Electron Density

List of Contributors xvii

Preface xxv

1 Levy-Perdew-Sahni Equation and the Kohn-Sham Inversion Problem 1
Ashish Kumar and Manoj K. Harbola

1.1 Introduction 1

1.2 One Equation ¿ Several Methods; Universal Nature of Different Density-Based Kohn-Sham Inversion Algorithms 2

1.3 General Penalty Method for Density-to-Potential Inversion 12

1.4 Understanding Connection Between Density and Wavefunction-Based Inversion Methods Using LPS Equation 16

1.5 Concluding Remarks 19

Acknowledgments 19

References 20

2 Electron Density, Density Functional Theory, and Chemical Concepts 27
Swapan K. Ghosh

2.1 Introduction 27

2.2 Viewing Chemical Concepts Through a DFT Window 27

2.3 Electron Fluid, Quantum Fluid Dynamics, Electronic Entropy, and a Local Thermodynamic Picture 30

2.4 Miscellaneous Offshoots from Electron Density Experience 31

2.5 Concluding Remarks 31

Acknowledgments 32

References 32

3 Local and Nonlocal Descriptors of the Site and Bond Chemical Reactivity of Molecules 35
José L. Gázquez, Paulino Zerón, Maurizio A. Pantoja-Hernández and Marco Franco-Pérez

3.1 Introduction 35

3.2 Local and Nonlocal Reactivity Indexes 38

3.3 Site and Bond Reactivities 42

3.4 Concluding Remarks 46

Acknowledgment 47

References 47

4 Relativistic Treatment of Many-Electron Systems Through DFT in CCG 53
Shamik Chanda and Amlan K. Roy

4.1 Introduction 53

4.2 Theoretical Framework 56

4.3 Computational Details 66

4.4 Results and Discussion 67

4.5 Future and Outlook 74

Acknowledgement 76

References 76

5 Relativistic Reduced Density Matrices: Properties and Applications 83
Somesh Chamoli, Malaya K. Nayak and Achintya Kumar Dutta

5.1 Introduction 83

5.2 Relativistic One-Body Reduced Density Matrix 84

5.3 Properties of Relativistic 1-RDM 85

5.4 Concluding Remarks 93

Acknowledgments 93

References 94

6 Many-Body Multi-Configurational Calculation Using Coulomb Green's Function 97
Bharti Kapil, Shivalika Sharma, Priyanka Aggarwal, Harsimran Kaur, Sunny Singh and Ram Kuntal Hazra

6.1 Introduction 97

6.2 Theoretical Development 98

6.3 Results and Discussion 123

6.4 Concluding Remarks 131

Acknowledgments 131

6.A Standard Equations and Integrals 132

References 133

7 Excited State Electronic Structure - Effect of Environment 137
Supriyo Santra and Debashree Ghosh

7.1 Introduction 137

7.2 Methodology 138

7.3 Representative Examples 143

7.4 Conclusion 146

Acknowledgement 146

References 146

8 Electron Density in the Multiscale Treatment of Biomolecules 149
Soumyajit Karmakar, Sunita Muduli, Atanuka Paul, and Sabyashachi Mishra

8.1 Introduction 149

8.2 Theoretical Background 150

8.3 Polarizable Density Embedding 155

8.4 Multi-Scale QM/MM with Extremely Localized Molecular Orbitals 157

8.5 Multiple Active Zones in QM/MM Modelling 159

8.6 Reactivity Descriptors with QM/MM Modeling 161

8.7 Treatment of Hydrogen Bonding with QM/MM 163

8.8 Quantum Refinement of Crystal Structure with QM/MM 164

8.9 Concluding Remarks 166

Acknowledgments 167

References 167

9 Subsystem Communications and Electron Correlation 173
Roman F. Nalewajski

9.1 Introduction 173

9.2 Discrete and Local Probability Networks in Molecular Bond Systems 174

9.3 Bond Descriptors of Molecular Communication Channels 177

9.4 Hartree-Fock Communications and Fermi Correlation 179

9.5 Communication Partitioning of Two-Electron Probabilities 181

9.6 Communications in Interacting Subsystems 184

9.7 Illustrative Application to Reaction HSAB Principle 188

9.8 Conclusion 191

References 192

10 Impacts of External Electric Fields on Aromaticity and Acidity for Benzoic Acid and Derivatives: Directionality, Additivity, and More 199
Meng Li, Xinjie Wan, Xin He, Chunying Rong, Dongbo Zhao, and Shubin Liu

