Quantum Frontiers of Atoms and Molecules

QUANTUM FRONTIERS OF ATOMS AND MOLECULES......Page 4
CONTENTS......Page 6
ATOMS AND MOLECULES AS THE QUANTUM FRONTIERS OF LIFE......Page 10
1. Introduction......Page 14
2. Dirac-Schrödinger Equivalence......Page 15
3.1. Binding Functions and the Chemical Bond......Page 19
3.2. Chemical Bond by Dirac Equation......Page 22
4. Conclusion......Page 30
References......Page 31
1. Why a Reappraisal Is Necessary......Page 34
2. The Relevance of the Classical Framework......Page 38
3. On the Two Kinds of Incompatibility......Page 42
4. Wholeness and the Proper Logic for Complementarity......Page 45
5. The Reduction of Duality......Page 47
References......Page 51
1. Complementarity Contextualized......Page 54
2. Complementarity: A Stumbling Block on the Way to Context......Page 58
3. The Duality Route to Context......Page 60
4. Incommensurability: Last Resort—and Last Exit......Page 63
5. The Concept of Action Quantization......Page 65
6. Tying Loose Ends......Page 68
Appendix......Page 70
Notes......Page 71
References......Page 72
Abstract......Page 74
1.Introduction......Page 75
2.Early History of the Slater Orbitals......Page 76
3.History of the STO Computer Programs......Page 77
4.Slater Orbitals & Gaussian Orbitals......Page 78
5.Types of Exponentially Decaying Orbital, Based on Eigen-functions for One-Electron Atoms......Page 80
6.2.Two-Electron Integrals......Page 82
7.1.Single-Center Expansion......Page 83
7.4.Fourier-Transform Method......Page 84
7.6.Elliptic Coordinate Method......Page 85
8.1.Introduction......Page 86
8.3.Programming Strategy......Page 87
8.4.Avoiding ETO Translations for Two-Electron Integrals over Three and Four Centers......Page 88
8.5.Numerical Results of Coulomb Resolutions: Efficiency......Page 90
8.6.Selected Exchange Integrals for the CH3F Molecule (Evaluated Using the Coulomb Resolution)......Page 92
9.Explicitly Correlated Methods for Molecules......Page 93
References......Page 95
1.Introduction......Page 104
A.Tunneling in Physics......Page 105
B.Tunneling in Chemistry......Page 106
C.Tunneling in Coupled Systems......Page 107
A.Dynamics of the Coupled System in the Absence of Driving......Page 108
A.Tunneling in the Coupled System in Absence of External Driving......Page 111
B.Tunneling Dynamics in the Coupled System in the Presence of an External Electric Field Coupled to the Tunneling Coordinate......Page 113
C.Tunneling Dynamics in the Presence of External Field Coupled to the Bond Stretching Mode......Page 115
D.Tunneling Dynamics of a Particle with Coordinate Dependent Mass......Page 118
References......Page 121
Abstract......Page 124
1. Introduction......Page 125
A. Ab initio Calculation......Page 126
B. Vibration – Rotation Calculation......Page 128
Atomic Calculation......Page 129
3.3. Spin-Orbit Effects Neglected......Page 130
3.4. Spin-Orbit Effects Included......Page 135
3.5. The Vibration-Rotation Calculation......Page 147
3.6. Dipole Moment......Page 148
References......Page 151
Abstract......Page 154
2. Excitons and Solitons in Infinite Polyethylene Chains......Page 155
3. Green’s Function of Homeopolar Excitons......Page 161
4. The Exciton Wave Function of Polyethylene Chain......Page 164
Conclusion......Page 167
References......Page 168
1. Introduction......Page 170
2. Theoretical Background and Computational Methods......Page 171
The CP Scheme......Page 172
The CHA Scheme......Page 173
2.2. Anharmonic Approach of Normal Mode Vibrations......Page 175
Density Fitting......Page 176
3.1. Formamide Dimers......Page 177
The Geometry Structure......Page 178
Harmonic and Anharmonic Frequencies......Page 181
The Geometry Structure......Page 183
Harmonic and Anharmonic Frequencies......Page 186
3.3. Guanine-Cytosine DNA Base Pair......Page 189
The Geometry Structure......Page 190
Harmonic and Anharmonic Frequencies......Page 191
3.4. Adenine-Thymine DNA Base Pair......Page 193
4. Conclusion......Page 195
References......Page 196
Abstract......Page 204
1.Introduction......Page 205
2.1.Space......Page 206
2.1.1.Number......Page 207
2.2.2.Electron and Atom......Page 208
2.2.3.Mass......Page 210
3.Quantum Theory......Page 211
3.1.Wave Mechanics......Page 212
3.2.Bohmian Mechanics......Page 214
3.2.1.Quantum Potential......Page 215
3.2.3.Orbital Angular Momentum......Page 217
4.1.Interaction Theory......Page 218
4.2.Environmental Effects......Page 220
4.3.1.Periodicity......Page 221
