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CHM 364 Physical Chemistry 2 (Grinnell College)

This textbook supports Physical Chemistry II, with emphasis on quantum mechanics with applications in quantum chemistry and spectroscopy.

Chemistry

Author: Elaine Marzluff
Publisher: Grinnell College
Source: LibreTexts
Language: EN
Category: Basic Sciences

Read online Download PDF (open licence)

Contents· 164 sections

01: The Dawn of the Quantum Theory
1.01: Blackbody Radiation Cannot Be Explained Classically
1.02: Quantum Hypothesis Used for Blackbody Radiation Law
1.03: Photoelectric Effect Explained with Quantum Hypothesis
1.04: The Hydrogen Atomic Spectrum
1.05: The Rydberg Formula and the Hydrogen Atomic Spectrum
1.06: Matter Has Wavelike Properties
1.07: de Broglie Waves can be Experimentally Observed
1.08: The Bohr Theory of the Hydrogen Atom
1.09: The Heisenberg Uncertainty Principle
1.E: The Dawn of the Quantum Theory (Exercises)
02: The Classical Wave Equation
2.01: The One-Dimensional Wave Equation
2.02: The Method of Separation of Variables
2.03: Oscillatory Solutions to Differential Equations
2.04: The General Solution is a Superposition of Normal Modes
2.05: A Vibrating Membrane
2.E: The Classical Wave Equation (Exercises)
03: The Schrodinger Equation and a Particle in a Box
3.01: The Schrodinger Equation
3.02: Linear Operators in Quantum Mechanics
3.03: The Schrodinger Equation is an Eigenvalue Problem
3.04: Wavefunctions Have a Probabilistic Interpretation
3.05: The Energy of a Particle in a Box is Quantized
3.06: Wavefunctions Must Be Normalized
3.07: The Average Momentum of a Particle in a Box is Zero
3.08: The Uncertainty Principle - Estimating Uncertainties from Wavefunctions
3.09: A Particle in a Three-Dimensional Box
3.E: The Schrodinger Equation and a Particle in a Box (Exercises)
04: Postulates and Principles of Quantum Mechanics
4.01: The Wavefunction Specifies the State of a System
4.02: Quantum Operators Represent Classical Variables
4.03: Observable Quantities Must Be Eigenvalues of Quantum Mechanical Operators
4.04: The Time-Dependent Schrodinger Equation
4.05: Eigenfunctions of Operators are Orthogonal
4.06: Commuting Operators Allow Infinite Precision
4.E: Postulates and Principles of Quantum Mechanics (Exercises)
05: The Harmonic Oscillator and the Rigid Rotor
5.01: A Harmonic Oscillator Obeys Hooke's Law
5.02: The Equation for a Harmonic-Oscillator Model of a Diatomic Molecule Contains the Reduced Mass of the Molecule
5.03: The Harmonic Oscillator Approximates Molecular Vibrations
5.04: The Harmonic Oscillator Energy Levels
5.05: The Harmonic Oscillator and Infrared Spectra
5.06: The Harmonic Oscillator Wavefunctions involve Hermite Polynomials
5.07: Hermite Polynomials are either Even or Odd Functions
5.08: The Energy Levels of a Rigid Rotor
5.09: The Rigid Rotator is a Model for a Rotating Diatomic Molecule
5.E: The Harmonic Oscillator and the Rigid Rotor (Exercises)
06: The Hydrogen Atom
6.01: The Schrodinger Equation for the Hydrogen Atom Can Be Solved Exactly
6.02: The Wavefunctions of a Rigid Rotator are Called Spherical Harmonics
6.03: The Three Components of Angular Momentum Cannot be Measured Simultaneously with Arbitrary Precision
6.04: Hydrogen Atomic Orbitals Depend upon Three Quantum Numbers
6.05: s-orbitals are Spherically Symmetric
6.06: Orbital Angular Momentum and the p-Orbitals
6.07: The Schrodinger Wave Equation for the Hydrogen Atom
6.08: The Helium Atom Cannot Be Solved Exactly
6.E: The Hydrogen Atom (Exercises)
07: Approximation Methods
7.01: The Variational Method Approximation
7.02: Linear Variational Method and the Secular Determinant
7.03: Trial Functions Can Be Linear Combinations of Functions That Also Contain Variational Parameters
7.04: Perturbation Theory Expresses the Solutions in Terms of Solved Problems
7.E: Approximation Methods (Exercises)
08: Multielectron Atoms
8.01: Atomic and Molecular Calculations are Expressed in Atomic Units
8.02: Perturbation Theory and the Variational Method for Helium
8.03: Hartree-Fock Equations are Solved by the Self-Consistent Field Method
8.04: An Electron has an Intrinsic Spin Angular Momentum
8.05: Wavefunctions must be Antisymmetric to Interchange of any Two Electrons