10.1 Introduction 199

10.2 Methodology 199

10.3 Computational Details 202

10.4 Results and Discussion 203

10.5 Conclusions 213

Acknowledgments 213

References 213

11 A Divergence and Rotational Component in Chemical Potential During Reactions 217
Jean-Louis Vigneresse

11.1 Introduction 217

11.2 Chemical Descriptors 218

11.3 Charge and Energy Exchange 219

11.4 Fitness Landscape Diagrams 219

11.5 Chemical Reactions 220

11.6 Examining the Charge Exchange 221

11.7 Significance and Applications 225

11.8 Conclusions 227

Acknowledgments 227

References 228

12 Deep Learning of Electron Density for Predicting Energies: The Case of Boron Clusters 231
Pinaki Saha and Minh Tho Nguyen

12.1 Introduction 231

12.2 Deep Learning of Electron Density 233

12.3 Neural Networks for Neutral Boron Clusters 235

12.4 Concluding Remarks 242

Acknowledgements 243

References 243

13 Density-Based Description of Molecular Polarizability for Complex Systems 247
Dongbo Zhao, Xin He, Paul W. Ayers and Shubin Liu

13.1 Introduction 247

13.2 Methodology and Computations 248

13.3 Results and Discussion 250

13.4 Conclusions and Perspectives 260

Acknowledgment 261

References 261

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 265
Prabhat Ranjan, Preeti Nanda, Ramon Carbó-Dorca, and Tanmoy Chakraborty

14.1 Introduction 265

14.2 Methodology 266

14.3 Results and Discussion 267

14.4 Conclusion 275

Acknowledgments 275

Funding 276

References 276

15 "Phylogenetic" Screening of External Potential Related Response Functions 279
Pawe³ Szarek

15.1 Introduction 279

15.2 Alchemical Approach 281

15.3 The "Family Tree" 281

15.4 First-order Sensitivities 282

15.5 Second-Order Sensitivities 283

15.6 Alchemical Hardness 285

15.7 Alchemical Characteristic Radius 289

15.8 Linear Response Function 291

15.9 Conclusions 292

References 293

16 On the Nature of Catastrophe Unfoldings Along the Diels-Alder Cycloaddition Pathway 299
Leandro Ayarde-Henríquez, Cristian Guerra, Mario Duque-Noreña, Patricia Pérez, Elizabeth Rincón and Eduardo Chamorro

16.1 Introduction 299

16.2 Molecular Symmetry and Elementary Catastrophe Unfoldings 301

16.3 Concluding Remarks 306

Acknowledgments 307

References 307

17 Designing Principles for Ultrashort H···H Nonbonded Contacts and Ultralong C-C Bonds 313
Nilangshu Mandal and Ayan Datta

17.1 Introduction 313

17.2 Governing Factors for Ultrashort H···H Nonbonded Contacts 315

17.3 Elongation Strategies for C-C Bonds 319

17.4 Concluding Remarks 323

Acknowledgments 324

References 324

18 Accurate Determination of Materials Properties: Role of Electron Density 329
Anup Pramanik, Sourav Ghoshal, Santu Biswas, Biplab Rajbanshi and Pranab Sarkar

18.1 Introduction 329

18.2 Materials Properties: Structure and Electronic Properties 330

18.3 Molecules to Materials, Essential Role of Electron Density 333

18.4 Further Approximations in DFT 339

18.5 Solar Cell Materials, Interfacial Charge Transfer Phenomena 340

18.6 Concluding Remarks 348

Acknowledgements 349

References 349

19 A Conceptual DFT Analysis of Mechanochemical Processes 355
Ruchi Jha, Shanti Gopal Patra, Debdutta Chakraborty, and Pratim Kumar Chattaraj

