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Quantum Chemistry

Chemistry

Publisher: Pacific Union College
Source: LibreTexts
Language: EN
Category: Basic Sciences

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Contents· 158 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 Schrödinger Equation
3.02: Linear Operators in Quantum Mechanics
3.03: The Schrödinger 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 Schrödinger 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 Schrödinger 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 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 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: Chemical Bonding in Diatomic Molecules
9.01: The Born-Oppenheimer Approximation Simplifies the Schrödinger Equation for Molecules
9.02: The H₂⁺ Prototypical Species
9.03: The Overlap Integral
9.04: Chemical Bond Stability
9.05: Bonding and Antibonding Orbitals
9.06: A Simple Molecular-Orbital Treatment of H₂ Places Both Electrons in a Bonding Orbital
9.07: Molecular Orbitals Can Be Ordered According to Their Energies
9.08: Molecular-Orbital Theory Does not Predict a Stable Diatomic Helium Molecule
9.09: Electrons Populate Molecular Orbitals According to the Pauli Exclusion Principle
9.10: Molecular Orbital Theory Predicts that Molecular Oxygen is Paramagnetic
9.11: Photoelectron Spectra Support the Existence of Molecular Orbitals
9.12: Molecular-Orbital Theory Also Applies to Heteronuclear Diatomic Molecules
9.13: An SCF-LCAO-MO Wave Function Is a Molecular Orbital Formed from a Linear Combination of Atomic Orbitals and Whose Coefficients Are Determined Self-Consistently
9.14: Molecular Term Symbols Describe Electronic States of Molecules
9.15: Molecular Term Symbols Designate Symmetry
9.16: Most Molecules Have Excited Electronic States
9.E: Chemical Bond in Diatomic Molecules (Exercises)
10: Bonding in Polyatomic Molecules
10.01: Hybrid Orbitals Account for Molecular Shape
10.02: Hybrid Orbitals in Water
10.03: Why is BeH₂ Linear and H₂O Bent?
10.04: Photoelectron Spectroscopy
10.05: The \(\pi\)-Electron Approximation of Conjugation
10.06: Butadiene is Stabilized by a Delocalization Energy
10.07: Benzene and Aromaticity
10.E: Bonding in Polyatomic Molecules (Exercises)
11: Computational Quantum Chemistry
11.01: Overview of Quantum Calculations
11.02: Gaussian Basis Sets
11.03: Extended Basis Sets
11.04: Orbital Polarization Terms in Basis Sets
11.05: The Ground-State Energy of H₂
11.06: Quantum Calculations
11.E: Computational Quantum Chemistry (Exercises)
12: Group Theory - The Exploitation of Symmetry
12.01: The Exploitation of Symmetry
12.02: Symmetry Elements
12.03: Symmetry Operations Define Groups
12.04: Symmetry Operations as Matrices
12.05: The (C 3V) Point Group
12.06: Character Tables
12.07: Characters of Irreducible Representations
12.08: Using Symmetry to Solve Secular Determinants
12.09: Generating Operators
12.E: Group Theory - The Exploitation of Symmetry (Exercises)
13: Molecular Spectroscopy
13.01: The Electromagnetic Spectrum
13.02: Rotations Accompany Vibrational Transitions
13.03: Unequal Spacings in Vibration-Rotation Spectra
13.04: Unequal Spacings in Pure Rotational Spectra
13.05: Vibrational Overtones
13.06: Electronic Spectra Contain Electronic, Vibrational, and Rotational Information
13.07: The Franck-Condon Principle
13.08: Rotational Spectra of Polyatomic Molecules
13.09: Normal Modes in Polyatomic Molecules
13.10: Irreducible Representation of Point Groups
13.11: Time-Dependent Perturbation Theory
13.12: The Selection Rule for the Rigid Rotor
13.13: The Harmonic Oscillator Selection Rule
13.14: Group Theory Determines Infrared Activity
13.E: Molecular Spectroscopy (Exercises)
14: Nuclear Magnetic Resonance Spectroscopy
14.01: Nuclei Have Intrinsic Spin Angular Momenta
14.02: Magnetic Moments Interact with Magnetic Fields
14.03: Proton NMR Spectrometers Operate at Frequencies Between 60 MHz and 750 MHz
14.04: The Magnetic Field Acting upon Nuclei in Molecules Is Shielded
14.05: Chemical Shifts Depend upon the Chemical Environment of the Nucleus
14.06: Spin-Spin Coupling Can Lead to Multiplets in NMR Spectra
14.07: Spin-Spin Coupling Between Chemically Equivalent Protons is Not Observed
14.09: Second-Order Spectra Can Be Calculated Exactly Using the Variational Method
14.E: Nuclear Magnetic Resonance Spectroscopy (Exercises)
15: Lasers Laser Spectroscopy and Photochemistry
15.01: Electronically Excited Molecules can Relax by a Number of Processes
15.02: The Dynamics of Transitions can be Modeled by Rate Equations
15.03: A Two-Level System Cannot Achieve a Population Inversion
15.04: Population Inversion can be Achieved in a Three-Level System
15.05: What is Inside a Laser?
15.06: The Helium-Neon Laser
15.07: High-Resolution Laser Spectroscopy
15.08: Pulsed Lasers Can by Used to Measure the Dynamics of Photochemical Processes
15.E: Lasers, Laser Spectroscopy, and Photochemistry (Exercises)