8.06: Antisymmetric Wavefunctions can be Represented by Slater Determinants
8.07: Hartree-Fock Calculations Give Good Agreement with Experimental Data
8.08: Term Symbols Gives a Detailed Description of an Electron Configuration
8.09: The Allowed Values of J - the Total Angular Momentum Quantum Number
8.10: Hund's Rules Determine the Term Symbols of the Ground Electronic States
8.11: Using Atomic Term Symbols to Interpret Atomic Spectra
8.E: Multielectron Atoms (Exercises)
09: Computational Quantum Chemistry
9.01: Overview of Quantum Calculations
9.02: Gaussian Basis Sets
9.03: Extended Basis Sets
9.04: Orbital Polarization Terms in Basis Sets
9.E: Computational Quantum Chemistry (Exercises)
10: Chemical Bonding in Diatomic Molecules
10.01: The Born-Oppenheimer Approximation Simplifies the Schrodinger Equation for Molecules
10.02: The H Prototypical Species
10.03: The Overlap Integral
10.04: Chemical Bond Stability
10.05: Bonding and Antibonding Orbitals
10.06: A Simple Molecular-Orbital Treatment of H Places Both Electrons in a Bonding Orbital
10.07: Molecular Orbitals Can Be Ordered According to Their Energies
10.08: Molecular-Orbital Theory Does not Predict a Stable Diatomic Helium Molecule
10.09: Electrons Populate Molecular Orbitals According to the Pauli Exclusion Principle
10.10: Molecular Orbital Theory Predicts that Molecular Oxygen is Paramagnetic
10.11: Photoelectron Spectroscopy
10.12: Molecular-Orbital Theory Also Applies to Heteronuclear Diatomic Molecules
10.13: Molecular Term Symbols Describe Electronic States of Molecules
10.14: Molecular Term Symbols Designate Symmetry
10.E: Chemical Bond in Diatomic Molecules (Exercises)
11: Bonding in Polyatomic Molecules
11.01: Hybrid Orbitals Account for Molecular Shape
11.02: Hybrid Orbitals in Water
11.03: BeH is Linear and HO is Bent
11.04: The pi-Electron Approximation of Conjugation
11.05: Butadiene is Stabilized by a Delocalization Energy
11.06: Benzene and Aromaticity
11.E: Bonding in Polyatomic Molecules (Exercises)
12: Molecular Spectroscopy
12.01: The Electromagnetic Spectrum
12.02: Rotations Accompany Vibrational Transitions
12.03: Unequal Spacings in Vibration-Rotation Spectra
12.04: Unequal Spacings in Pure Rotational Spectra
12.05: Vibrational Overtones
12.06: Electronic Spectra Contain Electronic Vibrational and Rotational Information
12.07: The Franck-Condon Principle
12.08: Rotational Spectra of Polyatomic Molecules
12.09: Normal Modes in Polyatomic Molecules
12.10: Time-Dependent Perturbation Theory
12.11: The Selection Rule for the Rigid Rotor
12.12: The Harmonic Oscillator Selection Rule
12.13: Group Theory Determines Infrared Activity
12.E: Molecular Spectroscopy (Exercises)
13: Lasers Laser Spectroscopy and Photochemistry
13.01: Electronically Excited Molecules can Relax by a Number of Processes
13.02: The Dynamics of Transitions can be Modeled by Rate Equations
13.03: A Two-Level System Cannot Achieve a Population Inversion
13.04: Population Inversion can be Achieved in a Three-Level System
13.05: What is Inside a Laser
13.06: The Helium-Neon Laser
13.07: Modern Applications of Laser Spectroscopy
13.E: Lasers Laser Spectroscopy and Photochemistry (Exercises)
14: Math Chapters
14.01: Complex Numbers
14.02: Probability and Statistics
14.03: Determinants
14.3.01: The Solutions of Simultaneous Linear Equations
14.3.02: Calculation of a 3 3 determinant
14.3.03: The Determinant as a Volume
14.3.04: Properties of Determinants
14.3.05: Problems
14.04: Vectors
14.05: Spherical Coordinates
14.06: Matrices
14.07: Numerical Methods
14.08: Partial Differentiation
14.09: Series and Limits
14.10: Fourier Analysis
14.10.01: Fourier Analysis in Matlab
14.10.02: Fourier Synthesis of Periodic Waveforms
14.11: The Binomial Distribution and Stirling's Appromixation
14.12: Formula Sheets
14.12.01: Some Important Numbers
14.12.02: Quadratic Equation
14.12.03: Logarithms and Exponentials
14.12.04: Trigonometric Identities
14.12.05: Complex Numbers
14.12.06: Operators
14.12.07: Taylor Series
14.12.08: Fourier Series
14.12.09: Derivatives and Primitives (Indefinite Integrals)
14.12.10: Definite integrals
14.12.11: Differentiation Rules
14.12.12: Partial Derivatives
14.12.13: Coordinate Systems