19.1 Introduction 355

19.2 Theoretical Background 356

19.3 Results and Discussions 358

19.4 Concluding Remarks 373

Acknowledgments 373

References 373

20 Molecular Electron Density and Electrostatic Potential and Their Applications 379
Shyam V.K. Panneer, Masiyappan Karuppusamy, Kanagasabai Balamurugan, Sathish K. Mudedla, Mahesh K. Ravva and Venkatesan Subramanian

20.1 Introduction 379

20.2 Topography Analysis of Scalar Fields 380

20.3 Usefulness of MESP and MED Analysis for Understanding Weak Interactions 382

20.4 Conclusion 397

Acknowledgment 398

Conflict of Interest 398

References 398

21 Origin and Nature of Pancake Bonding Interactions: A Density Functional Theory and Information-Theoretic Approach Study 401
Dongbo Zhao, Xin He and Shubin Liu

21.1 Introduction 401

21.2 Methodology 402

21.3 Computational Details 404

21.4 Results and Discussion 404

21.5 Concluding Remarks 410

Acknowledgment 411

References 411

22 Electron Spin Density and Magnetism in Organic Diradicals 415
Suranjan Shil, Debojit Bhattacharya and Anirban Misra

22.1 Introduction 415

22.2 Quantitative Relation Between Magnetic Exchange Coupling Constant and Spin Density 416

22.3 Spin Density Alternation 416

22.4 Concluding Remarks 427

Acknowledgements 427

References 428

23 Stabilization of Boron and Carbon Clusters with Transition Metal Coordination - An Electron Density and DFT Study 431
Amol B. Rahane, Rudra Agarwal, Pinaki Saha, Nagamani Sukumar and Vijay Kumar

23.1 Introduction 431

23.2 Computational Details 434

23.3 Results and Discussion 435

Acknowledgments 458

References 458

24 DFT-Based Computational Approach for Structure and Design of Materials: The Unfinished Story 465
Ravi Kumar, Mayank Khera, Shivangi Garg, and Neetu Goel

24.1 Introduction 465

24.2 Different Frameworks of DFT 466

24.3 DFT Implemented Computational Packages 470

24.4 DFT as Backbone of Electronic Structure Calculations 472

24.5 Concluding Remarks 480

Acknowledgment 481

References 481

25 Structure, Stability and Bonding in Ligand Stabilized C 3 Species 491
Sudip Pan and Zhong-hua Cui

25.1 Introduction 491

25.2 Computational Details 492

25.3 Structures and Energetics 493

25.4 Bonding 495

25.5 Conclusions 500

Acknowledgements 501

References 501

26 The Role of Electronic Activity Toward the Analysis of Chemical Reactions 505
Swapan Sinha and Santanab Giri

26.1 Introduction 505

26.2 Theoretical Backgrounds and Computational Details 506

26.3 Results and Discussions 509

26.4 Concluding Remarks 522

Acknowledgments 522

References 522

27 Prediction of Radiative Efficiencies and Global Warming Potential of Hydrofluoroethers and Fluorinated Esters Using Various DFT Functionals 527
Kanika Guleria, Suresh Tiwari, Dali Barman, Snehasis Daschakraborty, and Ranga Subramanian

27.1 Introduction 527

27.2 Computational Methodology 528

27.3 RE and GWP Calculation Methodology 528

27.4 Results and Discussions 529

27.5 Concluding Remarks 547

Acknowledgment 547

References 548

28 Density Functional Theory-Based Study on Some Natural Products 551
Abhishek Kumar, Ambrish K. Srivastava, Ratnesh Kumar, and Neeraj Misra

28.1 Introduction 551

28.2 Computational Details 552

28.3 Results and Discussion 552

28.4 Conclusion 558

Acknowledgments 558

References 558

Index 561