Electron Density

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.

• List of Contributors xviiPreface xxv1 Levy–Perdew–Sahni Equation and the Kohn–Sham Inversion Problem 1Ashish Kumar and Manoj K. Harbola1.1 Introduction 11.2 One Equation ⟹ Several Methods; Universal Nature of Different Density-Based Kohn–Sham Inversion Algorithms 21.2.1 Generating Functional S[ρ] of Density-Based Kohn–Sham Inversion 21.2.2 Condition on Generating Functional S[ρ] 41.2.3 Examples of Different Generating Functionals 51.2.4 Application to Spherical Systems 71.2.5 Using Random Numbers to do Density-to-Potential Inversion 101.3 General Penalty Method for Density-to-Potential Inversion 121.4 Understanding Connection Between Density and Wavefunction-Based Inversion Methods Using LPS Equation 161.5 Concluding Remarks 19Acknowledgments 19References 202 Electron Density, Density Functional Theory, and Chemical Concepts 27Swapan K. Ghosh2.1 Introduction 272.2 Viewing Chemical Concepts Through a DFT Window 272.3 Electron Fluid, Quantum Fluid Dynamics, Electronic Entropy, and a Local Thermodynamic Picture 302.4 Miscellaneous Offshoots from Electron Density Experience 312.5 Concluding Remarks 31Acknowledgments 32References 323 Local and Nonlocal Descriptors of the Site and Bond Chemical Reactivity of Molecules 35José L. Gázquez, Paulino Zerón, Maurizio A. Pantoja-Hernández and Marco Franco-Pérez3.1 Introduction 353.2 Local and Nonlocal Reactivity Indexes 383.3 Site and Bond Reactivities 423.4 Concluding Remarks 46Acknowledgment 47References 474 Relativistic Treatment of Many-Electron Systems Through DFT in CCG 53Shamik Chanda and Amlan K. Roy4.1 Introduction 534.2 Theoretical Framework 564.2.1 Dirac Equation 564.2.2 Relativistic Density Functional Theory: Dirac–Kohn–Sham Method 584.2.3 Decoupling of Dirac Hamiltonian: DKH Methodology 604.2.4 DFT in Cartesian Grid 624.2.4.1 Basic Methodology 624.2.4.2 Hartree Potential in CCG 634.2.4.3 Hartree Fock Exchange Through FCT in CCG 654.2.4.4 Orbital-Dependent Hybrid Functionals via RS-FCT 654.3 Computational Details 664.4 Results and Discussion 674.4.1 One-Electron Atoms 674.4.2 Many-Electron Systems 684.4.2.1 Grid Optimization 684.4.2.2 Ground-State Energy of Atoms and Molecules 704.4.3 Application to Highly Charged Ions: He- and Li-Isoelectronic Series 714.5 Future and Outlook 74Acknowledgement 76References 765 Relativistic Reduced Density Matrices: Properties and Applications 83Somesh Chamoli, Malaya K. Nayak and Achintya Kumar Dutta5.1 Introduction 835.2 Relativistic One-Body Reduced Density Matrix 845.3 Properties of Relativistic 1-RDM 855.3.1 Natural Spinors: An Efficient Framework for Low-cost Calculations 875.3.1.1 Correlation Energy 885.3.1.2 Bond Length and Harmonic Vibrational Frequency 905.3.2 Natural Spinors as an Interpretive Tool 935.4 Concluding Remarks 93Acknowledgments 93References 946 Many-Body Multi-Configurational Calculation Using Coulomb Green’s Function 97Bharti Kapil, Shivalika Sharma, Priyanka Aggarwal, Harsimran Kaur, Sunny Singh and Ram Kuntal Hazra6.1 Introduction 976.2 Theoretical Development 986.2.1 Presence of Magnetic Field 996.2.1.1 3D Electron Gas Model 996.2.1.2 2D Electron Gas Model 1036.2.1.3 3D Exciton Model 1076.2.1.4 2D Exciton Model 1096.2.2 Absence of Magnetic Field 1146.2.2.1 3D He-Isoelectronic Ions 1146.2.2.2 2D He-Isoelectronic Ions 1196.2.2.3 Energy Calculation Through Perturbation 