equation ⟹
Several Methods
Universal Nature of Different Density-Based Kohn-Sham Inversion Algorithms
1.2.1 Generating Functional S[?] of Density-Based Kohn-Sham Inversion
1.2.2 Condition on Generating Functional S[?]
1.2.3 Examples of Different Generating Functionals
1.2.4 Application to Spherical Systems
1.2.5 Using Random Numbers to do Density-to-Potential Inversion
1.3 General Penalty Method for Density-to-Potential Inversion
1.4 Understanding Connection Between Density and Wavefunction-Based Inversion Methods Using LPS Equation
1.5 Concluding Remarks
Acknowledgments
References
Chapter 2 Electron Density, Density Functional Theory, and Chemical Concepts
2.1 Introduction
2.2 Viewing Chemical Concepts Through a DFT Window
2.3 Electron Fluid, Quantum Fluid Dynamics, Electronic Entropy, and a Local Thermodynamic Picture
2.4 Miscellaneous Offshoots from Electron Density Experience
2.5 Concluding Remarks
Acknowledgments
References
Chapter 3 Local and Nonlocal Descriptors of the Site and Bond Chemical Reactivity of Molecules
3.1 Introduction
3.2 Local and Nonlocal Reactivity Indexes
3.3 Site and Bond Reactivities
3.4 Concluding Remarks
Acknowledgment
References
Chapter 4 Relativistic Treatment of Many-Electron Systems Through DFT in CCG
4.1 Introduction
4.2 Theoretical Framework
4.2.1 Dirac Equation
4.2.2 Relativistic Density Functional Theory: Dirac-Kohn-Sham Method
4.2.3 Decoupling of Dirac Hamiltonian: DKH Methodology
4.2.4 DFT in Cartesian Grid
4.2.4.1 Basic Methodology
4.2.4.2 Hartree Potential in CCG
4.2.4.3 Hartree Fock Exchange Through FCT in CCG
4.2.4.4 Orbital-Dependent Hybrid Functionals via RS-FCT
4.3 Computational Details
4.4 Results and Discussion
4.4.1 One-Electron Atoms
4.4.2 Many-Electron Systems
4.4.2.1 Grid Optimization
4.4.2.2 Ground-State Energy of Atoms and Molecules
4.4.3 Application to Highly Charged Ions: He- and Li-Isoelectronic Series
4.5 Future and Outlook
Acknowledgement
References
Chapter 5 Relativistic Reduced Density Matrices: Properties and Applications
5.1 Introduction
5.2 Relativistic One-Body Reduced Density Matrix
5.3 Properties of Relativistic 1-RDM
5.3.1 Natural Spinors: An Efficient Framework for Low-cost Calculations
5.3.1.1 Correlation Energy
5.3.1.2 Bond Length and Harmonic Vibrational Frequency
5.3.2 Natural Spinors as an Interpretive Tool
5.4 Concluding Remarks
Acknowledgments
References
Chapter 6 Many-Body Multi-Configurational Calculation Using Coulomb Green's Function
6.1 Introduction
6.2 Theoretical Development
6.2.1 Presence of Magnetic Field
6.2.1.1 3D Electron Gas Model
6.2.1.2 2D Electron Gas Model
6.2.1.3 3D Exciton Model
6.2.1.4 2D Exciton Model
6.2.2 Absence of Magnetic Field
6.2.2.1 3D He-Isoelectronic Ions
6.2.2.2 2D He-Isoelectronic Ions
6.2.2.3 Energy Calculation Through Perturbation
6.2.2.4 Current Density of 2-e System
6.3 Results and Discussion
6.3.1 3D Interacting Electron Gas
6.3.2 2D Interacting Electron Gas
6.3.3 3D Exciton Complexes
6.3.4 2D Exciton Complexes
6.3.5 3D He-Isoelectronic Species
6.3.5.1 Analysis of E0(2) of He-Isoelectronic Ions
6.3.5.2 Analysis of E0(3) of He-Isoelectronic Ions
6.3.6 2D He-Isoelectronic Species
6.4 Concluding Remarks
Acknowledgments
References
Chapter 7 Excited State Electronic Structure?-?Effect of Environment
7.1 Introduction
7.2 Methodology
7.2.1 Quantum Mechanical Methods
7.2.1.1 Time-Dependent Density Functional Theory
7.2.1.2 Active Space-Based Methods
7.2.1.3 Configuration Interaction-Based Approaches
7.2.1.4 Equation of Motion Coupled Cluster
7.2.2 Molecular Mechanical Methods
7.2.2.1 ONIOM
7.2.2.2 Mechanical Embedding
7.2.2.3 Electronic Embedding
7.2.2.4 Polarizable Embedding
