Reviews in Computational Chemistry

Reviews in Computational Chemistry Volume 21......Page 3
Preface......Page 7
Contents......Page 13
Contributors......Page 19
Contributors to Previous Volumes......Page 21
Introduction......Page 31
Translation Invariance Properties in a Crystal......Page 36
The Direct Lattice......Page 37
The Reciprocal Lattice......Page 41
Bloch Theorem and Periodic Boundary Conditions......Page 42
One-Electron Electrostatic Hamiltonian......Page 46
A Monoatomic Linear Chain......Page 51
A Two-Dimensional Periodic Example: Graphite......Page 53
Three-Dimensional Periodic Examples......Page 64
From the Band Structure to the Total Energy......Page 67
Use of Symmetry in Reciprocal Space......Page 70
Total Energy, Energy Differences, and Derivatives......Page 73
Cohesive Energy......Page 74
Polymorphism......Page 82
Magnetic Phases......Page 84
Positional Isomorphous Phases......Page 86
Energy Derivatives......Page 87
The Slab Model......Page 96
Specifying the Surface Plane—Miller Indices......Page 97
Choosing the Surface Termination......Page 98
Surface Formation Energy and Stability......Page 100
Surface Relaxation and Reconstruction......Page 101
Adsorption on Surfaces......Page 104
Interfaces......Page 107
Defects in Solids......Page 110
How to Model a Defect......Page 111
The Supercell Approach......Page 113
Examples......Page 115
Appendix 1: Available Periodic Programs......Page 134
Appendix 2: Performance of the Periodic Program Crystal......Page 136
Appendix 3: Acronyms......Page 141
References......Page 142
Introduction......Page 157
Basic Elements of Molecular Similarity......Page 158
The Electron Density as Molecular Descriptor......Page 162
Molecular Quantum Similarity......Page 164
Extension to Other Operators......Page 167
Stochastic Manipulations and Graphical Representations of the Similarity Matrix......Page 170
Electron Densities for Molecular Quantum Similarity......Page 173
Statement of the Problem......Page 184
Quantum Similarity Maximization—MaxiSim and QSSA......Page 187
Structural Alignment......Page 191
Comparison of Alignment Techniques......Page 193
Quantum Similarity Indices......Page 194
Quantum Atoms-in-Molecules Similarity......Page 197
The Hirshfeld Approach......Page 198
AIM-Based Methods......Page 199
Atom-Centered Basis Function Approach......Page 200
Physical Connotations of (Self) Similarity Measures......Page 201
Chirality and the Holographic Electron Density Theorem......Page 207
Mathematical Aspects of Quantum Similarity......Page 210
The Cramer Steroid Set—A Worked Out Example of MQS......Page 221
Acknowledgments......Page 226
References......Page 227
Enumerating Molecules: Why......Page 239
From Graph Theory to Chemistry......Page 241
Counting Structures: How Many Isomers Has Decane?......Page 245
Enumerating Labeled and Unlabeled Graphs......Page 263
Enumerating Molecules......Page 267
Sampling Structures: What is the Decane Isomer With the Highest Boiling Point?......Page 285
Sampling Labeled and Unlabeled Graphs......Page 286
Sampling Molecules......Page 287
Chemical Information......Page 291
Structure Elucidation......Page 296
Combinatorial Library Design......Page 300
Molecular Design with Inverse-QSAR......Page 302
Conclusion and Future Directions......Page 304
References......Page 305
Introduction......Page 317
The Problem......Page 320
Dimension Reduction......Page 321
Variable Elimination......Page 325
More Variables Than Objects......Page 326
Multicolinearity......Page 329
Identification of Multicolinearity......Page 334
Unsupervised Elimination......Page 337
Variable Selection......Page 339
Ridge Regression......Page 341
Principal Component Regression, Partial Least Squares, and Continuum Regression......Page 344
Best Variable Subset Selection......Page 348
Backward Elimination......Page 353
Stepwise Regression......Page 354
All Subset Regression......Page 356
Other Stopping Rules......Page 357
Case Study......Page 359
Stepwise Regression......Page 360
Best Subset Regression......Page 362
Supervised and Unsupervised Variable Selection......Page 364
Published Variable Selection Methods......Page 369
Conclusions......Page 371
Appendix......Page 372
References......Page 373
Introduction to Biomolecular Electrostatics......Page 379
Polar Interactions......Page 381
Nonpolar Interactions......Page 382
Poisson–Boltzmann Theory: A Brief Overview......Page 384
Discretization Methods......Page 387
Multilevel Solvers......Page 389
Software for Computational Electrostatics......Page 390
Solvation Free Energies......Page 392
Conformational Free Energies......Page 395
Binding Free Energies......Page 397
Titration Calculations......Page 399
Other Applications......Page 400
Conclusions......Page 401
References......Page 402
Introduction......Page 411
Formal Representation of GRNs......Page 413
An Example of a GRN: The Lac Operon......Page 414
Hierarchies of GRN Models: From Probabilistic Graphs to Deterministic Models......Page 418
A Guide to Databases and Knowledgebases on the Internet......Page 420
Pathway Databases and Platforms......Page 423
Current Gene, Interaction, and Pathway Ontologies......Page 425
Whole-Cell Modeling Platforms......Page 426
An Ontology for Cellular Processes......Page 427
The PATIKA Pathway Ontology......Page 430
Extracting Models from Pathways Databases......Page 431
Pathway and Dynamic Analysis Tools for GRNs......Page 432
Recurring Network Motifs......Page 433
Network Stability Analysis......Page 434
Predicting Dynamics and Bistability from Network Structure Alone......Page 436
Concluding Remarks......Page 437
References......Page 438
Author Index......Page 443
Subject Index......Page 461