Frontiers of Quantum Chemistry (eBook)

Marek Janusz WójcikProfessor Marek Janusz Wójcik received his Ph. D. and habilitation from Jagiellonian University. He has been a research associate at National Research Council, Canada and University of Chicago, and has been a visiting professor at numerous universities and institutes in Japan, USA, Canada, Sweden, France, Germany, Malaysia and South Africa. He is a professor of Jagiellonian University.His important contributions include Quantum-Mechanical Models for Spectra of Hydrogen-Bonded Systems, Theoretical Modeling of Vibrational Spectra of Water, Aqueous Ionic Solutions and Ices, Theoretical Studies of Multidimensional Proton Tunneling and Car-Parrinello Simulations of Spectra of Hydrogen-Bonded Crystals.He received Chevalier Cross of the Order of Rebirth of Poland.Hiroshi NakatsujiProfessor Hiroshi Nakatsuji received his Ph.D. from Kyoto University. He completed two years of postdoctoral studies at Yeshiva University, New York and University of North Carolina. From 1990 he was professor at the Graduate School of Engineering, Kyoto University. In 2004 - 2006 he was Director of the Fukui Institute for Fundamental Chemistry and from 2006 he is Director of the Quantum Chemistry Research Institute in Kyoto.His important contributions include General Methods of Solving the Schrödinger and Dirac Equations, SAC-CI Theory for Molecular Excited and Ionized States, Dipped Adcluster Model for Surface-Molecule Interactions and Reactions, Theory for the Direct Determination of Density Matrix, Intuitive Force Concept for Molecular Geometry and Chemical Reaction and Electronic Mechanism and Relativistic Effect in NMR Chemical Shifts.He received several awards, such as CSJ Award, Fukui Medal and Senior CMOA Medal. He is General Secretary of the International Academy Quantum Molecular Science.Bernard KirtmanProfessor Bernard Kirtman received his Ph.D. from Harvard University. He spent two years at the University of Washington as a research associate and three years at the University of California, Berkeley as an Assistant Professor before joining the faculty at the University of California, Santa Barbara in 1965, where he is currently a Professor in the Department of Chemistry & Biochemistry.He is internationally well known for his highly cited work in electronic structure theory and computational methods, as well as studies of molecular electronic/vibrational and nonlinear optical properties along with the vector potential approach for the computation of such properties in periodic systems. He has received the UCSB Academic Senate Distinguished Teaching Award and the ICCMSE Award for Theoretical/Computational Chemistry. An international symposium honoring his scientific contributions was held in Rhodes, Greece in 2009. Professor Kirtman is also a coauthor of the monograph "Calculations on Nonlinear Optical Properties of Large Systems" published by Springer.Yukihiro OzakiProfessor Yukihiro Ozaki received his Ph.D. from Osaka University. He spent for two years and a half at National Research Council, Canada as a research associate. He joined Kwansei Gakuin University in 1989, where he is a professor in the Department of Chemistry.He has been internationally famous for molecular spectroscopy studies including those for vibrational spectroscopy and electronic spectroscopy. He has also been active in application of quantum chemistry to molecular spectroscopy.  He received several international awards such as the Tomas Hirschfield Award, Gerald Birth Award and Bomen-Michelson Award. He is also a coeditor of the book "Far- and Deep- Ultraviolet Spectroscopy" published by Springer.

Preface 5
Contents 7
1 Rigorous and Empirical Approaches to Correlated Single-Particle Theories 9
Abstract 9
1.1 Introduction 9
1.2 Correlation in Single-Particle Many-Body Theories 13
1.3 Correlation in Kohn-Sham Density Functional Theory 15
1.4 Correlation in Semiempirical Methods 19
1.5 Basis Set Aspect of a COT 23
1.6 Conclusions 24
Acknowledgements 25
References 25
