Lowe John P., Peterson Kirk A. Quantum Chemistry

3rd edition. — Elsevier Academic Press, 2006. - 703 p.
This book is written for courses taught at the first-year graduate/senior undergraduate levels, which accounts for its implicit assumption that many readers will be relatively unfamiliar with much of the mathematics and physics underlying the subject. Our experience over the years has supported this assumption; many chemistry majors are exposed to the requisite mathematics and physics, yet arrive at our courses with poor understanding or recall of those subjects. That makes this course an opportunity for such students to experience the satisfaction of finally seeing how mathematics, physics, and chemistry are intertwined in quantum chemistry. It is for this reason that treatments of the simple and extended Hückel methods continue to appear, even though these are no longer the methods of choice for serious computations.Preface to the Third EditionPreface to the Second EditionPreface to the First EditionClassical Waves and the Time-Independent SchrЁodinger Wave EquationWaves
The ClassicalWave Equation StandingWaves in a Clamped String
Light as an ElectromagneticWave
The Photoelectric Effect
TheWave Nature of Matter
A Diffraction Experiment with Electrons
SchrЁodinger’s Time-IndependentWave Equation
Conditions on ψ
Some Insight into the SchrЁodinger EquationProblems
Multiple Choice QuestionsQuantum Mechanics of Some Simple SystemsThe Particle in a One-Dimensional Box
Detailed Examination of Particle-in-a-Box Solutions
The Particle in a One-Dimensional Box with One Finite Wall
The Particle in an Infinite Box with a Finite Central Barrier
The Free Particle in One Dimension
The Particle in a Ring of Constant Potential
The Particle in a Three-Dimensional Box: Separation of Variables
The Scattering of Particles in One DimensionProblems
Multiple Choice QuestionsThe One-Dimensional Harmonic OscillatorSome Characteristics of the Classical One-Dimensional Harmonic Oscillator
The Quantum-Mechanical Harmonic Oscillator
Solution of the Harmonic Oscillator SchrЁodinger Equation
Quantum-Mechanical Average Value of the Potential Energy
Vibrations of Diatomic MoleculesProblems
Multiple Choice QuestionsThe Hydrogenlike Ion, Angular Momentum, and the Rigid RotorThe SchrЁodinger Equation and the Nature of Its Solutions
Separation of Variables
Solution of the R, Θ, and Ф Equations
Atomic Units
Angular Momentum and Spherical Harmonics
Angular Momentum and Magnetic Moment
Angular Momentum in Molecular Rotation – The Rigid RotorProblems
Multiple Choice QuestionsMany-Electron AtomsThe Independent Electron Approximation
Simple Products and Electron Exchange Symmetry
Electron Spin and the Exclusion Principle
Slater Determinants and the Pauli Principle
Singlet and Triplet States for the 1s2s Configuration of Helium
The Self-Consistent Field, Slater-Type Orbitals, and the Aufbau Principle Electron Angular Momentum in Atoms
Overview
Problems
Multiple Choice QuestionsPostulates and Theorems of Quantum MechanicsTheWavefunction Postulate
The Postulate for Constructing Operators
The Time-Dependent SchrЁodinger Equation Postulate
The Postulate Relating Measured Values to Eigenvalues
The Postulate for Average Values
Hermitian Operators
Proof That Eigenvalues of Hermitian Operators Are Real
Proof That Nondegenerate Eigenfunctions of a Hermitian Operator Form an Orthogonal Set
Demonstration That All Eigenfunctions of a Hermitian Operator May Be Expressed as an Orthonormal Set
Proof That Commuting Operators Have Simultaneous Eigenfunctions
Completeness of Eigenfunctions of a Hermitian Operator
The Variation Principle
The Pauli Exclusion Principle
Measurement, Commutators, and Uncertainty
Time-Dependent StatesProblems
Multiple Choice QuestionsThe Variation MethodThe Spirit of the Method
Nonlinear Variation: The Hydrogen Atom
Nonlinear Variation: The Helium Atom
Linear Variation: The Polarizability of the Hydrogen Atom
Linear Combination of Atomic Orbitals: The H₂⁺ Molecule – Ion
Molecular Orbitals of Homonuclear Diatomic Molecules
Basis Set Choice and the VariationalWavefunction
Beyond the Orbital Approximation
Problems
Multiple Choice QuestionsThe Simple HЁuckel Method and ApplicationsThe Importance of Symmetry
The Assumption of σ–π Separability
The Independent π-Electron Assumption
Setting up the HЁuckel Determinant
Solving the HMO Determinantal Equation for Orbital Energies
Solving for the Molecular Orbitals
