Ideas of quantum chemistry:
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| Format: | Buch |
| Sprache: | English |
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Elsevier
2014
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| Ausgabe: | 2. ed. |
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| Beschreibung: | XXXV, 1037 S. Ill., graph. Darst. 24 cm |
| ISBN: | 9780444594365 |
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| 245 | 1 | 0 | |a Ideas of quantum chemistry |c by Lucjan Piela |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Amsterdam [u.a.] |b Elsevier |c 2014 | |
| 300 | |a XXXV, 1037 S. |b Ill., graph. Darst. |c 24 cm | ||
| 336 | |b txt |2 rdacontent | ||
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Datensatz im Suchindex
| _version_ | 1804151785263202304 |
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| adam_text | Titel: Ideas of quantum chemistry
Autor: Piela, Lucjan
Jahr: 2014
Contents
Sources of Photographs and Figures.....................................................................xxi
Introduction....................................................................................................xxiii
Chapter 1: The Magjc of Quantum Mechanics.......................................................1
1.1 History of a Revolution........................................................................................3
1.2 Postulates of Quantum Mechanics.....................................................................15
1.3 The Heisenberg Uncertainty Principle...............................................................35
1.4 The Copenhagen Interpretation of the World.....................................................40
1.5 Disproving the Heisenberg Principle-Einstein-Podolsky-Rosen s Recipe........40
1.6 Schrödinger s Cat...............................................................................................42
1.7 Bilocation...........................................................................................................43
1.8 The Magic of Erasing the Past...........................................................................46
1.9 A Test for a Common Sense: The Bell Inequality.............................................47
1.10 Photons Violate the Bell Inequality....................................................................50
1.11 Teleportation......................................................................................................51
1.12 Quantum Computing..........................................................................................53
Chapter 2: The Schrödinger Equation.................................................................61
2.1 Symmetry of the Hamiltonian and Its Consequences........................................63
2.1.1 TTie Non-Relativistic Hamiltonian and Conservation Laws......................63
2.1.2 Invariance with Respect to Translation......................................................68
2.1.3 Invariance with Respect to Rotation..........................................................69
2.1.4 Invariance with Respect to Permutation of Identical Particles
(Fermions and Bosons)..............................................................................71
2.1.5 Invariance of the Total Charge...................................................................71
2.1.6 Fundamental and Less Fundamental Invariances......................................71
2.1.7 Invariance with Respect to Inversion-Parity.............................................72
2.1.8 Invariance with Respect to Charge Conjugation........................................76
2.1.9 Invariance with Respect to the Symmetry of the Nuclear Framework......76
2.1.10 Conservation of Total Spin........................................................................76
2.1.11 Indices of Spectroscopic States.................................................................77
2.2 Schrödinger Equation for Stationary States.......................................................77
2.2.1 Wave Functions of Class Q........................................................................80
2.2.2 Boundary Conditions.................................................................................81
2.3 The Time-Dependent Schrödinger Equation.....................................................84
2.3.1 Evolution in Time......................................................................................85
2.3.2 Time Dependence of Mechanical Quantities.............................................86
2.3.3 Energy Is Conserved..................................................................................87
2.3.4 Symmetry Is Conserved.............................................................................87
2.3.5 Meditations at a Spring..............................................................................89
2.3.6 Linearity.....................................................................................................90
2.4 Evolution After Switching a Perturbation..........................................................90
2.4.1 The Two-State Model-Time-Independent Perturbation............................91
2.4.2 Two States-Degeneracy.............................................................................92
2.4.3 The Two-State Model - An Oscillating Perturbation.................................93
2.4.4 Two States-Resonance Case......................................................................93
2.4.5 Short-Time Perturbation-The First-Order Approach.................................94
2.4.6 Time-Independent Perturbation and the Fermi Golden Rule.....................95
2.4.7 The Most Important Case: Periodic Perturbation......................................97
Chapter 3: Beyond the Schrödinger Equation.....................................................103
3.1 A Glimpse of Classical Relativity Theory.......................................................106
3.1.1 The Vanishing of Apparent Forces...........................................................106
3.1.2 The Galilean Transformation...................................................................110
3.1.3 The Michelson-Morley Experiment.........................................................111
3.1.4 The Galilean Transformation Crashes.....................................................112
3.1.5 The Lorentz Transformation....................................................................113
3.1.6 New Law of Adding Velocities................................................................116
3.1.7 The Minkowski Space-Time Continuum.................................................117
3.1.8 How Do We Get E==mc2 ?.......................................................................120
3.2 Toward Relativistic Quantum Mechanics........................................................122
3.3 The Dirac Equation..........................................................................................124
3.3.1 The Dirac Electronic Sea and the Day of Glory......................................124
3.3.2 The Dirac Equations for Electrons and Positrons....................................128
3.3.3 Spinors and Bispinors..............................................................................128
3.3.4 What Next?..............................................................................................130
