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Chem 110B: Physical Chemistry II

Group theory. Application of quantum mechanics to polyatomic molecules and molecular spectroscopy. Intermolecular forces and the gas, liquid and solid states. Distributions, ensembles and partition functions. Transport properties.

Chemistry

Author: Delmar Larsen
Publisher: University of California, Davis
Source: LibreTexts
License: CC BY-NC-SA
Language: EN
Category: Basic Sciences

Read online Download PDF (open licence)

Contents· 99 sections

AGENDA
Rethinking Hybridization
Text
10: Bonding in Polyatomic Molecules
10.1: Hybrid Orbitals Account for Molecular Shape
10.2: Different Hybrid Orbitals Used for Bonding in Water
10.3: Why is BeH2 Linear and H2O Bent
10.4: Photoelectron Spectroscopy
10.5: The Pi-Electron Approximation of Conjugated Hydrocarbons
10.6: Butadiene is Stabilized by a Delocalization Energy
11: Computational Quantum Chemistry
11.0: Overview of Quantum Calculations
11.1: Gaussian Basis Sets
11.2: Extended Basis Sets
11.3: Orbital Polarization Terms
11.4: The Ground-State Energy of H2
11.5: Quantum Calculations
12: Group Theory - Exploiting Symmetry
12.1: Using Symmetry to Simplify Calculations
12.2: The Symmetry of Molecules
12.3: Symmetry Operations Define Groups
12.4: Symmetry Operations can be Represented by Matrices
12.5: The \(C 3V\) Point Group Has a 2-D Irreducible Representation
12.6: Character Tables
12.7: Relations involving Characters
12.8: Using Symmetry to Predict Zero in a Secular Determinant
12.9: Generating Operators for Irreducible Representations
13: Molecular Spectroscopy
13-01. Different Regions of the Electromagnetic Spectrum Are Used to Investigate Different Molecular Processes
13-02. Rotational Transitions Accompany Vibrational Transitions
13-03. Vibration-Rotation Interaction Accounts for the Unequal Spacing of the Lines in the P and R Branches of a Vibration-Rotation Spectrum
13-04. The Lines in a Pure Rotational Spectrum Are Not Equally Spaced
13-05. Overtones Are Observed in Vibrational Spectra
13-06. Electronic Spectra Contain Electronic Vibrational and Rotational Information
13-07. The Franck-Condon Principle Predicts the Relative Intensities of Vibronic Transitions
13-08. The Rotational Spectrum of a Polyatomic Molecule Depends Upon the Principal Moments of Inertia of the Molecule
13-09. The Vibrations of Polyatomic Molecules Are Represented by Normal Coordinates
13.10: Irreducible Representation of Point Groups
13.11: Time-Dependent Perturbation Theory
13.12: The Selection Rule for the Rigid Rotator
13.13: The Harmonic Oscillator Selection Rule
13.14: Group Theory Determines Infrared Activity
13.E: Molecular Spectroscopy (Exercises)
14: Nuclear Magnetic Resonance Spectroscopy
14.1: Nuclei Have Intrinsic Spin Angular Momenta
14.2: Magnetic Moments Interact with Magnetic Fields
14.3: Proton NMR Spectrometers Operate at Frequencies Between 60 MHz and 750 MHz
14.4: The Magnetic Field Acting upon Nuclei in Molecules Is Shielded
14.5: Chemical Shifts is Sensitive to Chemical Environment of the Nucleus
14.6: Spin-Spin Coupling Results in Multiplets in NMR Spectra
14.7: Spin-Spin Coupling Between Chemically Equivalent Protons Is Not Observed
14.8: The n 1 Rule Applies Only to First-Order Spectra
14.9: Second-Order Spectra Can Be Calculated Exactly Using the Variational Method
15: Lasers Laser Spectroscopy and Photochemistry
15.1: Electronically Excited Molecules
15.2: Transitions Modeled as Kinetics
15.3: Two-Level Systems Cannot Form Population Inversions
15.4: Population Inversion via Three-Level Systems
15.5: Laser Fundamentals
15.6: The Helium-Neon Laser
15.7: High-Resolution Laser Spectroscopy
15.8: Photochemical Dynamics
16: The Properties of Gases
16.01: Gases Behave Ideally if Dilute
16.2: van der Waals and Redlich-Kwong Equations
16.3: A Cubic Equation of State
16.4: The Law of Corresponding States
16.5: The Second Virial Coefficient
16.6: The Repulsive Term in the Lennard-Jones Potential
16.7: Van der Waals Constants in Terms of Molecular Parameters
16.E: The Properties of Gases (Exercises)
17: Boltzmann Factor and Partition Functions
17.01: The Boltzmann Factor Is One of the Most Important Quantities in the Physical Sciences
17.2: The Thermal Boltzman Distribution
17.3: We Postulate That the Average Ensemble Energy Is Equal to the Observed Energy of a System
17.4: The Heat Capacity at Constant Volume
17.5: Express the Pressure in Terms of a Partition Function
17.6: Partition Functions of Systems of Distinguishable Molecules are Products of Molecular Partition Functions
17.7: Partition Function of Indistinguishable Components
17.8: A Molecular Partition Function Can Be Decomposed into Partition Functions for Each Degree of Freedom
17.E: Exercises
18: Partition Functions and Ideal Gases
18.1: The Translational Partition Function of a Monatomic Ideal Gas
18.2: Most Atoms Are in the Ground Electronic State at Room Temperature
18.3: The Energy of a Diatomic Molecule Can Be Approximated as a Sum of Separate Terms
18.4: Most Molecules Are in the Ground Vibrational State at Room Temperature
18.5: Most Molecules Are in Excited Rotational States at Ordinary Temperatures
18.6: Rotational Partition Functions Contain a Symmetry Number
18.7: The Vibrational Partition Function
18.8: The Rotational Partition Function Depends on the Shape of the Molecule
18.9: Molar Heat Capacities
18.E: Partition Functions and Ideal Gases (Exercises)
Worksheets
1: Valence Bond Orbitals for Hydrogen
2: Symmetry and Assigning Point Groups
3: Using Symmetry to Solve Integrals
4: Deriving Selection Rules with Symmetry
5: Translation Partition Function
6: Rotational Partition Functions