Chemical modelling : applications and theory

Chemical Modelling: Applications and Theory comprises critical literature reviews of molecular modelling, both theoretical and applied. Molecular modelling in this context refers to modelling the structure, properties and reactions of atoms, molecules & materials. Each chapter is compiled by experts in their fields and provides a selective review of recent literature. With chemical modelling covering such a wide range of subjects, this Specialist Periodical Report serves as the first port of call to any chemist, biochemist, materials scientist or molecular physicist needing to acquaint themselves of major developments in the area. Specialist Periodical Reports provide systematic and detailed review coverage in major areas of chemical research. Compiled by teams of leading authorities in the relevant subject areas, the series creates a unique service for the active research chemist, with regular, in-depth accounts of progress in particular fields of chemistry. Subject coverage within different volumes of a given title is similar and publication is on an annual or biennial basis. Current subject areas covered are Amino Acids, Peptides and Proteins, Carbohydrate Chemistry, Catalysis, Chemical Modelling. Applications and Theory, Electron Paramagnetic Resonance, Nuclear Magnetic Resonance, Organometallic Chemistry. Organophosphorus Chemistry, Photochemistry and Spectroscopic Properties of Inorganic and Organometallic Compounds. From time to time, the series has altered according to the fluctuating degrees of activity in the various fields, but these volumes remain a superb reference point for researchers.

David PughT.E. SimosP.L.A. Popelier and F.M. Aicken and S.E. O'BrienR.I. Maurer and C.J. ReynoldsPekka Pyykko and Hermann StollMichael SpringborgS. WilsonJanos J. Ladik

Chapter 1 Electric Multipoles, Polarizabilities and Hyperpolarizabilities	p. 1
1 Introduction	p. 1
2 Perturbation of Molecules by Static Electric Fields: General Theory	p. 2
2.1 Analytic Derivatives of the Energy	p. 3
3 Frequency-Dependent Polarizabilities: General Theory	p. 4
3.1 Time-Dependent Perturbation Theory: The Sum over States Method	p. 5
3.1.1 Second Order Effects	p. 6
3.1.2 Third Order Effects	p. 7
3.2 Measurement of the Dynamic Hyperpolarizabilities	p. 7
4 Methods of Calculation: Development from 1970 to 1998	p. 7
4.1 Permanent Multipoles	p. 8
4.2 Static Polarizabilities and Hyperpolarizabilities	p. 8
4.3 Dynamic Response Functions	p. 10
4.4 The First Hyperpolarizability of Organic Donor/Acceptor Molecules	p. 11
4.5 Calculations of the Second Hyperpolarizability	p. 13
5 Review of Literature: 1998-May 1999	p. 14
5.1 Dipole and Quadrupole Moments	p. 14
5.2 Polarizabilities and Hyperpolarizabilities of Small Molecules	p. 15
5.2.1 Diatomic Molecules	p. 15
5.2.2 Butadiene	p. 17
5.2.3 Static Polarizabilities and Hyperpolarizabilities by ab initio Methods	p. 18
5.2.4 Dynamic Polarizabilities and Hyperpolarizabilities by ab initio Methods	p. 19
5.2.5 Density Functional Calculations	p. 19
5.2.6 Clusters and Small Homologous Series	p. 20
5.2.7 Excited State Polarizabilities	p. 21
5.3 Polarizabilities and Hyperpolarizabilities of Larger Molecules	p. 21
5.3.1 Ab initio Calculations	p. 21
5.3.2 Semi-Empirical Methods	p. 22
5.3.3 Linear Conjugated Chains	p. 24
5.3.4 Vibrational Polarization	p. 26
5.3.5 Fullerenes	p. 27
5.3.6 Solvent Effects, Crystal Fields	p. 28
5.3.7 New Theoretical Developments	p. 29
References	p. 30
Chapter 2 Atomic Structure Computations	p. 38
1 Introduction	p. 38
2 Methods with Coefficients Dependent on the Frequency of the Problem	p. 39
2.1 Exponential Multistep Methods	p. 39
2.1.1 The Derivation of Exponentially-Fitted Methods for General Problems	p. 40
