The chemical bond: a fundamental quantum-mechanical picture
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2004
|
| Schriftenreihe: | Springer series in chemical physics
76 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Aus dem Japan. übers. |
| Beschreibung: | XV, 206 S. graph. Darst. |
| ISBN: | 3540206388 |
Internformat
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
1 The Electron: A Primadonna in Chemical Bonding ....... 1
1.1 The Electrostatic Potential Felt by the Electron
is Reflected in the Color of Matter....................... 2
1.2 The Electron in a Square Well Potential.................... 3
1.3 The Electron Spin: As Important as the Energy ............ 8
1.4 A Brief History of the Quantum Mechanical Description
of the Electron............................................. 12
1.4.1 The Birth of the Bohr Theory ........................ 12
1.4.2 The Birth of the Schrôdinger Theory.................. 14
2 Fundamentals of Quantum Mechanics:
A Prerequisite for Understanding the Chemical Bond .... 21
2.1 Basic Concepts, Postulates, Definitions and Methodology .... 21
2.1.1 Wavefunction Determines the Probability
of Finding the Electron.............................. 21
2.1.2 Energy Eigenstates are Stationary.................... 22
2.1.3 Any Physical Quantity has a Corresponding Operator
which has its own Set of Eigenfunctions
and Eigenvalues...................................... 24
2.1.4 Operators of Any Physical Quantity are Linear:
Quantum Mechanical States are Superposable........... 24
2.1.5 Eigenfunctions axe Normalizable...................... 25
2.1.6 Superposition of Non-Degenerate States does not
Lead to an Eigenstate................................ 25
2.1.7 Superposition of Degenerate States does Lead
to an Eigenstate..................................... 26
2.1.8 Definition of Hermitian Operators.................... 26
2.1.9 Eigenfunctions of Hermitian Operators are Orthogonal 28
2.1.10 Eigenfunctions of Hermitian Operators are Complete . 29
2.1.11 The Outcome of Observation:
Eigenvalues vs. Expectation Values................... 29
2.1.12 The Product of Two Operators:
Commutators and Simultaneous Eigenfunctions........ 30
2.1.13 Perturbation Method: Non-Degenerate Case............. 31
2.1.14 Perturbation Method: Degenerate Case ................ 34
XII
Contents
2.1.15 Calculus of Variation ............................. 38
2.2 Application of the Concepts Presented in Sect. 2.1
to the Problem of the Square Well Potential................ 41
2.2.1 Normalization of Eigenfunctions...................... 41
2.2.2 Orthogonality of Eigenfunctions...................... 41
2.2.3 Superposition of State: Example 1.................... 42
2.2.4 Superposition of States: Example 2................... 43
2.2.5 Expectation Value of the Energy...................... 44
2.2.6 Superposition of States: Example 3................... 44
2.2.7 An Example of the Perturbation Method:
A Non-Degenerate Case................................ 46
2.2.8 An Example of the Calculus of Variation:
A Non-Degenerate Case................................ 48
3 One-Electron Atoms: The Fundamental System..................... 51
3.1 The Derivation of Energy and Orbital Angular Momentum
of the Electron in a Coulombic Potential: An Outline ..... 52
3.2 The Derivation of the Eigenfunctions and Eigenvalues
of Energy and Orbital Angular Momentum
for a Single Electron in a Coulombic Potential ........... 54
3.2.1 A General Discussion of the Schrödinger Equation .... 54
3.2.2 An Eigenvalue Equation to Describe
the Angular Component (A Digression):
Orbital Angular Momentum Operators
from the View Point of Classical Mechanics.......... 56
3.2.3 The Eigenvalue Equation to Describe
the Angular Component:
Eigenfunctions and Eigenvalues....................... 57
3.2.4 The Eigenvalue Equation to Describe
the Radial Component:
Eigenfunctions and Eigenvalues...................... 59
3.2.5 Total Spatial Eigenfunction of the One-Electron Atom 61
3.3 Some Comments on the Solution for One-Electron Atoms.... 64