4.3.2.Electronegativity......Page 224
4.3.3.Covalence......Page 226
References......Page 227
Abstract......Page 230
2. Scaling Laws......Page 231
3. Example Atoms......Page 234
4. Application to Analysis of Molecules......Page 237
Another Molecule with Two Atoms......Page 239
A Third Molecule with Two Atoms......Page 240
A Molecule with Three Atoms......Page 241
Another Molecule with Three Atoms......Page 242
A Molecule with Four Atoms......Page 243
A Molecule with Five Atoms......Page 244
6. Analysis of a Much Larger Molecule......Page 245
7. Analyses of Current Benchmark Reactions......Page 247
Analysis of the Right Side of the Reaction, CH3+H2:......Page 250
8. Results and Discussion......Page 251
Appendix 1. Essential Data about First-Order Ionization Potentials......Page 252
Appendix 2. The Algebraic Model for Ionization Potentials......Page 257
Appendix 3. Hydrogen, the Basis for all Scaling Laws......Page 259
Appendix 4. The Periodic Arch......Page 262
References and Notes......Page 263
1. Introduction......Page 264
2.1. Absolute Electronegativity and Hardness......Page 266
2.2. Systematic Electronegativity and Hardness......Page 268
3.1. Affinity and Ionization Fields by Second Quantization......Page 274
3.2. Observability of Electronegativity and Hardness......Page 275
4. Electronegativity and Hardness Electrodynamical Counterpart......Page 279
5. Conclusion......Page 283
References......Page 284
1. Introduction......Page 290
2. An Internal Structure of Carbon and Oxygen Atoms and their Isotopes......Page 301
3. Graphite and Fullerenes......Page 307
4. The Shell-Nodal Structure of Diamond......Page 312
5. The Formation of Bindings in Hydrocarbon Compounds......Page 314
6. Shell-Nodal Structure of Oxygen Compounds......Page 319
7. Intra-Atomic Bindings and the Binding Energy of the Carbon Atom......Page 326
8. Interatomic (Molecular Level) Binding Energies......Page 332
9. Conclusion......Page 333
References......Page 335
Abstract......Page 338
1. Introduction......Page 339
3.1. Choice of the Force Field for Molecular Mechanics Computations......Page 342
3.2. Choice of Subject under Study and Initial Approximation Preparation......Page 343
3.4. Computations by Means of the QM/MM Method......Page 345
3.5. AIM Analysis......Page 348
References......Page 350
Introduction......Page 356
Short Overview of QTAIM......Page 359
Indoles......Page 361
1,3-Azoles......Page 366
Anthocyanidins......Page 370
References......Page 374
Introduction......Page 380
Ferrous-Dioxygen Species......Page 381
Ferric-Peroxo Species......Page 383
Fe(IV)-Oxo and Fe(III)-Oxo Species......Page 385
Non-Oxo Fe(IV) Species......Page 389
Porphyrin Radical-Type Structures......Page 390
Metal-Nitric Oxide Complexes......Page 391
References......Page 395
1. Introduction......Page 400
2. Structural Modelling Procedures......Page 401
3.1. Geometrical and Electronic Structure of the Graphene Nano-Object......Page 403
3.2. Methods of Graphene Preparation......Page 406
3.3. Applications......Page 407
3.5. Topological Defects in Graphene......Page 408
3.6.1. Ideal Graphene......Page 410
 3.6.2. Nano-cones and Nanohorns......Page 411
3.7.1. How the Fullerenes Are Formed......Page 416
3.7.2. Multilayer (Onion-Like) Fullerenes......Page 418
3.7.3. Fullerene Modeling......Page 421
3.8.1. Atomic and Electronic Structure......Page 422
 3.8.2. Properties of the Carbon Nanotubes......Page 425
3.8.3. Modelling the Combination Fullerene Nanotube (nanoBuds) and Nanotube-Nanotube......Page 426
3.9. Exotic Nano-Configurations......Page 430
3.10. Complex Nano-Configurations: Carbon-Chalcogenides......Page 433
3.11. Prospective of the Wealth of Nano-Objects as Revealed by Atomic-Scale Modelling......Page 434
References......Page 435
1.1. Introduction......Page 438
1.2. Cluj Covering Software......Page 439
1.2.3. JSChem......Page 440
2. Cutting Procedures on (4,4) Tessellation......Page 441
2.1. Square (4,4) Lattice......Page 442
2.2. Polyhex (6,3) Covering......Page 443
2.2.1. Topology of Polyhex Tori......Page 445
2.2.2. π-Electronic Structure of Polyhex Tori......Page 447
2.2.3. Identical Polyhex Tori by the Cutting Procedure......Page 448
2.3.1. Bathroom Floor and Pentaheptite Tessellations......Page 449
2.3.2. Phenylenic and Naphthylenic Covering......Page 450
3.1. The Coalescence Process......Page 452
3.2. Isomerization of Peanut Tubulenes......Page 453
3.3. Isomerization of Tubercular Fullerenes......Page 455