3.3.5 Large and Small Components of the Bispinor.........................................130
3.3.6 How to Avoid Drowning in the Dirac Sea...............................................131
3.3.7 From Dirac to Schrödinger-How Is the Non-Relativistic
Hamiltonian Derived?..............................................................................132
3.3.8 How Does the Spin Appear?....................................................................133
3.3.9 Simple Questions.....................................................................................135
3.4 The Hydrogen-like Atom in Dirac Theory.......................................................135
3.4.1 Step by Step: Calculation of the Hydrogen-Like Atom Ground
State Within Dirac Theory.......................................................................136
3.5 Toward Larger Systems....................................................................................141
3.5.1 Non-Interacting Dirac Electrons..............................................................142
3.5.2 Dirac-Coulomb (DC) Model....................................................................143
3.6 Beyond the Dirac Equation..............................................................................145
3.6.1 The Breit Equation...................................................................................146
3.6.2 About QED..............................................................................................148
Chapter 4: Exact Solutions-Our Beacons..........................................................159
4.1 Free Particle.....................................................................................................161
4.2 Box with Ends..................................................................................................162
4.3 Cyclic Box.......................................................................................................167
4.3.1 Comparison of Two Boxes: Hexatriene and Benzene.............................168
4.4 Carbon Nanotubes............................................................................................170
4.5 Single Barrier...................................................................................................174
4.5.1 Ttonneling Effect Below the Barrier Height.............................................174
4.5.2 Surprises for Energies Larger than the Barrier........................................178
4.6 The Magic of Two Barriers..............................................................................181
4.6.1 Magic Energetic Gates (Resonance States).............................................181
4.6.2 Strange Flight Over the Barriers..............................................................185
4.7 Harmonic Oscillator.........................................................................................186
4.8 Morse Oscillator...............................................................................................192
4.8.1 Morse Potential........................................................................................192
4.9 Rigid Rotator....................................................................................................199
4.10 Hydrogen-Like Atom.......................................................................................201
4.10.1 Positronium and Its Short Life...in Molecules.........................................208
4.11 What Do All These Solutions Have in Common?...........................................211
4.12 Hooke Helium Atom (Harmonium).................................................................212
4.13 Hooke Molecules.............................................................................................213
4.14 Charming SUSY and New Solutions...............................................................217
4.14.1 SUSY Partners.........................................................................................218
4.14.2 Relation Between the SUSY Partners......................................................219
4.15 Beacons and Pearls of Physics.........................................................................224
Chapter 5: Two Fundamental Approximate Methods..........................................231
5.1 Variational Method...........................................................................................232
5.1.1 Variational Principle................................................................................232
5.1.2 Variational Parameters.............................................................................236
5.1.3 Linear Variational Parameters or the Ritz Method...................................238
5.2 Perturbational Method.....................................................................................240
5.2.1 Rayleigh-Schrödinger Approach.............................................................240
5.2.2 Hylleraas Variational Principle................................................................246
5.2.3 Hylleraas Equation...................................................................................247
5.2.4 Degeneracy..............................................................................................248
5.2.5 Convergence of the Perturbational Series................................................249
Chapter 6: Separation of Electronic and Nuclear Motions...................................257
6.1 Separation of the Center-of-Mass Motion.......................................................261
6.2 Exact (Non-Adiabatic) Theory.........................................................................265
6.3 Adiabatic Approximation.................................................................................268
6.4 Bom-Oppenheimer Approximation.................................................................269
6.5 Vibrations of a Rotating Molecule...................................................................271
6.5.1 One More Analogy..................................................................................273
6.5.2 What Vibrates, What Rotates?.................................................................274
6.5.3 The Fundamental Character of the Adiabatic Approximation-PES........276
6.6 Basic Principles of Electronic, Vibrational, and Rotational Spectroscopy......278
6.6.1 Vibrational Structure................................................................................278
6.6.2 Rotational Structure.................................................................................279
6.7 Approximate Separation of Rotations and Vibrations.....................................281
6.8 Understanding the IR Spectrum: HCl..............................................................282
6.8.1 Selection Rules........................................................................................282
6.8.2 Microwave Spectrum Gives the Intemuclear Distance............................285
6.8.3 IR Spectrum and Isotopic Effect..............................................................285
6.8.4 IR Spectrum gives the Intemuclear Distance...........................................286
6.8.5 Why We Have a Spectrum Envelope ....................................................287
6.8.6 Intensity of Isotopomers Peaks...............................................................287
