{"product_id":"electron-density-isbn-9781394217625","title":"Electron Density","description":"\u003cp\u003e\u003cb\u003eDiscover theoretical, methodological, and applied perspectives on electron density studies and density functional theory\u003c\/b\u003e \u003c\/p\u003e\u003cp\u003eElectron 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. \u003c\/p\u003e\u003cp\u003e\u003ci\u003eElectron Density: Concepts, Computation and DFT Applications\u003c\/i\u003e 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. \u003c\/p\u003e\u003cp\u003eReaders will also find: \u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eA balance of fundamentals and applications to facilitate use by both theoretical and computational scientists \u003c\/li\u003e\n\u003cli\u003eDetailed discussion of topics including the Levy-Perdew-Sahni equation, the Kohn Sham Inversion problem, and more \u003c\/li\u003e\n\u003cli\u003eAnalysis of DFT applications including the determination of structural, magnetic, and electronic properties\u003c\/li\u003e\n\u003c\/ul\u003e \u003cp\u003e\u003ci\u003eElectron Density: Concepts, Computation and DFT Applications \u003c\/i\u003eis ideal for academic researchers in quantum, theoretical, and computational chemistry and physics. \u003c\/p\u003e\u003cp\u003eList of Contributors xvii\u003c\/p\u003e \u003cp\u003ePreface xxv\u003cbr\u003e\u003cb\u003e\u003cbr\u003e1 Levy–Perdew–Sahni Equation and the Kohn–Sham Inversion Problem 1\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eAshish Kumar and Manoj K. Harbola\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e1.1 Introduction 1\u003c\/p\u003e \u003cp\u003e1.2 One Equation ⟹ Several Methods; Universal Nature of Different Density-Based Kohn–Sham Inversion Algorithms 2\u003c\/p\u003e \u003cp\u003e1.2.1 Generating Functional S[ρ] of Density-Based Kohn–Sham Inversion 2\u003c\/p\u003e \u003cp\u003e1.2.2 Condition on Generating Functional S[ρ] 4\u003c\/p\u003e \u003cp\u003e1.2.3 Examples of Different Generating Functionals 5\u003c\/p\u003e \u003cp\u003e1.2.4 Application to Spherical Systems 7\u003c\/p\u003e \u003cp\u003e1.2.5 Using Random Numbers to do Density-to-Potential Inversion 10\u003c\/p\u003e \u003cp\u003e1.3 General Penalty Method for Density-to-Potential Inversion 12\u003c\/p\u003e \u003cp\u003e1.4 Understanding Connection Between Density and Wavefunction-Based Inversion Methods Using LPS Equation 16\u003c\/p\u003e \u003cp\u003e1.5 Concluding Remarks 19\u003c\/p\u003e \u003cp\u003eAcknowledgments 19\u003c\/p\u003e \u003cp\u003eReferences 20\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Electron Density, Density Functional Theory, and Chemical Concepts 27\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eSwapan K. Ghosh\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e2.1 Introduction 27\u003c\/p\u003e \u003cp\u003e2.2 Viewing Chemical Concepts Through a DFT Window 27\u003c\/p\u003e \u003cp\u003e2.3 Electron Fluid, Quantum Fluid Dynamics, Electronic Entropy, and a Local Thermodynamic Picture 30\u003c\/p\u003e \u003cp\u003e2.4 Miscellaneous Offshoots from Electron Density Experience 31\u003c\/p\u003e \u003cp\u003e2.5 Concluding Remarks 31\u003c\/p\u003e \u003cp\u003eAcknowledgments 32\u003c\/p\u003e \u003cp\u003eReferences 32\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Local and Nonlocal Descriptors of the Site and Bond Chemical Reactivity of Molecules 35\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eJosé L. Gázquez, Paulino Zerón, Maurizio A. Pantoja-Hernández and Marco Franco-Pérez\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e3.1 Introduction 35\u003c\/p\u003e \u003cp\u003e3.2 Local and Nonlocal Reactivity Indexes 38\u003c\/p\u003e \u003cp\u003e3.3 Site and Bond Reactivities 42\u003c\/p\u003e \u003cp\u003e3.4 Concluding Remarks 46\u003c\/p\u003e \u003cp\u003eAcknowledgment 47\u003c\/p\u003e \u003cp\u003eReferences 47\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Relativistic Treatment of Many-Electron Systems Through DFT in CCG 53\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eShamik Chanda and Amlan K. Roy\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e4.1 Introduction 53\u003c\/p\u003e \u003cp\u003e4.2 Theoretical Framework 56\u003c\/p\u003e \u003cp\u003e4.2.1 Dirac Equation 56\u003c\/p\u003e \u003cp\u003e4.2.2 Relativistic Density Functional Theory: Dirac–Kohn–Sham Method 58\u003c\/p\u003e \u003cp\u003e4.2.3 Decoupling of Dirac Hamiltonian: DKH Methodology 60\u003c\/p\u003e \u003cp\u003e4.2.4 DFT in Cartesian Grid 62\u003c\/p\u003e \u003cp\u003e4.2.4.1 Basic Methodology 62\u003c\/p\u003e \u003cp\u003e4.2.4.2 Hartree Potential in CCG 63\u003c\/p\u003e \u003cp\u003e4.2.4.3 Hartree Fock Exchange Through FCT in CCG 65\u003c\/p\u003e \u003cp\u003e4.2.4.4 Orbital-Dependent Hybrid Functionals via RS-FCT 65\u003c\/p\u003e \u003cp\u003e4.3 Computational Details 66\u003c\/p\u003e \u003cp\u003e4.4 Results and Discussion 67\u003c\/p\u003e \u003cp\u003e4.4.1 One-Electron Atoms 67\u003c\/p\u003e \u003cp\u003e4.4.2 Many-Electron Systems 68\u003c\/p\u003e \u003cp\u003e4.4.2.1 Grid Optimization 68\u003c\/p\u003e \u003cp\u003e4.4.2.2 Ground-State Energy of Atoms and Molecules 70\u003c\/p\u003e \u003cp\u003e4.4.3 Application to Highly Charged Ions: He- and Li-Isoelectronic Series 71\u003c\/p\u003e \u003cp\u003e4.5 Future and Outlook 74\u003c\/p\u003e \u003cp\u003eAcknowledgement 76\u003c\/p\u003e \u003cp\u003eReferences 76\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Relativistic Reduced Density Matrices: Properties and Applications 83\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eSomesh Chamoli, Malaya K. Nayak and Achintya Kumar Dutta\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e5.1 Introduction 83\u003c\/p\u003e \u003cp\u003e5.2 Relativistic One-Body Reduced Density Matrix 84\u003c\/p\u003e \u003cp\u003e5.3 Properties of Relativistic 1-RDM 85\u003c\/p\u003e \u003cp\u003e5.3.1 Natural Spinors: An Efficient Framework for Low-cost Calculations 87\u003c\/p\u003e \u003cp\u003e5.3.1.1 Correlation Energy 88\u003c\/p\u003e \u003cp\u003e5.3.1.2 Bond Length and Harmonic Vibrational Frequency 90\u003c\/p\u003e \u003cp\u003e5.3.2 Natural Spinors as an Interpretive Tool 93\u003c\/p\u003e \u003cp\u003e5.4 Concluding Remarks 93\u003c\/p\u003e \u003cp\u003eAcknowledgments 93\u003c\/p\u003e \u003cp\u003eReferences 94\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Many-Body Multi-Configurational Calculation Using Coulomb Green’s Function 97\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eBharti Kapil, Shivalika Sharma, Priyanka Aggarwal, Harsimran Kaur, Sunny Singh and Ram Kuntal Hazra\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e6.1 Introduction 97\u003c\/p\u003e \u003cp\u003e6.2 Theoretical Development 98\u003c\/p\u003e \u003cp\u003e6.2.1 Presence of Magnetic Field 99\u003c\/p\u003e \u003cp\u003e6.2.1.1 3D Electron Gas Model 99\u003c\/p\u003e \u003cp\u003e6.2.1.2 2D Electron Gas Model 103\u003c\/p\u003e \u003cp\u003e6.2.1.3 3D Exciton Model 107\u003c\/p\u003e \u003cp\u003e6.2.1.4 2D Exciton Model 109\u003c\/p\u003e \u003cp\u003e6.2.2 Absence of Magnetic Field 114\u003c\/p\u003e \u003cp\u003e6.2.2.1 3D He-Isoelectronic Ions 114\u003c\/p\u003e \u003cp\u003e6.2.2.2 2D He-Isoelectronic Ions 119\u003c\/p\u003e \u003cp\u003e6.2.2.3 Energy Calculation Through Perturbation 122\u003c\/p\u003e \u003cp\u003e6.2.2.4 Current Density of 2-e System 123\u003c\/p\u003e \u003cp\u003e6.3 Results and Discussion 123\u003c\/p\u003e \u003cp\u003e6.3.1 3D Interacting Electron Gas 123\u003c\/p\u003e \u003cp\u003e6.3.2 2D Interacting Electron Gas 125\u003c\/p\u003e \u003cp\u003e6.3.3 3D Exciton Complexes 126\u003c\/p\u003e \u003cp\u003e6.3.4 2D Exciton Complexes 127\u003c\/p\u003e \u003cp\u003e6.3.5 3D He-Isoelectronic Species 128\u003c\/p\u003e \u003cp\u003e6.3.5.1 Analysis of E\u003csup\u003e(2)\u003c\/sup\u003e\u003csub\u003e0\u003c\/sub\u003e of He-Isoelectronic Ions 129\u003c\/p\u003e \u003cp\u003e6.3.5.2 Analysis of E\u003csup\u003e(3)\u003c\/sup\u003e\u003csub\u003e0\u003c\/sub\u003e of He-Isoelectronic Ions 129\u003c\/p\u003e \u003cp\u003e6.3.6 2D He-Isoelectronic Species 130\u003c\/p\u003e \u003cp\u003e6.4 Concluding Remarks 131\u003c\/p\u003e \u003cp\u003eAcknowledgments 131\u003c\/p\u003e \u003cp\u003e6.A Standard Equations and Integrals 132\u003c\/p\u003e \u003cp\u003eReferences 133\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Excited State Electronic Structure – Effect of Environment 137\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eSupriyo Santra and Debashree Ghosh\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e7.1 Introduction 137\u003c\/p\u003e \u003cp\u003e7.2 Methodology 138\u003c\/p\u003e \u003cp\u003e7.2.1 Quantum Mechanical Methods 138\u003c\/p\u003e \u003cp\u003e7.2.1.1 Time-Dependent Density Functional Theory 138\u003c\/p\u003e \u003cp\u003e7.2.1.2 Active Space-Based Methods 138\u003c\/p\u003e \u003cp\u003e7.2.1.3 Configuration Interaction-Based Approaches 139\u003c\/p\u003e \u003cp\u003e7.2.1.4 Equation of Motion Coupled Cluster 140\u003c\/p\u003e \u003cp\u003e7.2.2 Molecular Mechanical Methods 140\u003c\/p\u003e \u003cp\u003e7.2.2.1 Oniom 141\u003c\/p\u003e \u003cp\u003e7.2.2.2 Mechanical Embedding 141\u003c\/p\u003e \u003cp\u003e7.2.2.3 Electronic Embedding 142\u003c\/p\u003e \u003cp\u003e7.2.2.4 Polarizable Embedding 142\u003c\/p\u003e \u003cp\u003e7.3 Representative Examples 143\u003c\/p\u003e \u003cp\u003e7.3.1 Photo-Isomerization of Rhodopsin 143\u003c\/p\u003e \u003cp\u003e7.3.2 DNA-Base Excited States in Solution 143\u003c\/p\u003e \u003cp\u003e7.3.3 Green Fluorescent Proteins 145\u003c\/p\u003e \u003cp\u003e7.4 Conclusion 146\u003c\/p\u003e \u003cp\u003eAcknowledgement 146\u003c\/p\u003e \u003cp\u003eReferences 146\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Electron Density in the Multiscale Treatment of Biomolecules 149\u003cbr\u003e\u003c\/b\u003e\u003ci\u003eSoumyajit Karmakar, Sunita Muduli, Atanuka Paul, and Sabyashachi Mishra\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e8.1 Introduction 149\u003c\/p\u003e \u003cp\u003e8.2 Theoretical Background 150\u003c\/p\u003e \u003cp\u003e8.2.1 Hybrid Quantum Mechanics–Molecular Mechanics Approach 152\u003c\/p\u003e \u003cp\u003e8.3 Polarizable Density Embedding 155\u003c\/p\u003e \u003cp\u003e8.4 Multi-Scale QM\/MM with Extremely Localized Molecular Orbitals 157\u003c\/p\u003e \u003cp\u003e8.5 Multiple Active Zones in QM\/MM Modelling 159\u003c\/p\u003e \u003cp\u003e8.6 Reactivity Descriptors with QM\/MM Modeling 161\u003c\/p\u003e \u003cp\u003e8.7 Treatment of Hydrogen Bonding with QM\/MM 163\u003c\/p\u003e \u003cp\u003e8.8 Quantum Refinement of Crystal Structure with QM\/MM 164\u003c\/p\u003e \u003cp\u003e8.9 Concluding Remarks 166\u003c\/p\u003e \u003cp\u003eAcknowledgments 167\u003c\/p\u003e \u003cp\u003eReferences 167\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Subsystem Communications and Electron Correlation 173\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eRoman F. Nalewajski\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e9.1 Introduction 173\u003c\/p\u003e \u003cp\u003e9.2 Discrete and Local Probability Networks in Molecular Bond Systems 174\u003c\/p\u003e \u003cp\u003e9.3 Bond Descriptors of Molecular Communication Channels 177\u003c\/p\u003e \u003cp\u003e9.4 Hartree–Fock Communications and Fermi Correlation 179\u003c\/p\u003e \u003cp\u003e9.5 Communication Partitioning of Two-Electron Probabilities 181\u003c\/p\u003e \u003cp\u003e9.6 Communications in Interacting Subsystems 184\u003c\/p\u003e \u003cp\u003e9.7 Illustrative Application to Reaction HSAB Principle 188\u003c\/p\u003e \u003cp\u003e9.8 Conclusion 191\u003c\/p\u003e \u003cp\u003eReferences 192\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Impacts of External Electric Fields on Aromaticity and Acidity for Benzoic Acid and Derivatives: Directionality, Additivity, and More 199\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eMeng Li, Xinjie Wan, Xin He, Chunying Rong, Dongbo Zhao, and Shubin Liu\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e10.1 Introduction 199\u003c\/p\u003e \u003cp\u003e10.2 Methodology 199\u003c\/p\u003e \u003cp\u003e10.3 Computational Details 202\u003c\/p\u003e \u003cp\u003e10.4 Results and Discussion 203\u003c\/p\u003e \u003cp\u003e10.5 Conclusions 213\u003c\/p\u003e \u003cp\u003eAcknowledgments 213\u003c\/p\u003e \u003cp\u003eReferences 213\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 A Divergence and Rotational Component in Chemical Potential During Reactions 217\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eJean-Louis Vigneresse\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e11.1 Introduction 217\u003c\/p\u003e \u003cp\u003e11.2 Chemical Descriptors 218\u003c\/p\u003e \u003cp\u003e11.3 Charge and Energy Exchange 219\u003c\/p\u003e \u003cp\u003e11.4 Fitness Landscape Diagrams 219\u003c\/p\u003e \u003cp\u003e11.5 Chemical Reactions 220\u003c\/p\u003e \u003cp\u003e11.6 Examining the Charge Exchange 221\u003c\/p\u003e \u003cp\u003e11.6.1 Path