3.4. Isomerization of the (6,3) Net......Page 456
3.5. Isomerizations on the ((4,8)3) Net......Page 458
4. Operations on Maps......Page 460
4.1.2. Medial Med.......Page 461
4.1.4. Polygonal Pn Mapping (Diudea 2004)......Page 462
4.2.1. Leapfrog Le.......Page 463
4.2.2. Chamfering Q......Page 465
4.2.3. Septupling Operations on Maps......Page 466
4.3. Generalized Operations on Maps......Page 471
5.1. Operations on Multi-Shell Cages......Page 474
5.2. Operations on Centered Cages......Page 477
5.3. Euler Extended Formula for Multi-Shell Polyhedra......Page 479
5.4.1. 3-Periodic Tiling......Page 483
5.4.2. 2-Periodic Tiling......Page 485
References......Page 486
1.Introduction......Page 492
2.Topological Descriptors and Chemometrics......Page 493
3.1.Graph Entropies Based on Information Functionals......Page 496
4.1.Classical Information Indices......Page 497
4.2.Information Indices Based on Distances......Page 499
5. A Novel Information Functional: Degree-Degree Associations......Page 502
5.1.Numerical Example......Page 505
References......Page 506
1. Introduction......Page 512
2. Definitions......Page 513
3. Edge and Vertex PI Indices of Some Nanostructures......Page 514
Case 2.......Page 515
Result 2......Page 516
Proof......Page 517
4. Edge and Vertex Szeged Indices of Some Nanostructures......Page 521
Result 6......Page 522
Proof......Page 523
Result 8......Page 527
References......Page 529
Introduction......Page 534
2D Lattice Representation of DNA......Page 535
Highly Condensed Representation of DNA......Page 536
Spectral Representation of DNA......Page 537
Graphical Representation of Proteins......Page 538
Protein Distance Matrix......Page 541
Uniform Auxiliary Nomenclature for Proteins......Page 544
Acknowledgments......Page 545
References......Page 546
Abstract......Page 552
1. Introduction......Page 553
2.1. Scalar (Dot) Product Basics......Page 555
2.2. Basic Statistical Indices......Page 556
2.3. Linear Correlation......Page 562
2.4. Correlation by Normal Distribution Function......Page 565
2.5. Multilinear Correlation......Page 569
3.1. Multivariate Spectral Regression on Hilbert Space......Page 574
Step 1......Page 575
Step 3......Page 576
3.2. Algebraic Correlation Factor......Page 581
3.3. Algebraic vs. Statistic Correlations......Page 582
3.4. Spectral-SAR for Ionic Liquids......Page 584
4. Spectral-SAR Paths and Quantum-SAR Maps......Page 586
Family 2......Page 587
Family 3......Page 588
5. Conclusion......Page 591
Acknowledgments......Page 592
References......Page 593
Abstract......Page 602
1. Plots of Fitted and Experimental Values in MLR Studies......Page 603
2. An Alternative: Orthogonal Regression......Page 605
3.1. Some Probability Considerations......Page 606
3.3. The Result Obtained......Page 607
3.4. Enrichment Factors and Probability Mean: Utility and Difficulty......Page 609
4. ROC Curves......Page 610
5. Pharmacological-Activity Distribution Diagrams......Page 614
References......Page 617
1. Introduction......Page 620
2. Fuzzy Sets and Rules......Page 623
3. Medicinal Chemistry and FLT......Page 624
4. Fuzzy Clustering Methods......Page 625
5. Fuzzy ARTMAP Neural Networks......Page 628
6. Ontogenic Neuro-Fuzzy Algorithm: FCID3......Page 629
7. Prediction of Mixture Toxicities Based on a Fuzzy Set Method......Page 630
8. Robust Fuzzy Mappings in QSAR......Page 631
9. ANFIS: Adaptive Neuro-Fuzzy Inference System......Page 632
10. Fuzzy Regression in QSAR......Page 634
11. Conclusion......Page 635
List of Abbreviations......Page 636
References......Page 637
Abstract......Page 642
1. Introduction......Page 643
2. Statistical Methods......Page 645
3.1. Introduction......Page 647
3.3. Molecular Van Der Waals Volume......Page 649
3.4. Molecular Van Der Waals Surface......Page 650
3.5. Molecular Van Der Waals Compressibility Descriptors......Page 652
3.6. Molecular Van Der Waals Ovality Descriptors......Page 654
4.1. Introduction......Page 656
4.2. Brief Review of Several Topological Distance Indices......Page 657
(C) Platt Index......Page 658
(D) Balaban Index......Page 659
4.3. Generalized Topological Distance Indices......Page 660
5.1. Introduction......Page 664
5.2. Modeling of Alcohol Toxicity with Van Der Waals Molecular Descriptors......Page 665
5.3. Alcohol Toxicity Modeling with the Topological Descriptors GTRDIs......Page 669
6. GTDIS versus VDW MDS......Page 673
7. Conclusion......Page 674
References......Page 676
INDEX......Page 682