6.9 A Quasi-Harmonic Approximation..................................................................287
6.10 Polyatomic Molecule.......................................................................................289
6.10.1 Kinetic Energy Expression......................................................................289
6.10.2 Quasi-Rigid Model-Simplifying by Eckart Conditions..........................291
6.10.3 Approximation: Decoupling of Rotation and Vibration..........................293
6.10.4 Spherical, Symmetric, and Asymmetric Tops..........................................293
6.10.5 Separation of Translational, Rotational, and Vibrational Motions..........295
6.11 Types of States.................................................................................................296
6.11.1 Repulsive Potential..................................................................................296
6.11.2 Hook-like Curves.................................................................................296
6.11.3 Continuum...............................................................................................297
6.11.4 Wave Function Measurement ...............................................................301
6.12 Adiabatic, Diabatic, and Non-adiabatic Approaches.......................................302
6.13 Crossing of Potential Energy Curves for Diatomics........................................305
6.13.1 The Non-crossing Rule............................................................................305
6.13.2 Simulating the Harpooning Effect in the NaCl Molecule........................307
6.14 Polyatomic Molecules and Conical Intersection..............................................310
6.14.1 Branching Space and Seam Space...........................................................311
6.14.2 Conical Intersection.................................................................................312
6.14.3 Berry Phase..............................................................................................314
6.15 Beyond the Adiabatic Approximation..............................................................318
6.15.1 Vibronic Coupling...................................................................................318
6.15.2 Consequences for the Quest of Superconductors....................................322
6.15.3 Photostability of Proteins and DNA........................................................325
6.15.4 Muon-Catalyzed Nuclear Fusion.............................................................327
6.15.5 Russian Dolls, or a Molecule Within Molecule....................................329
Chapter 7: Motion of Nuclei............................................................................337
7.1 Rovibrational Spectra-An Example of Accurate Calculations:
Atom-Diatomic Molecule...............................................................................340
7.1.1 Coordinate System and Hamiltonian.......................................................341
7.1.2 Anisotropy of the Potential V..................................................................342
7.1.3 Adding the Angular Momenta in Quantum Mechanics...........................343
7.1.4 Application of the Ritz Method...............................................................344
7.2 Force Fields (FF)..............................................................................................345
7.3 Local Molecular Mechanics (MM)..................................................................349
7.3.1 Bonds That Cannot Break........................................................................349
7.3.2 Bonds That Can Break.............................................................................352
7.4 Global Molecular Mechanics...........................................................................352
7.4.1 Multiple Minima Catastrophe..................................................................352
7.4.2 Does the Global Minimum Count?..........................................................353
7.5 Small Amplitude Harmonic Motion-Normal Modes......................................355
7.5.1 Theory of Normal Modes........................................................................355
7.5.2 Zero-Vibration Energy.............................................................................364
7.6 Molecular Dynamics (MD)..............................................................................364
7.6.1 What Does MD Offer Us?.......................................................................366
7.6.2 What Should We Wony About?...............................................................367
7.6.3 MD of Non-equilibrium Processes..........................................................368
7.6.4 Quantum-Classical MD...........................................................................368
7.7 Simulated Annealing........................................................................................370
7.8 Langevin Dynamics.........................................................................................371
7.9 Monte Carlo Dynamics....................................................................................371
7.10 Car-Parrinello Dynamics..................................................................................377
7.11 Cellular Automata............................................................................................381
Chapter 8: Orbital Model of Electronic Motion in Atoms and Molecules...............389
8.1 Hartree-Fock Method-A Bird s-Eye View......................................................393
8.1.1 Spinorbitals as the One-Electron Building Blocks..................................394
8.1.2 Variables..................................................................................................395
8.1.3 Slater Determinant-An Antisymmetric Stamp........................................396
8.1.4 What Is the Hartree-Fock Method All About?.........................................398
8.2 Toward the Optimal Spinorbitals and the Fock Equation................................399
8.2.1 Dirac Notation for Integrals.....................................................................399
8.2.2 Energy Functional to Be Minimized........................................................400
8.2.3 Energy Minimization with Constraints....................................................401
8.2.4 Slater Determinant Subject to a Unitary Transformation........................404
8.2.5 The J and KOperators Are Invariant........................................................406
8.2.6 Diagonalization of the Lagrange Multipliers...........................................406
8.2.7 Optimal Spinorbitals Are Solutions of the Fock Equation
(General Hartree-Fock Method)..............................................................407
8.2.8 Unrestricted Hartree-Fock (UHF) Method...........................................408
8.2.9 The Closed-Shell Systems and the Restricted Hartree-Fock
(RHF) Method.........................................................................................408
8.2.10 Iterative Solution: The Self-Consistent Field Method.............................417
8.3 Total Energy in the Hartree-Fock Method.......................................................418
8.4 Computational Technique: Atomic Orbitals as Building Blocks
of the Molecular Wave Function......................................................................420