p\u003csub\u003eχη\u003c\/sub\u003e(ζ) and Charge Exchange 221\u003c\/p\u003e \u003cp\u003e11.6.2 Systematic Changes Depending on the Starting Points on p\u003csub\u003eχη\u003c\/sub\u003e(ζ) 223\u003c\/p\u003e \u003cp\u003e11.6.3 Specific Solutions Using a p\u003csub\u003eηω\u003c\/sub\u003e Path 224\u003c\/p\u003e \u003cp\u003e11.7 Significance and Applications 225\u003c\/p\u003e \u003cp\u003e11.8 Conclusions 227\u003c\/p\u003e \u003cp\u003eAcknowledgments 227\u003c\/p\u003e \u003cp\u003eReferences 228\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 Deep Learning of Electron Density for Predicting Energies: The Case of Boron Clusters 231\u003cbr\u003e \u003c\/b\u003e\u003ci\u003ePinaki Saha and Minh Tho Nguyen\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e12.1 Introduction 231\u003c\/p\u003e \u003cp\u003e12.2 Deep Learning of Electron Density 233\u003c\/p\u003e \u003cp\u003e12.3 Neural Networks for Neutral Boron Clusters 235\u003c\/p\u003e \u003cp\u003e12.4 Concluding Remarks 242\u003c\/p\u003e \u003cp\u003eAcknowledgements 243\u003c\/p\u003e \u003cp\u003eReferences 243\u003c\/p\u003e \u003cp\u003e\u003cb\u003e13 Density-Based Description of Molecular Polarizability for Complex Systems 247\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eDongbo Zhao, Xin He, Paul W. Ayers and Shubin Liu\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e13.1 Introduction 247\u003c\/p\u003e \u003cp\u003e13.2 Methodology and Computations 248\u003c\/p\u003e \u003cp\u003e13.2.1 Information-Theoretic Approach (ITA) Quantities 248\u003c\/p\u003e \u003cp\u003e13.2.2 The GEBF Method 249\u003c\/p\u003e \u003cp\u003e13.3 Results and Discussion 250\u003c\/p\u003e \u003cp\u003e13.4 Conclusions and Perspectives 260\u003c\/p\u003e \u003cp\u003eAcknowledgment 261\u003c\/p\u003e \u003cp\u003eReferences 261\u003c\/p\u003e \u003cp\u003e\u003cb\u003e14 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 265\u003cbr\u003e \u003c\/b\u003e\u003ci\u003ePrabhat Ranjan, Preeti Nanda, Ramon Carbó-Dorca, and Tanmoy Chakraborty\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e14.1 Introduction 265\u003c\/p\u003e \u003cp\u003e14.2 Methodology 266\u003c\/p\u003e \u003cp\u003e14.3 Results and Discussion 267\u003c\/p\u003e \u003cp\u003e14.3.1 Electronic Properties and CDFT-Based Descriptors 267\u003c\/p\u003e \u003cp\u003e14.4 Conclusion 275\u003c\/p\u003e \u003cp\u003eAcknowledgments 275\u003c\/p\u003e \u003cp\u003eFunding 276\u003c\/p\u003e \u003cp\u003eReferences 276\u003c\/p\u003e \u003cp\u003e\u003cb\u003e15 “Phylogenetic” Screening of External Potential Related Response Functions 279\u003cbr\u003e\u003c\/b\u003e\u003ci\u003ePaweł Szarek\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e15.1 Introduction 279\u003c\/p\u003e \u003cp\u003e15.2 Alchemical Approach 281\u003c\/p\u003e \u003cp\u003e15.3 The “Family Tree” 281\u003c\/p\u003e \u003cp\u003e15.4 First-order Sensitivities 282\u003c\/p\u003e \u003cp\u003e15.5 Second-Order Sensitivities 283\u003c\/p\u003e \u003cp\u003e15.5.1 Electric Dipole Polarizability 283\u003c\/p\u003e \u003cp\u003e15.5.2 “Polarizability Potential” – Local Polarization 284\u003c\/p\u003e \u003cp\u003e15.6 Alchemical Hardness 285\u003c\/p\u003e \u003cp\u003e15.6.1 Local Alchemical Hardness 287\u003c\/p\u003e \u003cp\u003e15.7 Alchemical Characteristic Radius 289\u003c\/p\u003e \u003cp\u003e15.8 Linear Response Function 291\u003c\/p\u003e \u003cp\u003e15.9 Conclusions 292\u003c\/p\u003e \u003cp\u003eReferences 293\u003c\/p\u003e \u003cp\u003e\u003cb\u003e16 On the Nature of Catastrophe Unfoldings Along the Diels–Alder Cycloaddition Pathway 299\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eLeandro Ayarde-Henríquez, Cristian Guerra, Mario Duque-Noreña, Patricia Pérez, Elizabeth Rincón and Eduardo Chamorro\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e16.1 Introduction 299\u003c\/p\u003e \u003cp\u003e16.2 Molecular Symmetry and Elementary Catastrophe Unfoldings 301\u003c\/p\u003e \u003cp\u003e16.2.1 The Case of Normal- and Inverse-Electron-Demand Diels–Alder Reactions 301\u003c\/p\u003e \u003cp\u003e16.2.2 The C—C Bond Breaking in a High Symmetry Environment 304\u003c\/p\u003e \u003cp\u003e16.2.3 The Photochemical Ring Opening of 1,3-Cyclohexadiene 305\u003c\/p\u003e \u003cp\u003e16.3 Concluding Remarks 306\u003c\/p\u003e \u003cp\u003eAcknowledgments 