7.3 Representative Examples
7.3.1 Photo-Isomerization of Rhodopsin
7.3.2 DNA-Base Excited States in Solution
7.3.3 Green Fluorescent Proteins
7.4 Conclusion
Acknowledgement
References
Chapter 8 Electron Density in the Multiscale Treatment of Biomolecules
8.1 Introduction
8.2 Theoretical Background
8.2.1 Hybrid Quantum Mechanics-Molecular Mechanics Approach
8.3 Polarizable Density Embedding
8.4 Multi-Scale QM/MM with Extremely Localized Molecular Orbitals
8.5 Multiple Active Zones in QM/MM Modelling
8.6 Reactivity Descriptors with QM/MM Modeling
8.7 Treatment of Hydrogen Bonding with QM/MM
8.8 Quantum Refinement of Crystal Structure with QM/MM
8.9 Concluding Remarks
Acknowledgments
References
Chapter 9 Subsystem Communications and Electron Correlation
9.1 Introduction
9.2 Discrete and Local Probability Networks in Molecular Bond Systems
9.3 Bond Descriptors of Molecular Communication Channels
9.4 Hartree-Fock Communications and Fermi Correlation
9.5 Communication Partitioning of Two-Electron Probabilities
9.6 Communications in Interacting Subsystems
9.7 Illustrative Application to Reaction HSAB Principle
9.8 Conclusion
References
Chapter 10 Impacts of External Electric Fields on Aromaticity and Acidity for Benzoic Acid and Derivatives: Directionality, Additivity, and More
10.1 Introduction
10.2 Methodology
10.3 Computational Details
10.4 Results and Discussion
10.5 Conclusions
Acknowledgments
References
Chapter 11 A Divergence and Rotational Component in Chemical Potential During Reactions
11.1 Introduction
11.2 Chemical Descriptors
11.3 Charge and Energy Exchange
11.4 Fitness Landscape Diagrams
11.5 Chemical Reactions
11.6 Examining the Charge Exchange
11.6.1 Path p??(?) and Charge Exchange
11.6.2 Systematic Changes Depending on the Starting Points on p??(?)
11.6.3 Specific Solutions Using a p?? Path
11.7 Significance and Applications
11.8 Conclusions
Acknowledgments
References
Chapter 12 Deep Learning of Electron Density for Predicting Energies: The Case of Boron Clusters
12.1 Introduction
12.2 Deep Learning of Electron Density
12.3 Neural Networks for Neutral Boron Clusters
12.4 Concluding Remarks
Acknowledgements
References
Chapter 13 Density-Based Description of Molecular Polarizability for Complex Systems
13.1 Introduction
13.2 Methodology and Computations
13.2.1 Information-Theoretic Approach (ITA) Quantities
13.2.2 The GEBF Method
13.3 Results and Discussion
13.4 Conclusions and Perspectives
Acknowledgment
References
Chapter 14 Conceptual Density Functional Theory-Based Study of Pure and TMs-Doped CdX (X =
S, Se, Te
TMs =
Cu, Ag, and Au) Nano Cluster for Water Splitting and Spintronic Applications
14.1 Introduction
14.2 Methodology
14.3 Results and Discussion
14.3.1 Electronic Properties and CDFT-Based Descriptors
14.4 Conclusion
Acknowledgments
Funding
References
Chapter 15 "Phylogenetic" Screening of External Potential Related Response Functions
15.1 Introduction
15.2 Alchemical Approach
15.3 The "Family Tree"
15.4 First-order Sensitivities
15.5 Second-Order Sensitivities
15.5.1 Electric Dipole Polarizability
15.5.2 "Polarizability Potential" - Local Polarization
15.6 Alchemical Hardness
15.6.1 Local Alchemical Hardness
15.7 Alchemical Characteristic Radius
15.8 Linear Response Function
15.9 Conclusions
References
Chapter 16 On the Nature of Catastrophe Unfoldings Along the Diels-Alder Cycloaddition Pathway
16.1 Introduction
16.2 Molecular Symmetry and Elementary Catastrophe Unfoldings
16.2.1 The Case of Normal- and Inverse-Electron-Demand Diels-Alder Reactions
16.2.2 The C C Bond Breaking in a High Symmetry Environment
16.2.3 The Photochemical Ring Opening of 1,3-Cyclohexadiene