8.4.1 Centering of the Atomic Orbital..............................................................422
8.4.2 Slater-type Orbitals (STOs)....................................................................423
8.4.3 Gaussian-type Orbitals (GTOs)..............................................................423
8.4.4 Linear Combination of the Atomic Orbitals (LCAO) Method................427
8.4.5 Basis Sets of Atomic Orbitals..................................................................431
8.4.6 The Hartree-Fock-Roothaan Method (SCF LCAO MO).........................431
8.4.7 Some Practical Problems.........................................................................434
8.5 Back to the Basics............................................................................................437
8.5.1 When Does the RHF Method Fail?..........................................................437
8.5.2 Fukutome Classes....................................................................................440
RESULTS OF THE HARTREE-FOCK METHOD..................................................446
8.6 Mendeleev Periodic Table................................................................................446
8.6.1 Similar to the Hydrogen Atom-The Orbital Model of an Atom..............446
8.6.2 Shells and Subshells................................................................................448
8.6.3 Educated Guess of Atomic Orbitals-The Slater Rules............................451
8.7 The Nature of the Chemical Bond...................................................................451
8.7.1 The Simplest Chemical Bond: H+2 in the MO Picture..............................452
8.7.2 Can We See a Chemical Bond?...............................................................456
8.8 Excitation Energy, Ionization Potential, and Electron Affinity
(RHF Approach)...............................................................................................458
8.8.1 Approximate Energies of Electronic States.............................................458
8.8.2 Singlet or Triplet Excitation?...................................................................460
8.8.3 Hund s Rules............................................................................................460
8.8.4 Hund s Rules for the Atomic Terms........................................................462
8.8.5 Ionization Potential and Electron Affinity (Koopmans s Theorem)........465
8.9 Toward Chemical Picture-Localization of MOs..............................................467
8.9.1 Can a Chemical Bond Be Defined in a Polyatomic Molecule?...............468
8.9.2 The External Localization Methods.........................................................469
8.9.3 The Internal Localization Methods..........................................................470
8.9.4 Examples of Localization........................................................................471
8.9.5 Localization in Practice-Computational Technique................................473
8.9.6 The Chemical Bonds of a, it, 8 Symmetry.............................................474
8.9.7 Electron Pair Dimensions and the Foundations of Chemistry.................475
8.9.8 Hybridization or Mixing One-Center AOs..............................................479
8.10 A Minimal Model of a Molecule.....................................................................489
8.11 Valence Shell Electron Pair Repulsion (VSEPR) Algorithm...........................491
8.12 The Isolobal Analogy.......................................................................................496
Chapter 9: Orbital Model of Electronic Motion in Periodic Systems......................505
9.1 Primitive Lattice...............................................................................................508
9.2 Wave Vector.....................................................................................................510
9.3 Inverse Lattice..................................................................................................513
9.4 First Brillouin Zone (FBZ)...............................................................................516
9.5 Properties of the FBZ.......................................................................................516
9.6 A Few Words on Bloch Functions...................................................................517
9.6.1 Waves in 1-D............................................................................................517
9.6.2 Waves in 2-D............................................................................................520
9.7 Infinite Crystal as a Limit of a Cyclic System.................................................523
9.7.1 Origin of the Band Structure....................................................................523
9.7.2 Bom-von Kérmân Condition in 1-D.......................................................524
9.7.3 ^-Dependence of Orbital Energy.............................................................526
9.8 A Triple Role of the Wave Vector....................................................................526
9.9 Band Structure.................................................................................................527
9.9.1 Bom-von Kârmân Boundary Condition in 3-D......................................527
9.9.2 Crystal Orbitals from Bloch Functions (LCAO CO Method).................528
9.9.3 SCF LCAO CO Equations.......................................................................531
9.9.4 Bandwidth................................................................................................532
9.9.5 Fermi Level and Energy Gap: Insulators, Metals,
and Semiconductors.................................................................................533
9.10 Solid-State Quantum Chemistry......................................................................539
9.10.1 Why Do Some Bands Go Up?.................................................................539
9.10.2 Why Do Some Bands Go Down?............................................................540
9.10.3 Why Do Some Bands Stay Constant?.....................................................541
9.10.4 More Complex Behavior Explainable-Examples....................................541
9.11 The Hartree-Fock Method for Crystals............................................................548
9.11.1 Secular Equation......................................................................................548
9.11.2 Integration in the FBZ..............................................................................549
9.11.3 Fock Matrix Elements..............................................................................550
9.11.4 Iterative Procedure (SCF LCAO CO)......................................................551
9.11.5 Total Energy.............................................................................................552
9.12 Long-Range Interaction Problem.....................................................................553
9.12.1 Fock Matrix Corrections..........................................................................554
9.12.2 Total Energy Corrections.........................................................................555
9.12.3 Multipole Expansion Applied to the Fock Matrix...................................557