307\u003c\/p\u003e \u003cp\u003eReferences 307\u003c\/p\u003e \u003cp\u003e\u003cb\u003e17 Designing Principles for Ultrashort H···H Nonbonded Contacts and Ultralong C—C Bonds 313\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eNilangshu Mandal and Ayan Datta\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e17.1 Introduction 313\u003c\/p\u003e \u003cp\u003e17.1.1 The Art of the Chemical Bond 314\u003c\/p\u003e \u003cp\u003e17.1.2 Designing and Decoding Chemical Bond 314\u003c\/p\u003e \u003cp\u003e17.2 Governing Factors for Ultrashort H···H Nonbonded Contacts 315\u003c\/p\u003e \u003cp\u003e17.2.1 London Dispersion Interaction 316\u003c\/p\u003e \u003cp\u003e17.2.2 Polarity and Charge Separation 317\u003c\/p\u003e \u003cp\u003e17.2.3 Conformations and Orientations 317\u003c\/p\u003e \u003cp\u003e17.2.4 Iron Maiden Effect 318\u003c\/p\u003e \u003cp\u003e17.3 Elongation Strategies for C—C Bonds 319\u003c\/p\u003e \u003cp\u003e17.3.1 Steric Crowding Effect 320\u003c\/p\u003e \u003cp\u003e17.3.2 Core–Shell Strategy and Scissor Effect 321\u003c\/p\u003e \u003cp\u003e17.3.3 Negative Hyperconjugation Effect 321\u003c\/p\u003e \u003cp\u003e17.4 Concluding Remarks 323\u003c\/p\u003e \u003cp\u003eAcknowledgments 324\u003c\/p\u003e \u003cp\u003eReferences 324\u003c\/p\u003e \u003cp\u003e\u003cb\u003e18 Accurate Determination of Materials Properties: Role of Electron Density 329\u003cbr\u003e\u003c\/b\u003e\u003ci\u003eAnup Pramanik, Sourav Ghoshal, Santu Biswas, Biplab Rajbanshi and Pranab Sarkar\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e18.1 Introduction 329\u003c\/p\u003e \u003cp\u003e18.2 Materials Properties: Structure and Electronic Properties 330\u003c\/p\u003e \u003cp\u003e18.2.1 Classification of Materials 330\u003c\/p\u003e \u003cp\u003e18.2.2 Electronic Properties of Materials 332\u003c\/p\u003e \u003cp\u003e18.3 Molecules to Materials, Essential Role of Electron Density 333\u003c\/p\u003e \u003cp\u003e18.3.1 The Density Functional Theory (DFT) 334\u003c\/p\u003e \u003cp\u003e18.3.2 The Hohenberg–Kohn Theorems 334\u003c\/p\u003e \u003cp\u003e18.3.3 The Hohenberg–Kohn Variational Theorems 335\u003c\/p\u003e \u003cp\u003e18.3.4 The Kohn–Sham (KS) Method 335\u003c\/p\u003e \u003cp\u003e18.3.5 Local Density Approximation 337\u003c\/p\u003e \u003cp\u003e18.3.6 Generalized Gradient Approximation 337\u003c\/p\u003e \u003cp\u003e18.3.7 Meta-GGA and Hybrid Functionals 338\u003c\/p\u003e \u003cp\u003e18.4 Further Approximations in DFT 339\u003c\/p\u003e \u003cp\u003e18.4.1 The Density Functional Tight-Binding Theory 339\u003c\/p\u003e \u003cp\u003e18.4.2 Self-Consistent-Charge Density-Functional Tight-Binding (SCC-DFTB) Method 340\u003c\/p\u003e \u003cp\u003e18.5 Solar Cell Materials, Interfacial Charge Transfer Phenomena 340\u003c\/p\u003e \u003cp\u003e18.5.1 The Time-Dependent Density Functional Theory 342\u003c\/p\u003e \u003cp\u003e18.5.2 TDDFT and Linear Response 343\u003c\/p\u003e \u003cp\u003e18.5.3 Excitation Energy and Excited State Properties 344\u003c\/p\u003e \u003cp\u003e18.5.3.1 Exciton Binding Energy 346\u003c\/p\u003e \u003cp\u003e18.5.3.2 Reorganization Energy 346\u003c\/p\u003e \u003cp\u003e18.5.3.3 The Rates of Charge Transfer and Recombination Processes 347\u003c\/p\u003e \u003cp\u003e18.6 Concluding Remarks 348\u003c\/p\u003e \u003cp\u003eAcknowledgements 349\u003c\/p\u003e \u003cp\u003eReferences 349\u003c\/p\u003e \u003cp\u003e\u003cb\u003e19 A Conceptual DFT Analysis of Mechanochemical Processes 355\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eRuchi Jha, Shanti Gopal Patra, Debdutta Chakraborty, and Pratim Kumar Chattaraj\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e19.1 Introduction 355\u003c\/p\u003e \u003cp\u003e19.2 Theoretical Background 356\u003c\/p\u003e \u003cp\u003e19.2.1 The Constrained Geometries Simulate External Force (COGEF) 356\u003c\/p\u003e \u003cp\u003e19.2.2 External Force is Explicitly Included (EFEI) 358\u003c\/p\u003e \u003cp\u003e19.3 Results and Discussions 358\u003c\/p\u003e \u003cp\u003e19.3.1 General Consideration 358\u003c\/p\u003e \u003cp\u003e19.3.2 Constrained Geometries Simulate External Force (COGEF) 360\u003c\/p\u003e \u003cp\u003e19.3.2.1 Mechanochemical CDFT Reactivity Descriptors and Their Application to Diatomic Molecules 362\u003c\/p\u003e \u003cp\u003e19.3.3 Understanding Ball Milling Mechanochemical