Manchester University Physical Chemistry I (CHEM 341)

by Kathy Davis

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Textbook for CHEM 341 at Manchester University (Physical Chemistry I). Foundations of quantum mechanics for describing atomic structure, molecular motion and chemical bonding, with specific applications to spectroscopy and chemical reactivity. Prerequisite(s): CHEM 113 (General Chemistry II), MATH 122 (Calculus II).

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Publisher
Manchester University
Subjects
Chemistry
Licence
CC BY-NC-SA 4.0, as LibreTexts states it. Non-commercial use only.
Who can read
Tweens profiles and older, judged from its title and subjects

Contents

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  1. Welcome!
  2. TitlePage
  3. InfoPage
  4. Table of Contents
  5. Licensing
  6. TitlePage
  7. InfoPage
  8. Table of Contents
  9. 1: Experiments That "Broke" (Classical) Physics
  10. 1.1: Prelude to the Foundations of Quantum Mechanics
  11. 1.2: Blackbody Radiation Cannot Be Explained Classically
  12. 1.3: Quantum Hypothesis used for Blackbody Radiation Law
  13. 1.4: Photoelectric Effect Explained with Quantum Hypothesis
  14. 1.5: Matter Has Wavelike Properties
  15. 1.6: de Broglie Waves can be Experimentally Observed
  16. 1.7: The Wave Properties of Matter
  17. 1.8: The Hydrogen Atomic Spectrum
  18. 1.9: The Rydberg Formula and the Hydrogen Atomic Spectrum
  19. 1.10: The Bohr Theory of the Hydrogen Atom
  20. 2: New Game, New Rules (Postulates of Quantum Mechanics)
  21. 2.1: Introduction to the Schrödinger Equation
  22. 2.2: The One-Dimensional Wave Equation
  23. 2.3: A Classical Wave Equation
  24. 2.4: The Schrödinger Equation
  25. 2.5: Invention of the Schrödinger Equation
  26. 2.6: The Wavefunction Specifies the State of a System
  27. 2.7: Quantum Operators Represent Classical Variables
  28. 2.8: Observable Quantities Must Be Eigenvalues of Quantum Mechanical Operators
  29. 2.9: The Eigenfunctions of Operators are Orthogonal
  30. 2.10: The Time-Dependent Schrödinger Equation
  31. 2.11: Implication of QM Postulates - Uncertainty, Part 1
  32. 2.12: Implication of QM Postulates - Uncertainty, Part 2
  33. 3: First QM System (Particle on a Line/Particle in a Box)
  34. 3.1: The Quantum Mechanical Free Particle
  35. 3.2: The Energy of a Particle in a Box is Quantized
  36. 3.3: The Average Momentum of a Particle in a Box is Zero
  37. 3.4: A Particle in a Two-Dimensional Box
  38. 3.5: A Particle in a Three-Dimensional Box
  39. 3.6: Particle in a Finite Box and Tunneling (optional)
  40. 4: QM for Rotational and Vibrational Motion
  41. 4.1: A Harmonic Oscillator Obeys Hooke's Law
  42. 4.2: The Harmonic Oscillator Wavefunctions involve Hermite Polynomials
  43. 4.3: Hermite Polynomials are either Even or Odd Functions
  44. 4.4: The Harmonic Oscillator Energy Levels
  45. 4.5: The Harmonic Oscillator Approximates Molecular Vibrations
  46. 4.6: The Rigid Rotator is a Model for a Rotating Diatomic Molecule
  47. 4.7: The Wavefunctions of a Rigid Rotator are Called Spherical Harmonics
  48. 4.8: The Energy Levels of a Rigid Rotor
  49. 5: Rotational and Vibrational Spectroscopy
  50. 5.1: The Harmonic Oscillator and Infrared Spectra
  51. 5.2: The Harmonic Oscillator Selection Rule
  52. 5.3: Rotations Accompany Vibrational Transitions
  53. 5.4: The Selection Rule for the Rigid Rotor