9.12.4 Multipole Expansion Applied to the Total Energy..................................561
9.13 Back to the Exchange Term.............................................................................563
9.14 Choice of Unit Cell..........................................................................................565
9.14.1 Field Compensation Method....................................................................568
9.14.2 The Symmetry of Subsystem Choice......................................................570
Chapter 10: Correlation of the Electronic Motions............................................577
VARIATIONAL METHODS USING EXPLICITLY CORRELATED
WAVE FUNCTION.......................................................................................................584
10.1 Correlation Cusp Condition.............................................................................5 84
10.2 The Hylleraas CI Method.................................................................................587
10.3 Two-Electron Systems.....................................................................................589
10.3.1 The Harmonic Helium Atom...................................................................589
10.3.2 The James-Coolidge and Kolos-Wolniewicz Functions..........................590
10.3.3 Neutrino Mass..........................................................................................593
10.4 Exponentially Correlated Gaussian Functions.................................................594
10.5 Electron Holes..................................................................................................595
10.5.1 Coulomb Hole (Correlation Hole)...........................................................595
10.5.2 Exchange Hole (Fermi Hole)...................................................................597
VARIATIONAL METHODS WITH SLATER DETERMINANTS.........................602
10.6 Static Electron Correlation...............................................................................602
10.7 Dynamic Electron Correlation.........................................................................602
10.8 Anticorrelation, or Do Electrons Stick Together in Some States?...................608
10.9 Valence Bond (VB) Method.............................................................................610
10.9.1 Resonance Theory-Hydrogen Molecule.................................................610
10.9.2 Resonance Theory-Polyatomic Case.......................................................612
10.10 Configuration Interaction (CI) Method............................................................615
10.10.1 Brillouin Theorem....................................................................................617
10.10.2 Convergence of the CI Expansion...........................................................618
10.10.3 Example of H2O.......................................................................................618
10.10.4 Which Excitations Are Most Important?.................................................620
10.10.5 Natural Orbitals (NOs)............................................................................621
10.10.6 Size Inconsistency of the CI Expansion..................................................622
10.11 Direct CI Method.............................................................................................622
10.12 Multireference CI Method...............................................................................623
10.13 Multiconfigurational Self-Consistent Field Method (MC SCF)......................624
10.13.1 Classical MC SCF Approach...................................................................625
10.13.2 Unitary MC SCF Method........................................................................626
10.14 Complete Active Space SCF (CAS SCF) Method...........................................628
NON-VARIATIONAL METHOD WITH SLATER DETERMINANTS.................629
10.15 Coupled Cluster (CC) Method.........................................................................629
10.15.1 Wave and Cluster Operators....................................................................630
10.15.2 Relationship Between CI and CC Methods.............................................632
10.15.3 Solution of the CC Equations..................................................................633
10.15.4 Example: CC with Double Excitations....................................................635
10.15.5 Size Consistency of the CC Method........................................................637
10.16 Equation-of-Motion Coupled Cluster (EOM-CC) Method..............................638
10.16.1 Similarity Transformation........................................................................638
10.16.2 Derivation of the EOM-CC Equations.....................................................638
10.17 Many-body Perturbation Theory (MBPT).......................................................641
10.17.1 Unperturbed Hamiltonian........................................................................641
10.17.2 Perturbation Theory-Slightly Different Presentation..............................642
10.17.3 MBPT Machinery-Part 1: Energy Equation............................................643
10.17.4 MBPT Machinery-Part 2: Wave Function Equation...............................645
10.17.5 Brillouin-Wigner Perturbation Theory....................................................647
10.17.6 Rayleigh-Schrödinger Perturbation Theory.............................................647
10.18 M0ller-Plesset Version of Rayleigh-Schrödinger Perturbation Theory...........648
10.18.1 Expression for MP2 Energy.....................................................................649
10.18.2 Is the MP2 Method Size Consistent?.......................................................651
10.18.3 Convergence of the Mpller-Plesset Perturbation Series...........................652
10.18.4 Special Status of Double Excitations.......................................................653
Chapter 11: Chasing Correlation Dragon: Density Functional Theory (DFT ).......663
11.1 Electronic Density-The Superstar...................................................................665
11.2 Electron Density Distributions- Bader Analysis..............................................667
11.2.1 Overall Shape of p...................................................................................667
11.2.2 Critical Points..........................................................................................669
11.2.3 Laplacian of the Electronic Density as a Magnifying Glass ................672
11.3 Two Important Hohenberg-Kohn Theorems....................................................675
11.3.1 Correlation Dragon Resides in Electron Density:
Equivalence of ^and p0..........................................................................675
11.3.2 A Secret of the Correlation Dragon: The Existence of
Energy Functional Minimized by p0........................................................677
11.4 The Kohn-Sham Equations..............................................................................680
11.4.1 A Kohn-Sham System of Non-interacting Electrons...............................680
11.4.2 Chasing the Correlation Dragon into an Unknown Part of the