2 Circular Dichroism Spectroscopy with the SAC-CI Methodology: A ChiraSac Study 29
Abstract 29
2.1 Introduction 30
2.2 Rotatory Strength 32
2.3 Gauge-Origin Dependency 33
2.4 Dependence of the CD Spectra on the Conformation of HPAA 33
2.5 Substituent Effect of Uridine Derivatives 37
2.6 Conformational Dependence of the CD Spectra of Deoxyguanosine 39
2.7 Double-Helical Structure of DNA and the Nature of Weak Interactions Involved 42
2.7.1 Monomer Model 42
2.7.2 Dimer Model 44
2.7.3 Tetramer Model 46
2.8 CD Spectra Is an Indicator of the Stacking Interaction in Double-Helical DNA 47
2.9 Similarities and Differences Between Double-Helical DNA and RNA 49
2.10 Conclusion 51
Acknowledgements 52
References 52
3 Frontiers of Coupled Cluster Chiroptical Response Theory 56
3.1 Introduction 56
3.2 Theoretical Underpinnings of Coupled Cluster Response Theory 58
3.2.1 Time-Independent Coupled Cluster Theory 58
3.2.2 Time-Dependent Coupled Cluster Response Theory 60
3.3 Applications of Coupled Cluster Chiroptical Response Theory 63
3.3.1 Comparison to Gas-Phase Optical Activity Data 63
3.3.2 Condensed-Phase Optical Activity 66
3.4 Conclusions and Prospectus 71
References 72
4 Response Theory and Molecular Properties 76
4.1 Introduction 76
4.2 Response Functions from the Action 79
4.3 Exact Response Functions 81
4.3.1 Static Properties 81
4.3.2 First-Order Properties 81
4.3.3 Second-Order Properties 83
4.4 TDHF and TDDFT Response Functions 83
4.4.1 Static Properties 85
4.4.2 First-Order Properties 86
4.4.3 Second-Order Properties 87
4.4.4 State-to-state Transition Properties 89
4.4.5 One-Electron Systems 91
4.5 Conclusions and Outlook 92
References 92
5 Response Properties of Periodic Materials Subjected to External Electric and Magnetic Fields 94
5.1 Introduction 95
5.2 Translationally Invariant One-Electron Operators for External Fields 96
5.2.1 Basics 96
5.2.2 LCAO-CO Formulation 100
5.3 Coupled Perturbed Hartree-Fock (CPHF) and Kohn-Sham (CPKS) Static (Hyper)polarizabilities 101
5.3.1 CPHF Treatment 101
5.3.2 Extension to CPKS 104
5.4 Linear and Nonlinear Optical Properties 106
5.4.1 Dynamic Linear Polarizabilities and Optical Spectra 106
5.4.2 Dynamic First Hyperpolarizabilities 109
5.5 Effects of Geometric Distortions on Cell Dipole and Polarizability 112
5.5.1 Infrared and Raman Intensities 113
5.5.2 The Piezoelectric Tensor 114
5.5.3 Extension to DFT 116
5.5.4 Converse Piezoelectric Effect 117
5.6 Summary and Prospects 118
References 119
6 Quantum Chemical Methods for Predicting and Interpreting Second-Order Nonlinear Optical Properties: From Small to Extended ?-Conjugated Molecules 123
Abstract 123
6.1 Introduction 124
6.2 Small Molecules in Gas Phase 125
6.3 Small Molecules in Solution 132
6.4 Extended ?-Conjugated Dyes 136
Acknowledgements 143
References 143
7 Embedding Methods in Quantum Chemistry 145
7.1 Introduction 145
7.2 General Embedding Strategies 146
7.3 Exact Embedding Potential 149
7.4 QM/MM and Related Approaches 152
7.4.1 Continuum Solvent Models 152
7.4.2 QM/MM Approaches 155
7.4.3 Effective Fragment Potential 158
7.5 Many-Body and Inclusion--Exclusion-Based Methods 160
7.5.1 Molecular Fractionation with Conjugate Caps 160
7.5.2 Fragment Molecular Orbital Method 164
7.5.3 Molecular Tailoring Approach 166
7.5.4 Kernel Energy Method 168
7.6 Quantum-Chemical Divide-and-Conquer Methods 170
7.6.1 Divide and Conquer 170
7.6.2 Density Matrix Embedding Theory 173
7.6.3 Frozen Density Embedding 175
7.7 Summary and Conclusions 178
References 179
8 Calculation of Vibrational Spectra of Large Molecules from Their Fragments 186
Abstract 186
8.1 Fragment Methodology 187
8.1.1 Introduction 187
8.1.2 Cartesian Coordinate-Based Transfer of Atomic Property Tensors 188
8.1.3 Geometry Optimization in Vibrational Normal Mode Coordinates 189
8.2 Peptides and Proteins 191
8.2.1 Proteins 191
8.2.2 Conformer Analysis of Peptides 195
8.3 Nucleic Acid 196
8.4 Crystals 197
8.4.1 Polymorphism of Small Molecular Crystal 197
8.4.2 Low-Frequency Vibrational Spectra of Crystalline Polymers 198
8.5 Conclusions 200
Acknowledgements 200