3.3.1 Degeneracy of the Spatial Eigenfunctions is n2֊Fold
without the Electron Spin Components,
and is 2n2-Fold with the Electron Spin Included..... 64
3.3.2 Representation of Real Forms
of Spherical Surface Harmonics....................... 65
3.3.3 A Relation between the Angular Dependence
of Spherical Harmonics
and the Orbital Angular Momentum..................... 66
3.3.4 The Radial Potential................................. 68
3.4 Angular Momentum in One-Electron Atoms..................... 70
3.4.1 The Definition of Orbital Angular Momentum
by the Commutative Relationship...................... 70
Contents XIII
3.4.2 The Generalized Angular Momentum................. 72
3.4.3 Eigenfunctions of the Electron Spin.............. 74
3.4.4 Electron Spin Operators.......................... 76
4 Multi-Electron Atoms: The Building Blocks that Produce
the Tremendous Variety of Molecules......................... 79
4.1 A Requirement Imposed on the Energy Eigenfunction
of Multi-Electron Atoms: The Pauli Exclusion Principle. 80
4.2 The Energy of Multi-Electron Atoms:
A Qualitative Consideration and the Concept
of Electronic Shell Structure.......................... 84
4.3 The Angular Momentum of Multi-Electron Atoms:
The Total Angular Momentum as a Physical Quantity
to Characterize the State of Multi-Electron Atoms...... 89
4.3.1 Spin-Orbit Interaction in One-Electron Atoms..... 90
4.3.2 Couplings of Orbital Angular Momentum
and Spin in Multi-Electron Atoms:
Russell-Saunders Coupling........................ 93
4.3.3 Coupled Angular Momentum
of Multi-Electron Atoms (Case 1):
Concrete Examples of the Procedure of Coupling... 95
4.3.4 Coupled Angular Momentum
of Multi-Electron Atoms (Case 2): Hund’s Rules... 98
4.3.5 Electronic Configuration in Atoms and Valence States. 100
4.4 An Example of the Solution of Multi-Electron Atoms
by the Hartree-Fock Method: For the Case of Ne.........103
5 Born-Oppenheimer Approximation:
Separation of Electronic Motion
from Nuclear Motion in Chemical Bonding.....................107
6 The Hydrogen Molecular Ion:
The Simplest, but the Most Fundamental System
for Understanding Chemical Bonds............................113
6.1 The Stability of the Ion (Explanation 1):
Explanation by Invoking the Wave Packet of the Electron ... 114
6.1.1 The Eigenfunction of the Ion
with the Proper Symmetry ..............-.........115
6.1.2 The Motion of the Wave Packet of the Electron in Hj 120
6.2 The Stability of the Ion (Explanation 2):
Qualitative Explanation in Terms
of the Uncertainty Principle ..........................123
6.3 The Stability of the Ion (Explanation 3):
An Explanation in Terms of the LCAO-MO Method..........124
XIV Contents
6.3.1 Determination of the LCAO-MO of H2
by the Use of Symmetry............................125
6.3.2 Determination of the LCAO-MO of H2
by Ritz’s Calculus of Variation...................126
6.3.3 Coulomb Integral and the Exchange Integral
of the Hj System...................................128
6.4 A Few Topics of Study in the H2 System................. 130
7 The Hydrogen Molecule:
Why are Two Neutral Hydrogen Atoms Stabilized
by Simply Approaching Each Other? ............................133
7.1 It is Spectroscopic Experiments on the H2 Molecule that
have Paved the Way to Quantum Chemical Theory...........134
7.2 The Heitler-London Theory................................136
7.2.1 Eigenfunctions and Eigenvalues of Energy Ignoring
the Effect of the Electron Spin...................136
7.2.2 Eigenfunctions and Eigenvalues Inclusive
of the Electron Spin...............................140
7.3 Development of the Heitler-London Theory................144
7.4 Molecular Orbital Treatments of the Hydrogen Molecule...146
8 Polyatomic Molecules: Towards an Understanding
of Chemical Bonds in Polyatomic Molecules.....................149
8.1 The Schrödinger Equation for Multi-Electron Systems
and its Approximate Solution.............................150
8.1.1 Outline of the Hartree-Fock Method to Include
the Interelectronic Interaction.................. 150