16.3 Concluding Remarks
Acknowledgments
References
Chapter 17 Designing Principles for Ultrashort H?H Nonbonded Contacts and Ultralong C C Bonds
17.1 Introduction
17.1.1 The Art of the Chemical Bond
17.1.2 Designing and Decoding Chemical Bond
17.2 Governing Factors for Ultrashort H?H Nonbonded Contacts
17.2.1 London Dispersion Interaction
17.2.2 Polarity and Charge Separation
17.2.3 Conformations and Orientations
17.2.4 Iron Maiden Effect
17.3 Elongation Strategies for C C Bonds
17.3.1 Steric Crowding Effect
17.3.2 Core-Shell Strategy and Scissor Effect
17.3.3 Negative Hyperconjugation Effect
17.4 Concluding Remarks
Acknowledgments
References
Chapter 18 Accurate Determination of Materials Properties: Role of Electron Density
18.1 Introduction
18.2 Materials Properties: Structure and Electronic Properties
18.2.1 Classification of Materials
18.2.2 Electronic Properties of Materials
18.3 Molecules to Materials, Essential Role of Electron Density
18.3.1 The Density Functional Theory (DFT)
18.3.2 The Hohenberg-Kohn Theorems
18.3.3 The Hohenberg-Kohn Variational Theorems
18.3.4 The Kohn-Sham (KS) Method
18.3.5 Local Density Approximation
18.3.6 Generalized Gradient Approximation
18.3.7 Meta-GGA and Hybrid Functionals
18.4 Further Approximations in DFT
18.4.1 The Density Functional Tight-Binding Theory
18.4.2 Self-Consistent-Charge Density-Functional Tight-Binding (SCC-DFTB) Method
18.5 Solar Cell Materials, Interfacial Charge Transfer Phenomena
18.5.1 The Time-Dependent Density Functional Theory
18.5.2 TDDFT and Linear Response
18.5.3 Excitation Energy and Excited State Properties
18.5.3.1 Exciton Binding Energy
18.5.3.2 Reorganization Energy
18.5.3.3 The Rates of Charge Transfer and Recombination Processes
18.6 Concluding Remarks
Acknowledgements
References
Chapter 19 A Conceptual DFT Analysis of Mechanochemical Processes
19.1 Introduction
19.2 Theoretical Background
19.2.1 The Constrained Geometries Simulate External Force (COGEF)
19.2.2 External Force is Explicitly Included (EFEI)
19.3 Results and Discussions
19.3.1 General Consideration
19.3.2 Constrained Geometries Simulate External Force (COGEF)
19.3.2.1 Mechanochemical CDFT Reactivity Descriptors and Their Application to Diatomic Molecules
19.3.3 Understanding Ball Milling Mechanochemical Processes with DFT Calculations and Microkinetic Modeling
19.3.4 Explicit Force
19.3.5 Dynamical Aspect of Mechanochemistry
19.4 Concluding Remarks
Acknowledgments
References
Chapter 20 Molecular Electron Density and Electrostatic Potential and Their Applications
20.1 Introduction
20.2 Topography Analysis of Scalar Fields
20.2.1 Molecular Electron Density
20.2.2 Topology of Molecular Electrostatic Potential
20.3 Usefulness of MESP and MED Analysis for Understanding Weak Interactions
20.3.1 MESP and MED Topography Analysis of Oligomers of Conjugated Polymers and their Interaction with PCBM Acceptors
20.3.2 Interaction of Small Molecules with Models of Single-Walled Carbon Nanotube and Graphene
20.3.2.1 Interaction of Nucleobases with Carbon Nanomaterials
20.3.2.2 Interaction of Chlorobenzene with Carbon Nanomaterials
20.3.2.3 Interaction of Carbohydrates with Carbon Nanomaterials
20.4 Conclusion
Acknowledgment
Conflict of Interest
References
Chapter 21 Origin and Nature of Pancake Bonding Interactions: A Density Functional Theory and Information-Theoretic Approach Study
21.1 Introduction
21.2 Methodology
21.2.1 Interaction Energy and Its Components in DFT
21.2.2 Information-Theoretic Approach Quantities
21.3 Computational Details
21.4 Results and Discussion
21.5 Concluding Remarks
Acknowledgment
References
Chapter 22 Electron Spin Density and Magnetism in Organic Diradicals