1226.2.2.4 Current Density of 2-e System 1236.3 Results and Discussion 1236.3.1 3D Interacting Electron Gas 1236.3.2 2D Interacting Electron Gas 1256.3.3 3D Exciton Complexes 1266.3.4 2D Exciton Complexes 1276.3.5 3D He-Isoelectronic Species 1286.3.5.1 Analysis of E(2)0 of He-Isoelectronic Ions 1296.3.5.2 Analysis of E(3)0 of He-Isoelectronic Ions 1296.3.6 2D He-Isoelectronic Species 1306.4 Concluding Remarks 131Acknowledgments 1316.A Standard Equations and Integrals 132References 1337 Excited State Electronic Structure – Effect of Environment 137Supriyo Santra and Debashree Ghosh7.1 Introduction 1377.2 Methodology 1387.2.1 Quantum Mechanical Methods 1387.2.1.1 Time-Dependent Density Functional Theory 1387.2.1.2 Active Space-Based Methods 1387.2.1.3 Configuration Interaction-Based Approaches 1397.2.1.4 Equation of Motion Coupled Cluster 1407.2.2 Molecular Mechanical Methods 1407.2.2.1 Oniom 1417.2.2.2 Mechanical Embedding 1417.2.2.3 Electronic Embedding 1427.2.2.4 Polarizable Embedding 1427.3 Representative Examples 1437.3.1 Photo-Isomerization of Rhodopsin 1437.3.2 DNA-Base Excited States in Solution 1437.3.3 Green Fluorescent Proteins 1457.4 Conclusion 146Acknowledgement 146References 1468 Electron Density in the Multiscale Treatment of Biomolecules 149Soumyajit Karmakar, Sunita Muduli, Atanuka Paul, and Sabyashachi Mishra8.1 Introduction 1498.2 Theoretical Background 1508.2.1 Hybrid Quantum Mechanics–Molecular Mechanics Approach 1528.3 Polarizable Density Embedding 1558.4 Multi-Scale QM/MM with Extremely Localized Molecular Orbitals 1578.5 Multiple Active Zones in QM/MM Modelling 1598.6 Reactivity Descriptors with QM/MM Modeling 1618.7 Treatment of Hydrogen Bonding with QM/MM 1638.8 Quantum Refinement of Crystal Structure with QM/MM 1648.9 Concluding Remarks 166Acknowledgments 167References 1679 Subsystem Communications and Electron Correlation 173Roman F. Nalewajski9.1 Introduction 1739.2 Discrete and Local Probability Networks in Molecular Bond Systems 1749.3 Bond Descriptors of Molecular Communication Channels 1779.4 Hartree–Fock Communications and Fermi Correlation 1799.5 Communication Partitioning of Two-Electron Probabilities 1819.6 Communications in Interacting Subsystems 1849.7 Illustrative Application to Reaction HSAB Principle 1889.8 Conclusion 191References 19210 Impacts of External Electric Fields on Aromaticity and Acidity for Benzoic Acid and Derivatives: Directionality, Additivity, and More 199Meng Li, Xinjie Wan, Xin He, Chunying Rong, Dongbo Zhao, and Shubin Liu10.1 Introduction 19910.2 Methodology 19910.3 Computational Details 20210.4 Results and Discussion 20310.5 Conclusions 213Acknowledgments 213References 21311 A Divergence and Rotational Component in Chemical Potential During Reactions 217Jean-Louis Vigneresse11.1 Introduction 21711.2 Chemical Descriptors 21811.3 Charge and Energy Exchange 21911.4 Fitness Landscape Diagrams 21911.5 Chemical Reactions 22011.6 Examining the Charge Exchange 22111.6.1 Path pχη(ζ) and Charge Exchange 22111.6.2 Systematic Changes Depending on the Starting Points on pχη(ζ) 22311.6.3 Specific Solutions Using a pηω Path 22411.7 Significance and Applications 22511.8 Conclusions 227Acknowledgments 227References 22812 Deep Learning of Electron Density for Predicting Energies: The Case of Boron Clusters 231Pinaki Saha and Minh Tho Nguyen12.1 Introduction 23112.2 Deep Learning of Electron Density 23312.3 Neural