Processes with DFT Calculations and Microkinetic Modeling 365\u003c\/p\u003e \u003cp\u003e19.3.4 Explicit Force 369\u003c\/p\u003e \u003cp\u003e19.3.5 Dynamical Aspect of Mechanochemistry 369\u003c\/p\u003e \u003cp\u003e19.4 Concluding Remarks 373\u003c\/p\u003e \u003cp\u003eAcknowledgments 373\u003c\/p\u003e \u003cp\u003eReferences 373\u003c\/p\u003e \u003cp\u003e\u003cb\u003e20 Molecular Electron Density and Electrostatic Potential and Their Applications 379\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eShyam V.K. Panneer, Masiyappan Karuppusamy, Kanagasabai Balamurugan, Sathish K. Mudedla, Mahesh K. Ravva and Venkatesan Subramanian\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e20.1 Introduction 379\u003c\/p\u003e \u003cp\u003e20.2 Topography Analysis of Scalar Fields 380\u003c\/p\u003e \u003cp\u003e20.2.1 Molecular Electron Density 380\u003c\/p\u003e \u003cp\u003e20.2.2 Topology of Molecular Electrostatic Potential 381\u003c\/p\u003e \u003cp\u003e20.3 Usefulness of MESP and MED Analysis for Understanding Weak Interactions 382\u003c\/p\u003e \u003cp\u003e20.3.1 MESP and MED Topography Analysis of Oligomers of Conjugated Polymers and their Interaction with PCBM Acceptors 382\u003c\/p\u003e \u003cp\u003e20.3.2 Interaction of Small Molecules with Models of Single-Walled Carbon Nanotube and Graphene 386\u003c\/p\u003e \u003cp\u003e20.3.2.1 Interaction of Nucleobases with Carbon Nanomaterials 386\u003c\/p\u003e \u003cp\u003e20.3.2.2 Interaction of Chlorobenzene with Carbon Nanomaterials 392\u003c\/p\u003e \u003cp\u003e20.3.2.3 Interaction of Carbohydrates with Carbon Nanomaterials 394\u003c\/p\u003e \u003cp\u003e20.4 Conclusion 397\u003c\/p\u003e \u003cp\u003eAcknowledgment 398\u003c\/p\u003e \u003cp\u003eConflict of Interest 398\u003c\/p\u003e \u003cp\u003eReferences 398\u003c\/p\u003e \u003cp\u003e\u003cb\u003e21 Origin and Nature of Pancake Bonding Interactions: A Density Functional Theory and Information-Theoretic Approach Study 401\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eDongbo Zhao, Xin He and Shubin Liu\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e21.1 Introduction 401\u003c\/p\u003e \u003cp\u003e21.2 Methodology 402\u003c\/p\u003e \u003cp\u003e21.2.1 Interaction Energy and Its Components in DFT 402\u003c\/p\u003e \u003cp\u003e21.2.2 Information-Theoretic Approach Quantities 403\u003c\/p\u003e \u003cp\u003e21.3 Computational Details 404\u003c\/p\u003e \u003cp\u003e21.4 Results and Discussion 404\u003c\/p\u003e \u003cp\u003e21.5 Concluding Remarks 410\u003c\/p\u003e \u003cp\u003eAcknowledgment 411\u003c\/p\u003e \u003cp\u003eReferences 411\u003c\/p\u003e \u003cp\u003e\u003cb\u003e22 Electron Spin Density and Magnetism in Organic Diradicals 415\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eSuranjan Shil, Debojit Bhattacharya and Anirban Misra\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e22.1 Introduction 415\u003c\/p\u003e \u003cp\u003e22.2 Quantitative Relation Between Magnetic Exchange Coupling Constant and Spin Density 416\u003c\/p\u003e \u003cp\u003e22.3 Spin Density Alternation 416\u003c\/p\u003e \u003cp\u003e22.3.1 Phenyl Nitroxide 416\u003c\/p\u003e \u003cp\u003e22.3.2 Methoxy Phenyl Nitroxide 417\u003c\/p\u003e \u003cp\u003e22.3.3 Phenyl Nitroxide Coupled Through Methylene 417\u003c\/p\u003e \u003cp\u003e22.3.4 Spin Density of Radical Systems 418\u003c\/p\u003e \u003cp\u003e22.3.5 Distance Dependence of Spin Density 418\u003c\/p\u003e \u003cp\u003e22.3.6 Geometry Dependence of Spin Density 423\u003c\/p\u003e \u003cp\u003e22.3.7 Dependence on Connecting Atoms 423\u003c\/p\u003e \u003cp\u003e22.4 Concluding Remarks 427\u003c\/p\u003e \u003cp\u003eAcknowledgements 427\u003c\/p\u003e \u003cp\u003eReferences 428\u003c\/p\u003e \u003cp\u003e\u003cb\u003e23 Stabilization of Boron and Carbon Clusters with Transition Metal Coordination – An Electron Density and DFT Study 431\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eAmol B. Rahane, Rudra Agarwal, Pinaki Saha, Nagamani Sukumar and Vijay Kumar\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e23.1 Introduction 431\u003c\/p\u003e \u003cp\u003e23.2 Computational Details 434\u003c\/p\u003e \u003cp\u003e23.3 Results and Discussion 435\u003c\/p\u003e \u003cp\u003e23.3.1 Structures and Stability of Metal Atom Encapsulated Boron Clusters 435\u003c\/p\u003e \u003cp\u003e23.3.2 