  54. 5.5: Unequal Spacings in Vibration-Rotation Spectra
  55. 5.6: Unequal Spacings in Pure Rotational Spectra
  56. 5.7: Vibrational Overtones
  57. 5.8: Normal Modes in Polyatomic Molecules
  58. 5.9: Group Theory Determines Infrared Activity
  59. 6: One-Electron Atoms and Ions
  60. 6.1: The Schrodinger Equation for the Hydrogen Atom Can Be Solved Exactly
  61. 6.2: Hydrogen Atomic Orbitals Depend upon Three Quantum Numbers
  62. 6.3: s-orbitals are Spherically Symmetric
  63. 6.4: Orbital Angular Momentum and the p-Orbitals
  64. 6.5: The Three Components of Angular Momentum Cannot be Measured Simultaneously with Arbitrary Precision
  65. 7: So You Can't Solve the Schrodinger Equation Exactly...What Next? (Approximation Methods)
  66. 7.1: The Helium Atom Cannot Be Solved Exactly
  67. 7.2: The Variational Method Approximation
  68. 7.3: Trial Functions Can Be Linear Combinations of Functions That Also Contain Variational Parameters
  69. 7.4: Perturbation Theory Expresses the Solutions in Terms of Solved Problems
  70. 7.5: Perturbation Theory and the Variational Method for Helium
  71. 7.6: Atomic and Molecular Calculations are Expressed in Atomic Units
  72. 7.7: Hartree-Fock Equations are Solved by the Self-Consistent Field Method
  73. 7.8: An Electron has an Intrinsic Spin Angular Momentum
  74. 7.9: Wavefunctions must be Antisymmetric to Interchange of any Two Electrons
  75. 8: Electronic Spectroscopy
  76. 8.1: Most Molecules Have Excited Electronic States
  77. 8.2: Electronic Spectra Contain Electronic, Vibrational, and Rotational Information
  78. 8.3: The Franck-Condon Principle
  79. 8.4: Term Symbols Gives a Detailed Description of an Electron Configuration
  80. 8.5: The Allowed Values of J - the Total Angular Momentum Quantum Number
  81. 8.6: Hund's Rules Determine the Term Symbols of the Ground Electronic States
  82. 8.7: Using Atomic Term Symbols to Interpret Atomic Spectra
  83. 9: Diatomic Molecules
  84. 9.1: The Born-Oppenheimer Approximation Simplifies the Schrödinger Equation for Molecules
  85. 9.2: The H₂⁺ Prototypical Species
  86. 9.3: The Overlap Integral
  87. 9.4: Chemical Bond Stability
  88. 9.5: Bonding and Antibonding Orbitals
  89. 9.6: A Simple Molecular-Orbital Treatment of H₂ Places Both Electrons in a Bonding Orbital
  90. 9.7: Molecular Orbitals Can Be Ordered According to Their Energies
  91. 9.8: Molecular-Orbital Theory Also Applies to Heteronuclear Diatomic Molecules
  92. 9.9: Molecular Term Symbols Describe Electronic States of Molecules
  93. 9.10: Molecular Term Symbols Designate Symmetry
  94. 10: Polyatomic Molecules
  95. 10.1: Hybrid Orbitals Account for Molecular Shape
  96. 10.2: Hybrid Orbitals in Water
  97. 10.3: BeH₂ is Linear and H₂O is Bent
  98. 10.4: Photoelectron Spectroscopy
  99. 10.5: The pi-Electron Approximation of Conjugation
  100. 10.6: Butadiene is Stabilized by a Delocalization Energy
  101. 10.7: Benzene and Aromaticity
  102. 11: Computational Quantum Chemistry
  103. 11.1: Overview of Quantum Calculations
  104. 11.2: Gaussian Basis Sets
  105. 11.3: Extended Basis Sets
  106. 11.4: Orbital Polarization Terms in Basis Sets
  107. 12: A Quantum Mechanical Approach to Electronic Spectroscopy
  108. 12.1: Quantum Mechanics for Nuclear Motion (Harmonic Oscillator and Rigid Rotor)
  109. Back Matter
  110. Index
  111. Glossary
  112. Detailed Licensing
  113. Detailed Licensing