Total Energy.............................................................................................681
11.4.3 Derivation of the Kohn-Sham Equations.................................................683
11.5 Trying to Guess the Appearance of the Correlation Dragon............................687
11.5.1 Local Density Approximation (LDA)......................................................687
11.5.2 Non-local Approximation (NLDA)..........................................................688
11.5.3 The Approximate Character of the DFT vs. the Apparent Rigor
of Ab Initio Computations.......................................................................689
11.6 On the Physical Justification for the Exchange-Correlation Energy................690
11.6.1 The Electron Pair Distribution Function..................................................690
11.6.2 Adiabatic Connection: From What Is Known Towards the Target..........691
11.6.3 Exchange-Correlation Energy vs. fjaver...................................................694
11.6.4 The Correlation Dragon Hides in the Exchange-Correlation Hole.........695
11.6.5 Electron Holes in Spin Resolution...........................................................695
11.6.6 The Dragon s Ultimate Hideout: The Correlation Hole..........................697
11.6.7 Physical Grounds for the DFT Functional.............................................700
11.7 Visualization of Electron Pairs: Electron Localization Function (ELF)..........701
11.8 The DFT Excited States...................................................................................705
11.9 The Hunted Correlation Dragon Before Our Eyes..........................................706
Chapter 12: The Molecule Subject to the Electric or Magnetic Field....................719
12.1 Hellmann-Feynman Theorem..........................................................................722
ELECTRIC PHENOMENA.........................................................................................724
12.2 The Molecule Immobilized in an Electric Field..............................................724
12.2.1 The Electric Field as a Perturbation.........................................................726
12.2.2 The Homogeneous Electric Field............................................................731
12.2.3 The Non-Homogeneous Electric Field: Multipole
Polarizabilities and Hyperpolarizabilities................................................738
12.3 How to Calculate the Dipole Moment.............................................................740
12.3.1 Coordinate System Dependence..............................................................740
12.3.2 Hartree-Fock Approximation...................................................................741
12.3.3 Atomic and Bond Dipoles.......................................................................741
12.3.4 Within the ZDO Approximation..............................................................743
12.4 How to Calculate the Dipole Polarizability.....................................................743
12.4.1 Sum Over States Method (SOS)..............................................................743
12.4.2 Finite Field Method.................................................................................746
12.4.3 What Is Going on at Higher Electric Fields?...........................................751
12.5 A Molecule in an Oscillating Electric Field....................................................752
MAGNETIC PHENOMENA.......................................................................................755
12.6 Magnetic Dipole Moments of Elementary Particles........................................755
12.6.1 Electron....................................................................................................755
12.6.2 Nucleus....................................................................................................757
12.6.3 Dipole Moment in the Field.....................................................................758
12.7 NMR Spectra-Transitions Between the Nuclear Quantum States...................761
12.8 Hamiltonian of the System in the Electromagnetic Field................................762
12.8.1 Choice of the Vector and Scalar Potentials..............................................763
12.8.2 Refinement of the Hamiltonian................................................................763
12.9 Effective NMR Hamiltonian............................................................................767
12.9.1 Signal Averaging......................................................................................767
12.9.2 Empirical Hamiltonian.............................................................................768
12.9.3 Nuclear Spin Energy Levels....................................................................772
12.10 The Ramsey Theory of the NMR Chemical Shift............................................778
12.10.1 Shielding Constants.................................................................................779
12.10.2 Diamagnetic and Paramagnetic Contributions.........................................780
12.11 The Ramsey Theory of the NMR Spin-Spin Coupling Constants...................781
12.11.1 Diamagnetic Contributions......................................................................781
12.11.2 Paramagnetic Contributions.....................................................................782
12.11.3 Coupling Constants..................................................................................783
12.11.4 The Fermi Contact Coupling Mechanism................................................784
12.12 Gauge-Invariant Atomic Orbitals (GIAOs)......................................................785
12.12.1 London Orbitals.......................................................................................786
12.12.2 Integrals Are Invariant.............................................................................787
Chapter 13: Intermodular Interactions..........................................................793
INTERMOLECULAR INTERACTIONS (THEORY).............................................796
13.1 Idea of the Rigid Interaction Energy................................................................797
13.2 Idea of the Internal Relaxation.........................................................................797
13.3 Interacting Subsystems....................................................................................798
13.3.1 Natural Division.......................................................................................798
13.3.2 What Is Most Natural?.............................................................................799
13.4 Binding Energy................................................................................................800
13.5 Dissociation Energy.........................................................................................801
13.6 Dissociation Barrier.........................................................................................801
13.7 Supermolecular Approach................................................................................802
13.7.1 Accuracy Should Be the Same.................................................................802
13.7.2 Basis Set Superposition Error (BSSE)... and the Remedy....................803
13.7.3 Good and Bad News About the Supermolecular Method........................804