Networks for Neutral Boron Clusters 23512.4 Concluding Remarks 242Acknowledgements 243References 24313 Density-Based Description of Molecular Polarizability for Complex Systems 247Dongbo Zhao, Xin He, Paul W. Ayers and Shubin Liu13.1 Introduction 24713.2 Methodology and Computations 24813.2.1 Information-Theoretic Approach (ITA) Quantities 24813.2.2 The GEBF Method 24913.3 Results and Discussion 25013.4 Conclusions and Perspectives 260Acknowledgment 261References 26114 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 265Prabhat Ranjan, Preeti Nanda, Ramon Carbó-Dorca, and Tanmoy Chakraborty14.1 Introduction 26514.2 Methodology 26614.3 Results and Discussion 26714.3.1 Electronic Properties and CDFT-Based Descriptors 26714.4 Conclusion 275Acknowledgments 275Funding 276References 27615 “Phylogenetic” Screening of External Potential Related Response Functions 279Paweł Szarek15.1 Introduction 27915.2 Alchemical Approach 28115.3 The “Family Tree” 28115.4 First-order Sensitivities 28215.5 Second-Order Sensitivities 28315.5.1 Electric Dipole Polarizability 28315.5.2 “Polarizability Potential” – Local Polarization 28415.6 Alchemical Hardness 28515.6.1 Local Alchemical Hardness 28715.7 Alchemical Characteristic Radius 28915.8 Linear Response Function 29115.9 Conclusions 292References 29316 On the Nature of Catastrophe Unfoldings Along the Diels–Alder Cycloaddition Pathway 299Leandro Ayarde-Henríquez, Cristian Guerra, Mario Duque-Noreña, Patricia Pérez, Elizabeth Rincón and Eduardo Chamorro16.1 Introduction 29916.2 Molecular Symmetry and Elementary Catastrophe Unfoldings 30116.2.1 The Case of Normal- and Inverse-Electron-Demand Diels–Alder Reactions 30116.2.2 The C—C Bond Breaking in a High Symmetry Environment 30416.2.3 The Photochemical Ring Opening of 1,3-Cyclohexadiene 30516.3 Concluding Remarks 306Acknowledgments 307References 30717 Designing Principles for Ultrashort H···H Nonbonded Contacts and Ultralong C—C Bonds 313Nilangshu Mandal and Ayan Datta17.1 Introduction 31317.1.1 The Art of the Chemical Bond 31417.1.2 Designing and Decoding Chemical Bond 31417.2 Governing Factors for Ultrashort H···H Nonbonded Contacts 31517.2.1 London Dispersion Interaction 31617.2.2 Polarity and Charge Separation 31717.2.3 Conformations and Orientations 31717.2.4 Iron Maiden Effect 31817.3 Elongation Strategies for C—C Bonds 31917.3.1 Steric Crowding Effect 32017.3.2 Core–Shell Strategy and Scissor Effect 32117.3.3 Negative Hyperconjugation Effect 32117.4 Concluding Remarks 323Acknowledgments 324References 32418 Accurate Determination of Materials Properties: Role of Electron Density 329Anup Pramanik, Sourav Ghoshal, Santu Biswas, Biplab Rajbanshi and Pranab Sarkar18.1 Introduction 32918.2 Materials Properties: Structure and Electronic Properties 33018.2.1 Classification of Materials 33018.2.2 Electronic Properties of Materials 33218.3 Molecules to Materials, Essential Role of Electron Density 33318.3.1 The Density Functional Theory (DFT) 33418.3.2 The Hohenberg–Kohn Theorems 33418.3.3 The Hohenberg–Kohn Variational Theorems 33518.3.4 The Kohn–Sham (KS) Method 33518.3.5 Local Density Approximation 33718.3.6 Generalized Gradient Approximation 33718.3.7 Meta-GGA and Hybrid Functionals 33818.4 Further Approximations in DFT 33918.4.1 The Density Functional Tight-Binding Theory 33918.4.2 Self-Consistent-Charge Density-Functional Tight-Binding (SCC-DFTB) Method 34018.5 Solar