8.1.2 A Practical Solution to the Problem
of Interelectronic Interaction:
The Hartree-Fock-Roothaan Method...................158
8.2 Examples of SCF-MO Calculations and Comparisons
with Experimental Results................................161
8.2.1 Computation for HF.................................162
8.2.2 Some Comments on Point Groups.................... 165
8.2.3 Computed Orbital Energy as Compared
with Experimental Observation .....................169
8.2.4 The Relationship between Canonical Molecular
Orbitals and Localized Orbitals....................172
8.2.5 A Critical Review of the Hybridized Orbital
of Pauling.........................................175
8.3 Critical Comments on the Classification of Chemical Bonds . . 179
8.3.1 Ionic Bond: NaCl, for Example.................... 180
8.3.2 Ionic Bond: Is the Bonding in HC1 Covalent or Ionic? . 185
8.3.3 Coordinate Bond....................................186
Contents
XV
8.4 Some Topics and Prospects for the Study
of Chemical Bonding......................................187
8.4.1 Why does OFß not Exist,
while SF6 is a Stable Molecule?:
The Discovery of CLi6 as a Relevant Topic ........188
8.4.2 Molecules Comprising Rare Gas Atoms...........190
8.4.3 An Example of a Recent Study
of the Hydrogen Bond ...........................193
8.4.4 Interstellar Molecules............................194
References.......................................................197
Index............................................................203
|
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| illustrated | Illustrated |
| indexdate | 2024-07-09T19:20:35Z |
| institution | BVB |
| isbn | 3540206388 |
| language | English |
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| series | Springer series in chemical physics |
| series2 | Springer series in chemical physics |
| spelling | Shida, Tadamasa Verfasser aut Kagaku ketsugo The chemical bond a fundamental quantum-mechanical picture Tadamasa Shida Berlin [u.a.] Springer 2004 XV, 206 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer series in chemical physics 76 Aus dem Japan. übers. Chemische Bindung - Quantenchemie Chemical bonds Quantenchemie (DE-588)4047979-1 gnd rswk-swf Chemische Bindung (DE-588)4009843-6 gnd rswk-swf Chemische Bindung (DE-588)4009843-6 s Quantenchemie (DE-588)4047979-1 s DE-604 Springer series in chemical physics 76 (DE-604)BV000000670 76 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010626192&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Shida, Tadamasa The chemical bond a fundamental quantum-mechanical picture Springer series in chemical physics Chemische Bindung - Quantenchemie Chemical bonds Quantenchemie (DE-588)4047979-1 gnd Chemische Bindung (DE-588)4009843-6 gnd |
| subject_GND | (DE-588)4047979-1 (DE-588)4009843-6 |
| title | The chemical bond a fundamental quantum-mechanical picture |
| title_alt | Kagaku ketsugo |
| title_auth | The chemical bond a fundamental quantum-mechanical picture |
| title_exact_search | The chemical bond a fundamental quantum-mechanical picture |
| title_full | The chemical bond a fundamental quantum-mechanical picture Tadamasa Shida |
| title_fullStr | The chemical bond a fundamental quantum-mechanical picture Tadamasa Shida |
| title_full_unstemmed | The chemical bond a fundamental quantum-mechanical picture Tadamasa Shida |
| title_short | The chemical bond |
| title_sort | the chemical bond a fundamental quantum mechanical picture |
| title_sub | a fundamental quantum-mechanical picture |
| topic | Chemische Bindung - Quantenchemie Chemical bonds Quantenchemie (DE-588)4047979-1 gnd Chemische Bindung (DE-588)4009843-6 gnd |
| topic_facet | Chemische Bindung - Quantenchemie Chemical bonds Quantenchemie Chemische Bindung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010626192&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000670 |
| work_keys_str_mv | AT shidatadamasa kagakuketsugo AT shidatadamasa thechemicalbondafundamentalquantummechanicalpicture |