2.1.2 Exponentially-Fitted Methods	p. 41
2.1.3 Linear Multistep Methods	p. 42
2.1.4 Predictor-Corrector Methods	p. 44
2.1.5 New Insights in Exponentially-Fitted Methods	p. 49
2.1.6 A New Tenth Algebraic Order Exponentially-Fitted Method	p. 54
2.1.7 Open Problems in Exponentially Fitting	p. 58
2.2 Bessel and Neumann Fitted Methods	p. 58
2.3 Phase Fitted Methods	p. 66
2.3.1 A New Phase Fitted Method	p. 71
2.4 Numerical Illustrations for Exponentially-Fitted Methods and Phase Fitted Methods	p. 73
2.4.1 The Resonance Problem: Woods-Saxon Potential	p. 74
2.4.2 Modified Woods-Saxon Potential: Coulombian Potential	p. 76
2.4.3 The Bound-States Problem	p. 77
2.4.4 Remarks and Conclusion	p. 77
3 Theory for Constructing Methods with Constant Coefficients for the Numerical Solution of Schrodinger Type Equations	p. 84
3.1 Phase-lag Analysis for Symmetric Two-Step Methods	p. 84
3.2 Phase-lag Analysis of General Symmetric 2k-Step, k [set membership] N Methods	p. 85
3.3 Phase-lag Analysis of Dissipative (Non-Symmetric) Two-Step Methods	p. 87
3.4 Phase-lag Analysis of the Runga-Kutta Methods	p. 89
3.5 Phase-lag Analysis of the Runga-Kutta-Nystrom Methods	p. 91
4 Methods with Constant Coefficients	p. 93
4.1 Implicit Methods	p. 93
4.1.1 P-Stable Methods	p. 93
4.1.2 Methods with Non-Empty Interval of Periodicity	p. 104
4.2 Explicit Methods	p. 110
4.2.1 Fourth Algebraic Order Methods	p. 110
4.2.2 Sixth Algebraic Order Methods	p. 110
4.2.3 Eighth Algebraic Order Methods	p. 111
5 Variable-Step Methods	p. 114
6 P-Stable Methods of High Exponential Order	p. 117
7 Matrix Methods for the One-Dimensional Eigenvalue Schrodinger Equation	p. 119
7.1 Methods of Discretization	p. 119
7.1.1 Methods Which Lead to a Tridiagonal Form of the Matrix A	p. 120
7.1.2 Methods Which Lead to a Pentadiagonal Form of the Matrix A	p. 120
7.1.3 Methods Which Lead to a Heptadiagonal Form of the Matrix A	p. 120
7.1.4 Numerov Discretization	p. 120
7.1.5 Extended Numerov Form	p. 120
7.1.6 An Improved Four-Step Method	p. 121
7.1.7 An Improved Three-Step Method	p. 121
7.1.8 An Improved Hybrid Four-Step Method	p. 122
7.2 Discussion	p. 123
8 Runga-Kutta and Runga-Kutta-Nystrom Methods for Specific Schrodinger Equations	p. 123
9 Two Dimensional Eigenvalue Schrodinger Equation	p. 124
10 Numerical Illustrations for the Methods with Constant Coefficients and the Variable-Step Methods	p. 125
10.1 Methods with Constant Coefficients	p. 125
10.1.1 Remarks and Conclusion	p. 126
10.2 Variable-Step Methods	p. 127
10.2.1 Error Estimation	p. 127
10.2.2 Coupled Differential Equations	p. 128
10.3 Remarks and Conclusion	p. 132
Appendix	p. 133
References	p. 140
Chapter 3 Atoms in Molecules	p. 143
1 Introduction	p. 143
1.1 What Is AIM?	p. 143
1.2 Scope	p. 144
1.3 The Roots of AIM	p. 146
1.4 The Development of AIM	p. 147
1.5 Software	p. 149
2 Theoretical	p. 149
2.1 Open Systems	p. 149
2.2 Molecular Similarity and QSAR	p. 150
2.3 Electron Correlation	p. 151
2.4 Transferability	p. 151
2.5 Multipoles	p. 152
2.6 Molecular Dynamics	p. 152
2.7 Partitioning	p. 153
3 The Laplacian	p. 153
3.1 Alternative Wave Functions	p. 153
3.2 Relation to Bohm Quantum Potential	p. 154
3.3 Protonation	p. 154
4 Electron Densities from High-resolution X-ray Diffraction	p. 156
4.1 State of the Art	p. 156
4.2 Comparison between Experimental and Theoretical Densities	p. 156
4.3 Hydrogen Bonding	p. 160
4.4 Organic Compounds	p. 163
4.5 Transition Metal Compounds	p. 166
4.6 Minerals	p. 170
5 Chemical Bonding	p. 171
5.1 Theory	p. 171
5.2 Ligand Close Packing (LCP) Model	p. 172
5.3 Hypervalency	p. 172
5.4 Organic Compounds	p. 173
5.5 Transition Metal Compounds	p. 174
5.6 Minerals	p. 177
5.7 Solid State	p. 178
5.8 Compounds of Atmospheric Interest	p. 178
5.9 Van der Waals Complexes	p. 179
6 Hydrogen Bonding	p. 179
6.1 Review	p. 179