Cell Materials, Interfacial Charge Transfer Phenomena 34018.5.1 The Time-Dependent Density Functional Theory 34218.5.2 TDDFT and Linear Response 34318.5.3 Excitation Energy and Excited State Properties 34418.5.3.1 Exciton Binding Energy 34618.5.3.2 Reorganization Energy 34618.5.3.3 The Rates of Charge Transfer and Recombination Processes 34718.6 Concluding Remarks 348Acknowledgements 349References 34919 A Conceptual DFT Analysis of Mechanochemical Processes 355Ruchi Jha, Shanti Gopal Patra, Debdutta Chakraborty, and Pratim Kumar Chattaraj19.1 Introduction 35519.2 Theoretical Background 35619.2.1 The Constrained Geometries Simulate External Force (COGEF) 35619.2.2 External Force is Explicitly Included (EFEI) 35819.3 Results and Discussions 35819.3.1 General Consideration 35819.3.2 Constrained Geometries Simulate External Force (COGEF) 36019.3.2.1 Mechanochemical CDFT Reactivity Descriptors and Their Application to Diatomic Molecules 36219.3.3 Understanding Ball Milling Mechanochemical Processes with DFT Calculations and Microkinetic Modeling 36519.3.4 Explicit Force 36919.3.5 Dynamical Aspect of Mechanochemistry 36919.4 Concluding Remarks 373Acknowledgments 373References 37320 Molecular Electron Density and Electrostatic Potential and Their Applications 379Shyam V.K. Panneer, Masiyappan Karuppusamy, Kanagasabai Balamurugan, Sathish K. Mudedla, Mahesh K. Ravva and Venkatesan Subramanian20.1 Introduction 37920.2 Topography Analysis of Scalar Fields 38020.2.1 Molecular Electron Density 38020.2.2 Topology of Molecular Electrostatic Potential 38120.3 Usefulness of MESP and MED Analysis for Understanding Weak Interactions 38220.3.1 MESP and MED Topography Analysis of Oligomers of Conjugated Polymers and their Interaction with PCBM Acceptors 38220.3.2 Interaction of Small Molecules with Models of Single-Walled Carbon Nanotube and Graphene 38620.3.2.1 Interaction of Nucleobases with Carbon Nanomaterials 38620.3.2.2 Interaction of Chlorobenzene with Carbon Nanomaterials 39220.3.2.3 Interaction of Carbohydrates with Carbon Nanomaterials 39420.4 Conclusion 397Acknowledgment 398Conflict of Interest 398References 39821 Origin and Nature of Pancake Bonding Interactions: A Density Functional Theory and Information-Theoretic Approach Study 401Dongbo Zhao, Xin He and Shubin Liu21.1 Introduction 40121.2 Methodology 40221.2.1 Interaction Energy and Its Components in DFT 40221.2.2 Information-Theoretic Approach Quantities 40321.3 Computational Details 40421.4 Results and Discussion 40421.5 Concluding Remarks 410Acknowledgment 411References 41122 Electron Spin Density and Magnetism in Organic Diradicals 415Suranjan Shil, Debojit Bhattacharya and Anirban Misra22.1 Introduction 41522.2 Quantitative Relation Between Magnetic Exchange Coupling Constant and Spin Density 41622.3 Spin Density Alternation 41622.3.1 Phenyl Nitroxide 41622.3.2 Methoxy Phenyl Nitroxide 41722.3.3 Phenyl Nitroxide Coupled Through Methylene 41722.3.4 Spin Density of Radical Systems 41822.3.5 Distance Dependence of Spin Density 41822.3.6 Geometry Dependence of Spin Density 42322.3.7 Dependence on Connecting Atoms 42322.4 Concluding Remarks 427Acknowledgements 427References 42823 Stabilization of Boron and Carbon Clusters with Transition Metal Coordination – An Electron Density and DFT Study 431Amol B. Rahane, Rudra Agarwal, Pinaki Saha, Nagamani Sukumar and Vijay Kumar23.1 Introduction 43123.2 Computational