13.8 Perturbational Approach..................................................................................805
13.8.1 Intermolecular Distance-What Does It Mean?........................................805
13.8.2 Polarization Approximation (Two Molecules)........................................805
13.8.3 Intermolecular Interaction: Physical Interpretation.................................810
13.8.4 Electrostatic Energy in the Multipole Representation Plus the
Penetration Energy...................................................................................814
13.8.5 Induction Energy in the Multipole Representation..................................820
13.8.6 Dispersion Energy in the Multipole Representation................................822
13.8.7 Dispersion Energy Model-Calculation on Fingers..................................822
13.9 Symmetry Adapted Perturbation Theories (SAPT).........................................827
13.9.1 Polarization Approximation Is Illegal......................................................828
13.9.2 Constructing a Symmetry Adapted Function...........................................828
13.9.3 The Perturbation Is Always Large in Polarization Approximation..........829
13.9.4 Iterative Scheme of SAPT.......................................................................831
13.9.5 Symmetry Forcing...................................................................................835
13.9.6 A Link to the Variational Method-The Heitler-London
Interaction Energy....................................................................................838
13.9.7 Summary: The Main Contributions to the Interaction Energy................839
13.10 Convergence Problems and Padé Approximants.............................................842
13.11 Non-additivity of Intermolecular Interactions.................................................847
13.11.1 Interaction Energy Represents the Non-additivity
of the Total Energy...................................................................................847
13.11.2 Many-body Expansion of the Rigid Interaction Energy..........................848
13.11.3 What Is Additive, and What Is Not?........................................................850
13.11.4 Additivity of the Electrostatic Interaction...............................................850
13.11.5 Exchange Non-additivity.........................................................................851
13.11.6 Induction Non-additivity..........................................................................855
13.11.7 Additivity of the Second-order Dispersion Energy.................................858
13.11.8 Non-additivity of the Third-order Dispersion Interaction.......................859
ENGINEERING OF INTERMOLECULAR INTERACTIONS..............................860
13.12 Idea of Molecular Surface................................................................................860
13.12.1 Van der Waals Atomic Radii....................................................................860
13.12.2 Definition of Molecular Surface..............................................................860
13.12.3 Confining Molecular Space-The Nanovessels........................................860
13.12.4 Molecular Surface Under High Pressure.................................................861
13.13 Decisive Forces................................................................................................862
13.13.1 Distinguished Role of the Valence Repulsion and Electrostatic
Interaction................................................................................................862
13.13.2 Hydrogen Bond........................................................................................863
13.13.3 Coordination Interaction..........................................................................865
13.13.4 Hydrophobic Effect..................................................................................867
13.14 Construction Principles....................................................................................870
13.14.1 Molecular Recognition-Synthons...........................................................870
13.14.2 Key-and-Lock, Template-like, and Hand-Glove
Synthon Interactions................................................................................871
13.14.3 Convex and Concave-The Basics of Strategy in the Nanoscale..............875
Chapter 14: Chemical Reactions.....................................................................883
14.1 Hypersurface of the Potential Energy for Nuclear Motion..............................887
14.1.1 Potential Energy Minima and Saddle Points...........................................888
14.1.2 Distinguished Reaction Coordinate (DRC).............................................890
14.1.3 Steepest Descent Path (SDP)...................................................................891
14.1.4 Higher-Order Saddles..............................................................................891
14.1.5 Our Goal..................................................................................................892
14.2 Chemical Reaction Dynamics (A Pioneers Approach)...................................892
14.3 Accurate Solutions (Three Atoms)...................................................................896
14.3.1 Coordinate System and Hamiltonian.......................................................896
14.3.2 Solution to the Schrödinger Equation......................................................900
14.3.3 Berry Phase..............................................................................................901
14.4 Intrinsic Reaction Coordinate (IRC) or Statics................................................902
14.5 Reaction Path Hamiltonian Method.................................................................905
14.5.1 Energy Close to IRC................................................................................905
14.5.2 Vibrational Adiabatic Approximation......................................................907
14.5.3 Vibrational Non-adiabatic Model............................................................912
14.5.4 Application of the Reaction Path Hamiltonian Method to
the Reaction H2 + OH -» H20 + H........................................................914
14.6 Acceptor-Donor (AD) Theory of Chemical Reactions....................................921
14.6.1 An Electrostatic Preludium-The Maps of the Molecular Potential.........921
14.6.2 A Simple Model of Nucleophilic Substitution-MO, AD, and
VB Formalisms........................................................................................924
14.6.3 MO Picture - AD Picture.......................................................................924
14.6.4 Reaction Stages........................................................................................927
14.6.5 Contributions of the Structures as Reaction Proceeds.............................932
14.6.6 Nucleophilic Attack-The Model is More General:
H + Ethylene -* Ethylene + H~...........................................................936
14.6.7 The Model Looks Even More General: The Electrophilic Attack
H++H2-»H2 + H+.................................................................................938
14.6.8 The Model Also Works for the Nucleophilic Attack on the
