Fragmentation: Toward Accurate Calculations on Complex Molecular Systems

Edited by MARK S. GORDON, Department of Chemistry, Iowa State University, Ames, USA

List of Contributors   xi

Preface    xv

1 Explicitly Correlated Local Electron Correlation Methods       1
Hans-Joachim Werner, Christoph Koppl, Qianli Ma, and Max Schwilk

1.1 Introduction 1

1.2 Benchmark Systems 3

1.3 Orbital-Invariant MP2 Theory 6

1.4 Principles of Local Correlation 9

1.5 Orbital Localization 10

1.6 Local Virtual Orbitals 12

1.7 Choice of Domains 24

1.8 Approximations for Distant Pairs 26

1.9 Local Coupled-Cluster Methods (LCCSD) 33

1.10 Triple Excitations 41

1.11 Local Explicitly Correlated Methods 41

1.12 Technical Aspects 53

1.13 Comparison of Local Correlation and Fragment Methods 57

1.14 Summary 60

Appendix A: The LCCSD Equations 63

Appendix B: Derivation of the Interaction Matrices 65

References  67

2 Density and Potential Functional Embedding: Theory and Practice  81
Kuang Yu, Caroline M. Krauter, Johannes M. Dieterich, and Emily A. Carter

2.1 Introduction  81

2.2 Theoretical Background 82

2.3 Density Functional Embedding Theory  84

2.4 Potential Functional Embedding Theory   101 

2.5 Summary and Outlook 109

Acknowledgments 111

References  111

3 Modeling and Visualization for the Fragment Molecular Orbital Method with the Graphical User Interface FU, and Analyses of Protein–Ligand Binding    119
Dmitri G. Fedorov and Kazuo Kitaura

3.1 Introduction  119

3.2 Overview of FMO 120

3.3 Methodology  120

3.4 GUI Development 128

3.5 Conclusions 136 Acknowledgments 137 References 137

4 Molecules-in-Molecules Fragment-Based Method for the Accurate Evaluation of Vibrational and Chiroptical Spectra for Large Molecules  141
K. V. Jovan Jose and Krishnan Raghavachari

4.1 Introduction 141

4.2 Computational Methods and Theory 142

4.3 Results and Discussion 146

4.4 Summary 157

4.5 Conclusions 158 Acknowledgments 159 References 159

5 Effective Fragment Molecular Orbital Method     165
Casper Steinmann and Jan H. Jensen

5.1 Introduction 165

5.2 Effective Fragment Molecular Orbital Method 168

5.3 Summary and Future Developments 180

References  180

6 Effective Fragment Potential Method: Past, Present, and Future  183
Lyudmila V. Slipchenko and Pradeep K. Gurunathan

6.1 Overview of the EFP Method  183

6.2 Milestones in the Development of the EFP Method  185

6.3 Present: Chemistry at Interfaces and Photobiology 192

6.4 Future Directions and Outlook 202

References  203

7 Nucleation Using the Effective Fragment Potential and Two-Level Parallelism    209
Ajitha Devarajan, Alexander Gaenko, Mark S. Gordon, and Theresa L. Windus

7.1 Introduction  209

7.2 Methods   211

7.3 Results   217

7.4 Conclusions  223

Acknowledgments 223

References  224

8 Five Years of Density Matrix Embedding Theory  227
Sebastian Wouters, Carlos A. Jime´nez-Hoyos, and Garnet K.L. Chan

8.1 Quantum Entanglement 227

8.2 Density Matrix Embedding Theory 228

8.3 Bath Orbitals from a Slater Determinant  230

8.4 The Embedding Hamiltonian 232

8.5 Self-Consistency  234

8.6 Green’s Functions  236

8.7 Overview of the Literature  237

8.8 The One-Band Hubbard Model on the Square Lattice  237

8.9 Dissociation of a Linear Hydrogen Chain 240

8.10 Summary  240

Acknowledgments 241

References  241

9 Ab initio Ice, Dry Ice, and Liquid Water     245
So Hirata, Kandis Gilliard, Xiao He, Murat Kec¸eli, Jinjin Li, Michael A. Salim, Olaseni Sode, and Kiyoshi Yagi

9.1 Introduction 245

9.2 Computational Method 247

9.3 Case Studies 256

9.4 Concluding Remarks 284

9.5 Disclaimer 284 Acknowledgments 284 References 285

10 A Linear-Scaling Divide-and-Conquer Quantum Chemical Method for Open-Shell Systems and Excited States      297
Takeshi Yoshikawa and Hiromi Nakai

10.1 Introduction 297

10.2 Theories for the Divide-and-Conquer Method 298

10.3 Assessment of the Divide-and-Conquer Method 307

10.4 Conclusion  318

References  319

11 MFCC-Based Fragmentation Methods for Biomolecules        323
Jinfeng Liu, Tong Zhu, Xiao He, and John Z. H. Zhang

11.1 Introduction 323

11.2 Theory and Applications 324

11.3 Conclusion 345 Acknowledgments 346 References 346

Index 349