Details 43423.3 Results and Discussion 43523.3.1 Structures and Stability of Metal Atom Encapsulated Boron Clusters 43523.3.2 Bonding Characteristics in M@B18, M@B20, M@B22, and M@B24 Clusters 44023.3.3 Structures and Stability of Carbon Rings 44723.3.4 Bonding Characteristics in Carbon Rings 45023.4 Conclusions 457Acknowledgments 458References 45824 DFT-Based Computational Approach for Structure and Design of Materials: The Unfinished Story 465Ravi Kumar, Mayank Khera, Shivangi Garg, and Neetu Goel24.1 Introduction 46524.2 Different Frameworks of DFT 46624.2.1 Kohn Sham Density Functional Theory (KS-DFT) 46624.2.2 Time-Dependent Density Functional Theory (TD-DFT) 46724.2.3 Linear Response Time-Dependent Density-Functional Theory (LR-TDDFT) 46924.2.4 Discontinuous Galerkin Density Functional Theory (DGDFT) 46924.3 DFT Implemented Computational Packages 47024.4 DFT as Backbone of Electronic Structure Calculations 47224.4.1 Design of 2D Nano-Materials 47224.4.2 Non-covalent Interactions and Crystal Packing 47624.4.3 Designing of Organic Solar Cell 47724.5 Concluding Remarks 480Acknowledgment 481References 48125 Structure, Stability and Bonding in Ligand Stabilized C 3 Species 491Sudip Pan and Zhong-hua Cui25.1 Introduction 49125.2 Computational Details 49225.3 Structures and Energetics 49325.4 Bonding 49525.5 Conclusions 500Acknowledgements 501References 50126 The Role of Electronic Activity Toward the Analysis of Chemical Reactions 505Swapan Sinha and Santanab Giri26.1 Introduction 50526.2 Theoretical Backgrounds and Computational Details 50626.3 Results and Discussions 50926.3.1 Bimolecular Nucleophilic Substitution (SN2) Reaction 50926.3.2 Alkylation of Zintl Cluster 51226.3.3 Proton Transfer Reaction 51526.3.4 Water Activation by Frustrated Lewis Pairs (FLPs) 51926.4 Concluding Remarks 522Acknowledgments 522References 52227 Prediction of Radiative Efficiencies and Global Warming Potential of Hydrofluoroethers and Fluorinated Esters Using Various DFT Functionals 527Kanika Guleria, Suresh Tiwari, Dali Barman, Snehasis Daschakraborty, and Ranga Subramanian27.1 Introduction 52727.2 Computational Methodology 52827.3 RE and GWP Calculation Methodology 52827.4 Results and Discussions 52927.4.1 (Difluoromethoxy)trifluoromethane (CF3OCHF2) 52927.4.2 Difluoro(methoxy)methane (CH3OCHF2) 52927.4.3 Trifluoro(methoxy)methane (CF3OCH3) 53127.4.4 Bis(2,2,2-trifluoroethyl)ether (CF3CH2OCH2CF3) 53127.4.5 1,1,1,2,2-Pentafluoro-2-Methoxyethane (CF3CF2OCH3) 53427.4.6 Fluoro(fluoromethoxy)methane (CH2FOCH2F) 53727.4.7 Methyl 2,2,2-Difluoroacetate (CHF2C(O)OCH3) 53727.4.8 Ethyl 2,2,2-Trifluoroacetate (CF3C(O)OCH2CH3) 53727.4.9 2,2,2-Trifluoroethyl 2,2,2-trifluoroacetate (CF3C(O)OCH2CF3) 54027.4.10 1,1-Difluoroethyl Carbonofluoridate (FC(O)OCF2CH3) 54327.4.11 Methyl 2,2,2-trifluoroacetate (CF3C(O)OCH3) 54327.5 Concluding Remarks 547Acknowledgment 547References 54828 Density Functional Theory-Based Study on Some Natural Products 551Abhishek Kumar, Ambrish K. Srivastava, Ratnesh Kumar, and Neeraj Misra28.1 Introduction 55128.2 Computational Details 55228.3 Results and Discussion 55228.3.1 Geometrical Properties 55228.3.2 Vibrational Properties 55328.3.2.1 O–H Vibration 55528.3.2.2 C–H Vibration 55528.3.2.3 C–C Vibration 55528.3.2.4 C=O Vibration 55528.3.3 HOMO–LUMO and MESP Plots 55528.3.4 Chemical Reactivity 55728.4 Conclusion 558Acknowledgments 558References 558Index 561