Polarized Bond.........................................................................................938
14.7 Symmetry-Allowed and Symmetry-Forbidden Reactions...............................942
14.7.1 Woodward-Hoffmann Symmetry Rules..................................................942
14.7.2 AD Formalism.........................................................................................942
14.7.3 Electrocyclic Reactions............................................................................943
14.7.4 Cycloaddition Reaction...........................................................................944
14.7.5 Barrier Means a Cost of Opening the Closed Shells...............................948
14.8 Barrier for the Electron-Transfer Reaction......................................................949
14.8.1 Diabatic and Adiabatic Potential.............................................................949
14.8.2 Marcus Theory.........................................................................................951
14.8.3 Solvent-Controlled Electron Transfer......................................................955
Chapter 15: Information Processing- The Mission of Chemistry.........................969
15.1 Multilevel Supramolecular Structures (Statics)...............................................972
15.1.1 Complex Systems....................................................................................972
15.1.2 Self-organizing Complex Systems...........................................................973
15.1.3 Cooperative Interactions..........................................................................974
15.1.4 Combinatorial Chemistry-Molecular Libraries.......................................976
15.2 Chemical Feedback-A Steering Element (Dynamics)....................................978
15.2.1 A Link to Mathematics-Attractors..........................................................978
15.2.2 Bifurcations and Chaos............................................................................980
15.2.3 Brusselator Without Diffusion.................................................................982
15.2.4 Brusselator with Diffusion-Dissipative Structures..................................987
15.2.5 Hypercycles.............................................................................................988
15.2.6 From Self-Organization and Complexity to Information........................989
15.3 Information and Informed Matter....................................................................990
15.3.1 Abstract Theory of Information...............................................................990
15.3.2 Teaching Molecules.................................................................................992
15.3.3 Dynamic Information Processing of Chemical Waves............................994
15.3.4 The Mission of Chemistry.....................................................................1002
15.3.5 Molecules as Computer Processors.......................................................1003
Online Appendices
Appendix A : Reminding Matrices and Determinants............................................e 1
Appendix B : A Few Words on Spaces, Vectors, and Functions...............................e7
Appendix C : Croup Theory in Spectroscopy......................................................e 17
Appendix D : A Two-State Model.....................................................................e6S
Appendix E : Dirac Delta Function...................................................................e69
Appendix F : Translation versus Momentum and Rotation versus
Angular Momentum....................................................................e73
Appendix G : Vector and Scalar Potentials........................................................e81
Appendix H : Optimal Wave Function for the Hydrogen-Like Atom......................e91
Appendix I : Space- and Body-Fixed Coordinate Systems....................................e93
Appendix J : Orthogonalization.......................................................................e99
Appendix K : Diagonalization of a Matrix.......................................................e105
Appendix L : Secular Equation (H-eS)c = 0....................................................e107
Appendix M : Slater-Condon Rules..................................................................e109
Appendix N : Lagrange Multipliers Method.....................................................e121
Appendix O : Penalty Function Method...........................................................e127
Appendix P : Molecular Integrals with Gaussian Type Orbitals 1s......................el31
Appendix Q : Singlet and Triplet States for Two Electrons.................................e133
Appendix R : The Hydrogen Molecular Ion in the Simplest Atomic Basis Set.......e137
Appendix S : Population Analysis...................................................................e143
Appendix T : Dipole Moment of a Lone Pair....................................................e149
Appendix U : Second Quantization.................................................................e 153
Appendix V : Hydrogen Atom in Electric Field-The Variational Approach..........e159
Appendix W: NMR Shielding and Coupling Constants—Derivation.....................e163
Appendix X : Multipole Expansion..................................................................e169
Appendix Y : Pauli Deformation....................................................................e183
Appendix Z ; Acceptor-Donor Structure Contributions
in the MO Configuration............................................................e191
Acronyms......................................................................................................1013
Tables............................................................................................................1019
Name Index...................................................................................................1021
Subject Index.................................................................................................1029
|
| any_adam_object | 1 |
| author | Piela, Lucjan 1943- |
| author_GND | (DE-588)1045504769 |
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| discipline | Chemie / Pharmazie |
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| spelling | Piela, Lucjan 1943- Verfasser (DE-588)1045504769 aut Ideas of quantum chemistry by Lucjan Piela 2. ed. Amsterdam [u.a.] Elsevier 2014 XXXV, 1037 S. Ill., graph. Darst. 24 cm txt rdacontent n rdamedia nc rdacarrier Quantenchemie (DE-588)4047979-1 gnd rswk-swf 1\p (DE-588)4123623-3 Lehrbuch gnd-content Quantenchemie (DE-588)4047979-1 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027036878&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
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| title | Ideas of quantum chemistry |
| title_auth | Ideas of quantum chemistry |
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| title_full | Ideas of quantum chemistry by Lucjan Piela |
| title_fullStr | Ideas of quantum chemistry by Lucjan Piela |
| title_full_unstemmed | Ideas of quantum chemistry by Lucjan Piela |
| title_short | Ideas of quantum chemistry |
| title_sort | ideas of quantum chemistry |
| topic | Quantenchemie (DE-588)4047979-1 gnd |
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