Bonding Characteristics in M@B\u003csub\u003e18\u003c\/sub\u003e, M@B\u003csub\u003e20\u003c\/sub\u003e, M@B\u003csub\u003e22\u003c\/sub\u003e, and M@B\u003csub\u003e24\u003c\/sub\u003e Clusters 440\u003c\/p\u003e \u003cp\u003e23.3.3 Structures and Stability of Carbon Rings 447\u003c\/p\u003e \u003cp\u003e23.3.4 Bonding Characteristics in Carbon Rings 450\u003c\/p\u003e \u003cp\u003e23.4 Conclusions 457\u003c\/p\u003e \u003cp\u003eAcknowledgments 458\u003c\/p\u003e \u003cp\u003eReferences 458\u003c\/p\u003e \u003cp\u003e\u003cb\u003e24 DFT-Based Computational Approach for Structure and Design of Materials: The Unfinished Story 465\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eRavi Kumar, Mayank Khera, Shivangi Garg, and Neetu Goel\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e24.1 Introduction 465\u003c\/p\u003e \u003cp\u003e24.2 Different Frameworks of DFT 466\u003c\/p\u003e \u003cp\u003e24.2.1 Kohn Sham Density Functional Theory (KS-DFT) 466\u003c\/p\u003e \u003cp\u003e24.2.2 Time-Dependent Density Functional Theory (TD-DFT) 467\u003c\/p\u003e \u003cp\u003e24.2.3 Linear Response Time-Dependent Density-Functional Theory (LR-TDDFT) 469\u003c\/p\u003e \u003cp\u003e24.2.4 Discontinuous Galerkin Density Functional Theory (DGDFT) 469\u003c\/p\u003e \u003cp\u003e24.3 DFT Implemented Computational Packages 470\u003c\/p\u003e \u003cp\u003e24.4 DFT as Backbone of Electronic Structure Calculations 472\u003c\/p\u003e \u003cp\u003e24.4.1 Design of 2D Nano-Materials 472\u003c\/p\u003e \u003cp\u003e24.4.2 Non-covalent Interactions and Crystal Packing 476\u003c\/p\u003e \u003cp\u003e24.4.3 Designing of Organic Solar Cell 477\u003c\/p\u003e \u003cp\u003e24.5 Concluding Remarks 480\u003c\/p\u003e \u003cp\u003eAcknowledgment 481\u003c\/p\u003e \u003cp\u003eReferences 481\u003c\/p\u003e \u003cp\u003e\u003cb\u003e25 Structure, Stability and Bonding in Ligand Stabilized C 3 Species 491\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eSudip Pan and Zhong-hua Cui\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e25.1 Introduction 491\u003c\/p\u003e \u003cp\u003e25.2 Computational Details 492\u003c\/p\u003e \u003cp\u003e25.3 Structures and Energetics 493\u003c\/p\u003e \u003cp\u003e25.4 Bonding 495\u003c\/p\u003e \u003cp\u003e25.5 Conclusions 500\u003c\/p\u003e \u003cp\u003eAcknowledgements 501\u003c\/p\u003e \u003cp\u003eReferences 501\u003c\/p\u003e \u003cp\u003e\u003cb\u003e26 The Role of Electronic Activity Toward the Analysis of Chemical Reactions 505\u003cbr\u003e\u003c\/b\u003e\u003ci\u003eSwapan Sinha and Santanab Giri\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e26.1 Introduction 505\u003c\/p\u003e \u003cp\u003e26.2 Theoretical Backgrounds and Computational Details 506\u003c\/p\u003e \u003cp\u003e26.3 Results and Discussions 509\u003c\/p\u003e \u003cp\u003e26.3.1 Bimolecular Nucleophilic Substitution (S\u003csub\u003eN\u003c\/sub\u003e2) Reaction 509\u003c\/p\u003e \u003cp\u003e26.3.2 Alkylation of Zintl Cluster 512\u003c\/p\u003e \u003cp\u003e26.3.3 Proton Transfer Reaction 515\u003c\/p\u003e \u003cp\u003e26.3.4 Water Activation by Frustrated Lewis Pairs (FLPs) 519\u003c\/p\u003e \u003cp\u003e26.4 Concluding Remarks 522\u003c\/p\u003e \u003cp\u003eAcknowledgments 522\u003c\/p\u003e \u003cp\u003eReferences 522\u003c\/p\u003e \u003cp\u003e\u003cb\u003e27 Prediction of Radiative Efficiencies and Global Warming Potential of Hydrofluoroethers and Fluorinated Esters Using Various DFT Functionals 527\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eKanika Guleria, Suresh Tiwari, Dali Barman, Snehasis Daschakraborty, and Ranga Subramanian\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e27.1 Introduction 527\u003c\/p\u003e \u003cp\u003e27.2 Computational Methodology 528\u003c\/p\u003e \u003cp\u003e27.3 RE and GWP Calculation Methodology 528\u003c\/p\u003e \u003cp\u003e27.4 Results and Discussions 529\u003c\/p\u003e \u003cp\u003e27.4.1 (Difluoromethoxy)trifluoromethane (CF\u003csub\u003e3\u003c\/sub\u003eOCHF\u003csub\u003e2\u003c\/sub\u003e) 529\u003c\/p\u003e \u003cp\u003e27.4.2 Difluoro(methoxy)methane (CH\u003csub\u003e3\u003c\/sub\u003eOCHF\u003csub\u003e2\u003c\/sub\u003e) 529\u003c\/p\u003e \u003cp\u003e27.4.3 Trifluoro(methoxy)methane (CF\u003csub\u003e3\u003c\/sub\u003eOCH\u003csub\u003e3\u003c\/sub\u003e) 531\u003c\/p\u003e \u003cp\u003e27.4.4 