References 200
9 Describing Molecules in Motion by Quantum Many-Body Methods 203
9.1 Introducing 203
9.2 Electronic and Nuclear Schrödinger Equations 204
9.3 Many-Body Expansion of the Hamiltonian 206
9.4 Second Quantization 210
9.5 Vibrational Self-consistent-field Theory and the Mode--Mode Correlation Problem 212
9.6 Vibrational Coupled Cluster 214
9.7 A Tensor Perspective on VCC 217
9.7.1 Vibrational Coupled Cluster as a Tensor Decomposition 218
9.7.2 Decomposed Correlation Amplitudes with CP 219
9.8 Seperability and VCC and VCI Compared 220
9.9 Conclusions 224
References 224
10 Relativistic Time-Dependent Density Functional Theory for Molecular Properties 226
Abstract 226
10.1 Introduction 226
10.2 Theory 228
10.2.1 Polarizability 228
10.2.2 Time-Dependent Kohn–Sham Theory 230
10.2.3 Noncollinear Formulation for Exchange–Correlation Kernel 234
10.3 Implementation 237
10.3.1 Trial Vector Algorithm 237
10.3.2 Automatic Implementation 240
10.4 Applications 243
10.4.1 Dynamic Polarizabilities of SnH4 and PbH4 243
10.4.2 Excitation Spectra of HI 244
10.5 Conclusion 248
Acknowledgements 248
References 249
11 Warming Up Density Functional Theory 251
11.1 Introduction 252
11.2 Background 253
11.2.1 Ground-State DFT 254
11.2.2 Asymmetric Hubbard Dimer and Its Relevance 255
11.2.3 Ensemble DFT as a Route to Excitation Energies 256
11.2.4 Thermal DFT in a Nutshell 259
11.3 Some Recent Developments in Thermal DFT 260
11.3.1 Exact Conditions and Their Relevance 260
11.3.2 Exact Calculations on a Simple Model System 262
11.3.3 Beyond Equilibrium: Linear Response Thermal Time-Dependent DFT 265
11.4 Recent Applications of DFT in WDM 266
11.5 Relation of Thermal DFT to Quantum Chemistry 268
11.6 Conclusion 269
References 270
12 Quantum Chemistry at the High Pressures: The eXtreme Pressure Polarizable Continuum Model (XP-PCM) 274
12.1 Introduction 274
12.2 The Essential of the XP-PCM Method for Molecules Under High Pressure 275
12.3 Effect of the Pressure on the Electron Density Distribution 278
12.4 Effect of the Pressure on Equilibrium Geometry 280
12.4.1 On the Linear Dependence on Pressure of the Bond Distances 281
12.4.2 On the Origin of Forces Induced by the Pressure on the Nuclei 282
12.5 Effect of the Pressure on the Vibrational Frequencies of Molecular Systems 284
12.5.1 On the Curvature and Relaxation Effects of the Pressure on the Vibrational Frequencies 284
12.6 Conclusions 287
References 287
13 Transition States of Spin-State Crossing Reactions from Organometallics to Biomolecular Excited States 289
Abstract 289
13.1 Introduction 290
13.2 Non-radiative Rapid Decay Mechanism of a Significantly Ruffled Porphyrin 291
13.2.1 Geometrical Difference Amongst S0, S1, and T1 States 292
13.2.2 Excitation Energies and the Effect of Distortion 293
13.2.3 Non-adiabatic Decay Mechanism 295
13.3 Energy Dissipative Photo-Protective Mechanism of Carotenoid Spheroidene 297
13.3.1 Stationary Structures of S0 and T1 States 298
13.3.2 C15–C15? Bond Rotation and the MEISCP Geometry 300
13.3.3 Energy Dissipative Photo-Protection Mechanism 301
13.4 Dioxygen Binding Pathway in a Model Heme Compound 302
13.4.1 Dioxygen Binding Pathway via ISCP and MEISCP 303
13.4.2 Reaction Coordinates to the MEISCP 305
13.5 Spin-Blocking Effect in CO and H2 Binding Reactions to Group 6 Metallocenes 307
13.5.1 The CO Binding Reaction to [MoCp2] and [WCp2] 307
13.5.2 The H2 Binding Reaction to [MoCp2] and [WCp2] 308
13.5.3 Geometrical Parameters Controlling the MEISCP 309
13.6 Conclusion 310
Acknowledgements 311
References 311
14 Electron Communications and Chemical Bonds 314
Abstract 314
14.1 Introduction 315
14.2 Amplitude and Probability Channels 318
14.3 Entropic Multiplicities of Direct and Bridge-Bonds 321
14.4 Orbital Decoupling 329
14.5 Illustrative Applications 335
14.6 Amplitude Communications in Valence-Bond Structures 342
14.7 Conclusion 347
References 348
15 Molecular Dynamics Simulations of Vibrational Spectra of Hydrogen-Bonded Systems 351
Abstract 351
15.1 Introduction 351
15.2 Theory Background 354
15.2.1 Born–Oppenheimer Molecular Dynamics 354