22.1 Introduction
22.2 Quantitative Relation Between Magnetic Exchange Coupling Constant and Spin Density
22.3 Spin Density Alternation
22.3.1 Phenyl Nitroxide
22.3.2 Methoxy Phenyl Nitroxide
22.3.3 Phenyl Nitroxide Coupled Through Methylene
22.3.4 Spin Density of Radical Systems
22.3.5 Distance Dependence of Spin Density
22.3.6 Geometry Dependence of Spin Density
22.3.7 Dependence on Connecting Atoms
22.4 Concluding Remarks
Acknowledgements
References
Chapter 23 Stabilization of Boron and Carbon Clusters with Transition Metal Coordination - An Electron Density and DFT Study
23.1 Introduction
23.2 Computational Details
23.3 Results and Discussion
23.3.1 Structures and Stability of Metal Atom Encapsulated Boron Clusters
23.3.2 Bonding Characteristics in M@B18, M@B20, M@B22, and M@B24 Clusters
23.3.3 Structures and Stability of Carbon Rings
23.3.4 Bonding Characteristics in Carbon Rings
23.4 Conclusions
Acknowledgments
References
Chapter 24 DFT-Based Computational Approach for Structure and Design of Materials: The Unfinished Story
24.1 Introduction
24.2 Different Frameworks of DFT
24.2.1 Kohn Sham Density Functional Theory (KS-DFT)
24.2.2 Time-Dependent Density Functional Theory (TD-DFT)
24.2.3 Linear Response Time-Dependent Density-Functional Theory (LR-TDDFT)
24.2.4 Discontinuous Galerkin Density Functional Theory (DGDFT)
24.3 DFT Implemented Computational Packages
24.4 DFT as Backbone of Electronic Structure Calculations
24.4.1 Design of 2D Nano-Materials
24.4.2 Non-covalent Interactions and Crystal Packing
24.4.3 Designing of Organic Solar Cell
24.5 Concluding Remarks
Acknowledgment
References
Chapter 25 Structure, Stability and Bonding in Ligand Stabilized C3 Species
25.1 Introduction
25.2 Computational Details
25.3 Structures and Energetics
25.4 Bonding
25.5 Conclusions
Acknowledgements
References
Chapter 26 The Role of Electronic Activity Toward the Analysis of Chemical Reactions
26.1 Introduction
26.2 Theoretical Backgrounds and Computational Details
26.3 Results and Discussions
26.3.1 Bimolecular Nucleophilic Substitution (SN2) Reaction
26.3.2 Alkylation of Zintl Cluster
26.3.3 Proton Transfer Reaction
26.3.4 Water Activation by Frustrated Lewis Pairs (FLPs)
26.4 Concluding Remarks
Acknowledgments
References
Chapter 27 Prediction of Radiative Efficiencies and Global Warming Potential of Hydrofluoroethers and Fluorinated Esters Using Various DFT Functionals
27.1 Introduction
27.2 Computational Methodology
27.3 RE and GWP Calculation Methodology
27.4 Results and Discussions
27.4.1 (Difluoromethoxy)trifluoromethane (CF3OCHF2)
27.4.2 Difluoro(methoxy)methane (CH3OCHF2)
27.4.3 Trifluoro(methoxy)methane (CF3OCH3)
27.4.4 Bis(2,2,2-trifluoroethyl)ether (CF3CH2OCH2CF3)
27.4.5 1,1,1,2,2-Pentafluoro-2-Methoxyethane (CF3CF2OCH3)
27.4.6 Fluoro(fluoromethoxy)methane (CH2FOCH2F)
27.4.7 Methyl 2,2,2-Difluoroacetate (CHF2C(O)OCH3)
27.4.8 Ethyl 2,2,2-Trifluoroacetate (CF3C(O)OCH2CH3)
27.4.9 2,2,2-Trifluoroethyl 2,2,2-trifluoroacetate (CF3C(O)OCH2CF3)
27.4.10 1,1-Difluoroethyl Carbonofluoridate (FC(O)OCF2CH3)
27.4.11 Methyl 2,2,2-trifluoroacetate (CF3C(O)OCH3)
27.5 Concluding Remarks
Acknowledgment
References
Chapter 28 Density Functional Theory-Based Study on Some Natural Products
28.1 Introduction
28.2 Computational Details
28.3 Results and Discussion
28.3.1 Geometrical Properties
28.3.2 Vibrational Properties
28.3.2.1 O-H Vibration
28.3.2.2 C-H Vibration
28.3.2.3 C-C Vibration
28.3.2.4 C O Vibration
28.3.3 HOMO-LUMO and MESP Plots
28.3.4 Chemical Reactivity
28.4 Conclusion
Acknowledgments
References
Index
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