The Cyclopropenyl System: Handling Degeneracies
Charge Distributions from HMOs
Some Simplifying Generalizations
HMO Calculations on Some Simple Molecules
Summary: The Simple HMO Method for Hydrocarbons
Relation Between Bond Order and Bond Length
π-Electron Densities and Electron Spin Resonance Hyperfine Splitting Constants
Orbital Energies and Oxidation-Reduction Potentials
Orbital Energies and Ionization Energies
π-Electron Energy and Aromaticity
Extension to Heteroatomic Molecules
Self-Consistent Variations of α and β HMO Reaction Indices Conclusions
Problems
Multiple Choice QuestionsMatrix Formulation of the Linear Variation MethodMatrices and Vectors
Matrix Formulation of the Linear Variation Method
Solving the Matrix EquationProblemsThe Extended HЁuckel MethodThe Extended HЁuckel Method
Mulliken Populations
Extended HЁuckel Energies and Mulliken Populations
Extended HЁuckel Energies and Experimental Energies
ProblemsThe SCF-LCAO-MO Method and ExtensionsAb Initio Calculations
The Molecular Hamiltonian
The Form of theWavefunction
The Nature of the Basis Set
The LCAO-MO-SCF Equation
Interpretation of the LCAO-MO-SCF Eigenvalues
The SCF Total Electronic Energy
Basis Sets
The Hartree–Fock Limit
Correlation Energy
Koopmans’ Theorem
Configuration Interaction
Size Consistency and the Muller–Plesset and Coupled Cluster Treatments of Correlation
Multideterminant Methods
Density Functional Theory Methods
Examples of Ab Initio Calculations
Approximate SCF-MO Methods
ProblemsTime-Independent Rayleigh–SchrЁodinger Perturbation TheoryAn Introductory Example
Formal Development of the Theory for Nondegenerate States
A Uniform Electrostatic Perturbation of an Electron in a Wire
The Ground-State Energy to First-Order of Heliumlike Systems
Perturbation at an Atom in the Simple HЁuckel MO Method
Perturbation Theory for a Degenerate State
Polarizability of the Hydrogen Atom in the n=2 States
Degenerate-Level Perturbation Theory by Inspection
Interaction Between Two Orbitals: An Important Chemical Model
Connection Between Time-Independent Perturbation Theory and Spectroscopic Selection Rules
Problems
Multiple Choice QuestionsGroup TheoryAn Elementary Example
Symmetry Point Groups
The Concept of Class
Symmetry Elements and Their Notation
Identifying the Point Group of a Molecule
Representations for Groups
Generating Representations from Basis Functions
Labels for Representations
Some Connections Between the Representation Table and Molecular Orbitals
Representations for Cyclic and Related Groups
Orthogonality in Irreducible Inequivalent Representations
Characters and Character Tables
Using Characters to Resolve Reducible Representations
Identifying Molecular Orbital Symmetries
Determining in Which Molecular Orbital an Atomic Orbital Will Appear
Generating Symmetry Orbitals
Hybrid Orbitals and Localized Orbitals
Symmetry and Integration
Problems
Multiple Choice QuestionsQualitative Molecular Orbital TheoryThe Need for a Qualitative Theory
Hierarchy in Molecular Structure and in Molecular Orbitals
H₂⁺
Revisited
H₂: Comparisons with H₂⁺
Rules for Qualitative Molecular Orbital Theory
Application of QMOT Rules to Homonuclear Diatomic Molecules
Shapes of Polyatomic Molecules: Walsh Diagrams
Frontier Orbitals
Qualitative Molecular Orbital Theory of Reactions
ProblemsMolecular Orbital Theory of Periodic SystemsThe Free Particle in One Dimension
The Particle in a Ring
Benzene
General Form of One-Electron Orbitals in Periodic Potentials—Bloch’s Theorem
A Retrospective Pause
An Example: Polyacetylene with Uniform Bond Lengths
Electrical Conductivity
Polyacetylene with Alternating Bond Lengths—Peierls’ Distortion
Electronic Structure of All-Trans Polyacetylene
Comparison of EHMO and SCF Results on Polyacetylene
Effects of Chemical Substitution on the π Bands
Poly-Paraphenylene—A Ring Polymer
Energy Calculations
Two-Dimensional Periodicity and Vectors in Reciprocal Space
Periodicity in Three Dimensions—GraphiteProblemsAppendixesUseful Integrals
Determinants
Evaluation of the Coulomb Repulsion Integral Over 1s AOs
Angular Momentum Rules
The Pairing Theorem
HЁuckel Molecular Orbital Energies, Coefficients, Electron Densities, and Bond Orders for Some Simple Molecules
Derivation of the Hartree–Fock Equation
The Virial Theorem for Atoms and Diatomic Molecules
Bra-ket Notation
Values of Some Useful Constants and Conversion Factors
Group Theoretical Charts and Tables
Hints for Solving Selected Problems
Answers to Problems