15.2.2 Car–Parrinello Molecular Dynamics 355
15.2.3 Path Integral Molecular Dynamics 355
15.2.4 The Hybrid Molecular Dynamics 356
15.2.5 Post-molecular Dynamics Analysis 356
15.3 Applications 357
15.3.1 Intramolecular Hydrogen Bonds 357
15.3.2 Hydrogen Bonds in Gas Phase 358
15.3.3 Molecular Modelling of Hydrogen Bonding Interactions in the Crystal Field 361
15.3.4 The Hydrogen Bonds in Solution 365
15.3.5 The Hydrogen Bonds as Vital Interactions in Biology 368
15.4 Summary and Perspectives 370
Acknowledgements 370
References 371
16 Nuclear Quantum Effect and H/D Isotope Effect on Hydrogen-Bonded Systems with Path Integral Simulation 375
Abstract 375
16.1 Introduction 376
16.2 Development of a New Efficient Algorithm for PI Simulation 378
16.2.1 A Path Integral Simulation Based on Second-Order Trotter Expansion 379
16.2.2 A Path Integral Simulation Method Based on Fourth-Order Trotter Expansion 380
16.2.3 Numerical Calculations of Hydrogen Molecule 384
16.3 Applications of PI Simulation: Hydrogen-Bonded Systems 385
16.3.1 Protonated and Deprotonated Water Dimers 385
16.3.2 Fluoride Ion-Water Clusters 388
16.3.3 Hydrogen Maleate Anion 391
16.4 Summary 394
Acknowledgements 394
References 395
17 Vibrational Linear and Nonlinear Optical Properties: Theory, Methods, and Application 398
17.1 Introduction 399
17.2 How to Choose the Right Approach: Harmonic, Anharmonic, and Nonharmonic Molecules 400
17.3 Perturbation Theory 401
17.3.1 Bishop--Kirtman Perturbation Theory 401
17.3.2 Convergence Behavior 405
17.3.3 Treatments for Two-photon Absorption: BKPT and Beyond 406
17.4 Finite-Field Methods: The Nuclear Relaxation/Curvature Approach 408
17.4.1 Connection Between FF and PT Methods 410
17.4.2 Field-Induced Coordinates, FICs 410
17.4.3 Finite-Field Geometry Optimization Approach 412
17.5 Variational Methods 414
17.5.1 Introduction 414
17.5.2 Approaches Using Normal Modes 415
17.5.3 Approaches Using Curvilinear Coordinates 417
17.6 Time-Dependent Approaches to L& NLO Processes
17.7 Conclusions and Outlook 422
References 422
18 Ab Initio Molecular Dynamics Study on Photoisomerization Reactions: Applications to Azobenzene and Stilbene 427
Abstract 427
18.1 Introduction 427
18.2 Photoisomerization of Azobenzene in n?* Excitation 429
18.2.1 Past Experimental and Theoretical Studies 429
18.2.2 AIMD Study on Photoisomerization of Azobenzene 431
18.2.3 Vibrational Spectroscopy of Trans-Azobenzene in n?* State 433
18.3 Photoisomerization of Cis-Stilbene in ??* Excitation 437
18.3.1 Past Experimental and Theoretical Studies 437
18.3.2 Potential Energy Surface of the ??* State of SB and DmSB 439
18.3.3 Ab Initio Molecular Dynamics (AIMD) Simulations for SB and DmSB 442
18.4 Conclusion 445
Acknowledgements 447
References 447
19 Density Functional Theoretical Studies on Chemical Enhancement of Surface-Enhanced Raman Spectroscopy in Electrochemical Interfaces 450
Abstract 450
19.1 Introduction 450
19.2 Theory and Models 452
19.3 SERS of Interfacial Water 457
19.3.1 Anionic Water Clusters 458
19.3.2 Water-Halide Anionic Complexes 459
19.3.3 Water Adsorbed on Noble Metal Cathodes 461
19.4 SERS of Pyridine on Metal Electrodes 464
19.4.1 Bonding Interactions 464
19.4.2 Vibrational Frequency Shifts 466
19.4.3 Chemical Enhancement 469
19.5 Conclusion 472
Acknowledgements 473
References 473
20 Advances in Anharmonic Methods and Their Applications to Vibrational Spectroscopies 478
Abstract 478
20.1 Introduction 478
20.2 An Overview of Anharmonic Approaches 480
20.2.1 Introductory Remarks 480
20.2.2 Vibrational Self-consistent Field 481
20.2.3 Correlation-Corrected Vibrational Methods 481
20.2.4 Vibrational Second-Order Perturbation Theory 483
20.2.5 Other Approaches to Time-Independent Vibrational Schrödinger Equation 484
20.3 Applications 485
20.3.1 Exemplary Applications of VSCF Scheme 485
20.3.2 Exemplary Applications of VCI and VCC Methods 489
20.3.3 Exemplary Applications of Vibrational Perturbation Theory 491
20.3.4 Miscellaneous Other Examples 499
20.4 Summary and Future Perspectives 504
References 505