6.2 Relationships	p. 180
6.3 Cooperative Effect	p. 180
6.4 Bifurcated Hydrogen Bonds	p. 182
6.5 Low-barrier Hydrogen Bonds	p. 182
6.6 Dihydrogen Bonds	p. 184
6.7 Very Strong Hydrogen Bonds	p. 184
6.8 Organic Compounds	p. 184
6.9 Biochemical Compounds	p. 185
6.10 Compounds of Atmospheric Importance	p. 187
7 Reactions	p. 188
7.1 Organic Compounds	p. 188
7.2 Inorganic Compounds	p. 190
8 Conclusion	p. 192
9 Disclaimer	p. 192
References	p. 193
Chapter 4 Modelling Biological Systems	p. 199
1 Introduction	p. 199
2 G-Protein Coupled Receptors	p. 200
3 Protein-Protein Docking	p. 201
3.1 Traditional Docking Approaches	p. 201
3.2 Sequence-based Approaches to Docking	p. 202
4 Simulations on the Early Stages of Protein Folding	p. 202
5 Simulations on DNA	p. 205
5.1 Particle Mesh Ewald	p. 206
6 Free Energy Calculations	p. 206
6.1 Free Energy Calculations from a Single Reference Simulation	p. 208
6.2 Multimolecule Free Energy Methods	p. 209
6.3 Linear Response Method	p. 210
6.4 Free Energy Perturbation Methods with Quantum Energies	p. 211
6.5 Force Fields	p. 211
7 Continuum Methods	p. 212
7.1 Parameter Dependence	p. 213
7.2 pK[subscript a] Calculations	p. 214
7.3 Binding Studies	p. 216
7.4 Protein Folding and Stability	p. 217
7.5 Solvation and Conformational Energies	p. 219
7.6 Redox Studies	p. 220
7.7 Additional Studies	p. 221
8 Hybrid QM/MM Calculations	p. 221
8.1 Methodology Developments	p. 222
8.2 The Models	p. 223
8.3 The Link Atom Problem	p. 226
8.4 Miscellaneous Improvements	p. 228
8.5 The 'Onion' Approach	p. 229
8.6 Applications	p. 230
8.6.1 Nickel-Iron Hydrogenase	p. 230
8.6.2 [beta]-Lactam Hydrolysis	p. 230
8.6.3 Bacteriorhodopsin	p. 231
8.6.4 The Bacterial Photosynthetic Reaction Centre	p. 231
8.6.5 Other Studies	p. 232
9 Car-Parrinello Calculations	p. 232
Acknowledgement	p. 233
References	p. 233
Chapter 5 Relativistic Pseudopotential Calculations, 1993-June 1999	p. 239
1 Methods	p. 239
1.1 Introduction	p. 239
1.2 Model Potentials	p. 242
1.3 Shape-Consistent Pseudopotentials	p. 246
1.4 DFT-Based Pseudopotentials	p. 250
1.5 Soft-Core Pseudopotentials and Separability	p. 252
1.6 Energy-Consistent Pseudopotentials	p. 255
1.7 Core-Polarization Pseudopotentials	p. 257
1.8 Concluding Remarks	p. 259
2 Applications by Element	p. 260
3 Some Applications by Subject	p. 260
3.1 New Species	p. 260
3.2 Metal-Ligand Interactions	p. 260
3.3 Closed-Shell Interactions	p. 260
3.4 Chemical Reactions and Homogeneous Catalysis	p. 278
3.5 Chemisorption and Heterogeneous Catalysis	p. 278
3.6 Other	p. 278
Acknowledgements	p. 278
References	p. 278
Chapter 6 Density-Functional Theory	p. 306
1 Introduction	p. 306
2 Fundamentals	p. 307
2.1 Wavefunction-based Methods	p. 308
2.2 Approximating the Schrodinger Equation	p. 310
2.3 Density-functional Theory	p. 312
2.4 Hybrid Methods	p. 318
3 Structural Properties	p. 319
3.1 Structure Optimization	p. 320
3.2 Examples of Structure Optimizations	p. 322
4 Vibrations	p. 328
5 Relative Energies	p. 329
5.1 Dissociation Energies	p. 329
5.2 Comparing Isomers	p. 330
6 Chemical Reactions	p. 331
6.1 Transition States	p. 331
6.2 Hardness, Softness and Other Descriptors	p. 333
7 Weak Bonds	p. 338
7.1 Van Der Waals Bonds	p. 338
7.2 Hydrogen Bonds	p. 338
8 The Total Electron Density	p. 340
9 The Orbitals	p. 340
10 Excitations	p. 343
11 Spin Properties	p. 346
11.1 NMR Chemical Shifts	p. 346
11.2 Electron Spin	p. 347
11.3 Electronic Spin-Spin Couplings	p. 349
11.4 Nuclear Spin-Spin Couplings	p. 350
12 Electrostatic Fields	p. 350
13 Solvation	p. 352
13.1 Dielectric Continuum	p. 352
13.2 Point Charges	p. 353
14 Solids	p. 353
14.1 Band Structures	p. 354
14.2 Applications	p. 354
15 Liquids	p. 356
16 Surfaces as Catalysts	p. 357
17 Intermediate-sized Systems	p. 358
18 Conclusions	p. 359
Acknowledgements	p. 360