Bis(2,2,2-trifluoroethyl)ether (CF\u003csub\u003e3\u003c\/sub\u003eCH\u003csub\u003e2\u003c\/sub\u003eOCH\u003csub\u003e2\u003c\/sub\u003eCF\u003csub\u003e3\u003c\/sub\u003e) 531\u003c\/p\u003e \u003cp\u003e27.4.5 1,1,1,2,2-Pentafluoro-2-Methoxyethane (CF\u003csub\u003e3\u003c\/sub\u003eCF\u003csub\u003e2\u003c\/sub\u003eOCH\u003csub\u003e3\u003c\/sub\u003e) 534\u003c\/p\u003e \u003cp\u003e27.4.6 Fluoro(fluoromethoxy)methane (CH\u003csub\u003e2\u003c\/sub\u003eFOCH\u003csub\u003e2\u003c\/sub\u003eF) 537\u003c\/p\u003e \u003cp\u003e27.4.7 Methyl 2,2,2-Difluoroacetate (CHF\u003csub\u003e2\u003c\/sub\u003eC(O)OCH\u003csub\u003e3\u003c\/sub\u003e) 537\u003c\/p\u003e \u003cp\u003e27.4.8 Ethyl 2,2,2-Trifluoroacetate (CF\u003csub\u003e3\u003c\/sub\u003eC(O)OCH\u003csub\u003e2\u003c\/sub\u003eCH\u003csub\u003e3\u003c\/sub\u003e) 537\u003c\/p\u003e \u003cp\u003e27.4.9 2,2,2-Trifluoroethyl 2,2,2-trifluoroacetate (CF\u003csub\u003e3\u003c\/sub\u003eC(O)OCH\u003csub\u003e2\u003c\/sub\u003eCF\u003csub\u003e3\u003c\/sub\u003e) 540\u003c\/p\u003e \u003cp\u003e27.4.10 1,1-Difluoroethyl Carbonofluoridate (FC(O)OCF\u003csub\u003e2\u003c\/sub\u003eCH\u003csub\u003e3\u003c\/sub\u003e) 543\u003c\/p\u003e \u003cp\u003e27.4.11 Methyl 2,2,2-trifluoroacetate (CF\u003csub\u003e3\u003c\/sub\u003eC(O)OCH\u003csub\u003e3\u003c\/sub\u003e) 543\u003c\/p\u003e \u003cp\u003e27.5 Concluding Remarks 547\u003c\/p\u003e \u003cp\u003eAcknowledgment 547\u003c\/p\u003e \u003cp\u003eReferences 548\u003c\/p\u003e \u003cp\u003e\u003cb\u003e28 Density Functional Theory-Based Study on Some Natural Products 551\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eAbhishek Kumar, Ambrish K. Srivastava, Ratnesh Kumar, and Neeraj Misra\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e28.1 Introduction 551\u003c\/p\u003e \u003cp\u003e28.2 Computational Details 552\u003c\/p\u003e \u003cp\u003e28.3 Results and Discussion 552\u003c\/p\u003e \u003cp\u003e28.3.1 Geometrical Properties 552\u003c\/p\u003e \u003cp\u003e28.3.2 Vibrational Properties 553\u003c\/p\u003e \u003cp\u003e28.3.2.1 O–H Vibration 555\u003c\/p\u003e \u003cp\u003e28.3.2.2 C–H Vibration 555\u003c\/p\u003e \u003cp\u003e28.3.2.3 C–C Vibration 555\u003c\/p\u003e \u003cp\u003e28.3.2.4 C=O Vibration 555\u003c\/p\u003e \u003cp\u003e28.3.3 HOMO–LUMO and MESP Plots 555\u003c\/p\u003e \u003cp\u003e28.3.4 Chemical Reactivity 557\u003c\/p\u003e \u003cp\u003e28.4 Conclusion 558\u003c\/p\u003e \u003cp\u003eAcknowledgments 558\u003c\/p\u003e \u003cp\u003eReferences 558\u003c\/p\u003e \u003cp\u003eIndex 561\u003c\/p\u003e  \u003cp\u003e\u003cb\u003ePratim Kumar Chattaraj, PhD,\u003c\/b\u003e 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. \u003c\/p\u003e\u003cp\u003e\u003cb\u003eDebdutta Chakraborty, PhD,\u003c\/b\u003e is an Assistant Professor at Birla Institute of Technology Mesra, India.   \u003c\/p\u003e\u003cp\u003e\u003cb\u003eDiscover theoretical, methodological, and applied perspectives on electron density studies and density functional theory\u003c\/b\u003e \u003c\/p\u003e\u003cp\u003eElectron 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. \u003c\/p\u003e\u003cp\u003e\u003ci\u003eElectron Density: Concepts, Computation and DFT Applications\u003c\/i\u003e 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. \u003c\/p\u003e\u003cp\u003eReaders will also find: \u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eA balance of fundamentals and applications to facilitate use by both theoretical and computational scientists \u003c\/li\u003e\n\u003cli\u003eDetailed discussion of topics including the Levy-Perdew-Sahni equation, the Kohn Sham Inversion problem, and more \u003c\/li\u003e\n\u003cli\u003eAnalysis of DFT applications including the determination of structural, magnetic, and electronic properties\u003c\/li\u003e\n\u003c\/ul\u003e \u003cp\u003e\u003ci\u003eElectron Density: Concepts, Computation and DFT Applications \u003c\/i\u003eis ideal for academic researchers in quantum, theoretical, and computational chemistry and physics.\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47989116698853,"sku":"NP9781394217625","price":225.0,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9781394217625.jpg?v=1761782863","url":"https:\/\/k12savings.com\/es\/products\/electron-density-isbn-9781394217625","provider":"K12savings","version":"1.0","type":"link"}