References	p. 361
Chapter 7 Many-body Perturbation Theory and Its Application to the Molecular Electronic Structure Problem	p. 364
1 Introduction	p. 364
1.1 A Personal Note	p. 368
2 Theoretical Apparatus and Practical Algorithms	p. 369
2.1 Quantum Electrodynamics and Many-body Perturbation Theory	p. 369
2.1.1 The N-Dependence of Perturbation Expansions	p. 371
2.1.2 The Linked Diagram Theorem	p. 377
2.2 Many-body Perturbation Theory	p. 384
2.2.1 Closed-shell Molecules	p. 388
2.2.2 Open-shell Molecules	p. 400
2.3 Relativistic Many-body Perturbation Theory	p. 400
2.3.1 The Dirac Spectrum in the Algebraic Expansion	p. 403
2.3.2 Many-electron Relativistic Hamiltonians	p. 406
2.3.3 The 'No Virtual Pair' Approximation	p. 407
2.3.4 Quantum Electrodynamics and Virtual Pair Creation Processes	p. 409
2.4 The Algebraic Approximation	p. 409
2.4.1 Gaussian Basis Sets and Finite Nuclei	p. 410
2.4.2 Even-tempered Basis Sets	p. 410
2.4.3 Symmetric Sequences of Basis Sets	p. 411
2.4.4 Universal Basis Sets	p. 414
2.5 Higher Order Correlation Energy Components	p. 416
2.5.1 Fourth Order Energy Components	p. 416
2.5.2 Fifth Order Energy Components	p. 420
2.5.3 Higher Order Energy Components	p. 428
2.6 The Use of Multireference Functions in Perturbation Theory	p. 429
2.7 Concurrent Computation Many-body Perturbation Theory (ccMBPT)	p. 430
2.7.1 Parallel Computing and Its Impact	p. 430
2.7.2 Concurrent Computation and Performance Modelling: ccMBPT	p. 433
2.8 Analysis of Different Approaches to the Electron Correlation Problem in Molecules	p. 438
2.8.1 Configuration Mixing	p. 438
2.8.2 Coupled Electron Pair and Cluster Expansions	p. 440
3 Applications of Many-body Perturbation Theory	p. 441
3.1 Graphical User Interfaces	p. 441
3.2 Universal Basis Sets and Direct ccMBPT	p. 442
3.3 Finite Element Methods Applied to Many-body Perturbation Theory	p. 443
4 Future Directions	p. 444
Acknowledgements	p. 445
References	p. 445
Chapter 8 New Developments on the Quantum Theory of Large Molecules and Polymers	p. 453
1 Introduction	p. 453
2 The Treatment of Large Molecules Using Solid State Physical Methods Developed for Aperiodic Chains	p. 454
2.1 The Negative Factor Counting Methods with Correlation and Methods to Calculate Effective Total Energy per Unit Cell of Disordered Chains	p. 455
2.1.1 The Matrix Block Negative Factor Counting Method	p. 455
2.1.2 The Inclusion of Correlation in the Calculation of Density of States of Disordered Chains	p. 459
2.1.3 The Calculation of Effective Total Energy per Unit Cell	p. 460
2.2 Application to Proteins and Nucleotide Base Stacks	p. 461
2.3 Possible Application of the Negative Factor Counting Method to Large Molecules	p. 463
3 Correlation Corrected Energy Band Structures of Different Periodic Polymers	p. 464
3.1 Methods	p. 464
3.1.1 Inverse Dyson Equation with MP2 Self Energy	p. 464
3.1.2 Formulation of the Coupled Cluster Method for Quasi 1D Polymers	p. 465
3.1.3 Analytic Energy Gradients	p. 468
3.2 Examples of Correlation Corrected Band Structures of Quasi 1D Polymers	p. 471
4 Application of First Principles Density Functional Theory (DFT) to Polymers	p. 474
4.1 Methods	p. 474
4.2 Examples of LDA Calculations on Polymers	p. 476
5 Non-linear Optical Properties of Polymers	p. 478
5.1 Theory of Non-linear Optical Properties of Quasi 1D Periodic Polymers	p. 478
5.1.1 Solid State Physical Methods	p. 478
5.1.2 Large Clusters and Extrapolated Oligomers	p. 493
5.2 Results of Calculations of NLO Properties and Their Discussion	p. 494
5.2.1 Solid State Physical Calculations	p. 494
5.2.2 Extrapolated Oligomer Calculations	p. 495
6 Conformational Solitons in DNA and Their Possible Role in Cancer Inhibition	p. 496
Acknowledgement	p. 500
References	p. 500

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