Physical Chemistry Lecture Notes

Quantum Mechanics, Spectroscopy, and Statistical Mechanics

To accompany:T. W. Shattuck, Physical Chemistry, Academx Publishing Services, Inc., Sagamore Beach, MA. Part 2 2017 (revised 2021)[full text access].

You will need the Adobe Acrobat Reader to view these files. Most of the lecture notes have the same format: formula lines for the proofs but
without the reasons for each step. Room is provided in the right-hand column for you to fill in with the reasons each step was taken. In this way
you can concentrate on the flow of the proofs and the meaning of each formula and not worry about copying down each formula correctly for your notes.

Quantum Mechanics


Steps Toward Quantum Theory
Photoelectric Effect
Some Handy Integrals
Complex Waveforms, eix=cos x+isin x
Complex Waveforms- Euler Identity Proof
Classical Harmonic Oscillator
Particle in a Box
Expectation Values-Particle in a Box
Heisenberg Uncertainty Principle: Gaussian Distribution
Heisenberg Uncertainty Principle: Particle in a Box (short version)
Heisenberg Uncertainty Principle: Particle in a Box
Uncertainty and Wave Packets
Particle in a 2-D Box
Particle in a 3-D Box
Quantum Mechanical Tunneling
Fourier Transforms
Fourier Coefficients
Fourier Integration
Postulates of Quantum Mechanics
The Eigenvalues of Quantum Mechanical Operators are Real
The Momentum Operator is Hermitian
Time Dependent Quantum Mechanics
Classical Vibration and Rotation of Diatomics
Rotation In a Plane
Angular Momentum in 3D
Rigid Rotor - Rotation in Three Dimensions
Spherical Polar Coordinates
Harmonic Oscillator
Harmonic Oscillator Excited States
Hermite Equation and Harmonic Oscillator Excited States
  Quantum Mechanics Formula Sheet

Atomic Structure

Ground State of the Hydrogen Atom
Hydrogen Atomic Orbitals
Hydrogen Spherical Atomic Orbital Plots
Hydrogen Atom Most Probable and Average Radius
Many Electron Atoms-Independent Electron Approximation-Helium
Perturbation Method-Helium
Variation Method- Helium
Self-Consistent Field Theory (SCF)
Self-Consistent Field Atomic Orbital Energies
Atomic Orbital Ionization Energies
Aufbau Principle
Pauli Exclusion Principle
Total Orbital Angular Momentum, L
Atomic Term Symbols
Spin-Orbit Interaction
Atomic Spectroscopy
The Fine Arts and Science

Molecular Structure

Atomic Units
Slater Type Orbitals, STO's
Gaussian Basis Sets
Carbon 2p Gaussian Orbital
H2+ Molecular Orbitals - Variation Treatment
Ab initio Molecular Orbital Treatment for H2
Polarization Functions
Electron Correlation - Configuration Interaction
Atomic Orbital Ionization Energies
H2 Bond Strength
CNDO Calculations for LiH, Bent, and Linear Water
LiH Molecular Orbitals (CNDO)
LiH Molecular Orbitals (MNDO)
MOPAC Instructions for Diatomics
MOPAC Z-matrix Construction
Molecular Orbitals for Diatomics (color)     Molecular Orbitals for Diatomics (black and white)
Homonuclear Diatomics Bond Strengths
Homonuclear Diatomics Bond Strength Trends
Heteonuclear Diatomics Bond Strength Trends
Self Consistent Field Hartree Fock: Roothaan Equations
Density Functional Theory
Nitrogen Molecular Orbitals (AM1, exp. bond length)
Molecular Orbitals for Polyatomics
Bent and Linear Water (CNDO)
Walsh Diagram for Dihydrides
Walsh Diagram for Methylene Triplet State
Carbon Dioxide Molecular Orbitals (MNDO)
Ozone Molecular Orbitals: Linear and Bent (MNDO)
Ozone: Linear model MOPAC input file
Linear and Bent Triatomics
Walsh Diagram for Ozone (color)     Walsh Diagram for Ozone (black and white)
Ammonia, NH3, 90 and 109 deg bond angles (AM1)
sp Linear hybridization
Huckel Molecular Orbital Theory
How to Calculate Determinants
Kramer's Rule and Butadiene HMO Coefficients
Molecular Structure Formula Sheet


Rotational Spectroscopy - Diatomics
Rotational Spectroscopy - Symmetric Tops
Vibrational Spectroscopy and Anharmonicity
Classical Normal Mode Analysis
    Classical Normal Mode Analysis (text version)
Formaldehyde Vibrational Analysis (Spartan)
Formaldehyde Vibrational Analysis (Gaussian03)
Vibration- Rotation Spectroscopy
HCl-DCl Infrared Spectra
Diatomic Spectroscopic Constants
IR and Raman Selection Rules
Electronic Spectrscopy SO2 and N2-- Gas Phase
Benzene Electronic Absorption Spectrum -- Gas Phase
I2 and Br2 Electronic Absorption Spectrum -- Gas Phase
Acrolein Electronic Absorption
Acrolein & Chloro-acrolein Molecular Orbitals
Term Symbols and Molecular Spectroscopy
Refelction Symmetry (+ -) and Molecular Term Symbols
Birge- Sponer Extrapolation
Absorbance and Fluorescence Spectroscopy
Ultraviolet Photoelectron Spectroscopy: H2, N2, CO, and H2O
Ultraviolet Photoelectron Spectroscopy
Spin-Spin Splitting in NMR
Electron Spin Resonance
Electron Spin Resonance Examples
Distance Geometry
Spectroscopy Formula Sheet

Diffraction Techniques

Bravais Lattices
Path Length and Phase Difference
Path Length and Phase Difference Power Point version
Systematic Extinctions
Systematic Extinctions Power Point
Reciprocal Lattice Examples
Constructing the Reciprocal Lattice
Ewald Construction

Statistical Mechanics

Equipartition Theorem Predictions for Internal Energy and Cv
Averaging and Probability Distributions
Boltzman Distribution and the Most Probable Distribution
Effect of Quantum Size on the Population of States
Canonical Ensemble Partition Functions vs. Molecular Partition Functions
Translational Partition Function and beta
Internal Energy and q
Entropy and the Partition Function (from S = -kΣpi ln pi )
Entropy and the Partition Function (from Wmax)
Partition Functions
Electronic Partition Functions
Partition Functions and Units, Units, Units
Thermodynamic Functions from Partition Functions
Thermodynamics and Internal Degrees of Freedom
Vibrational Contribution to Internal Energy and Free Energy vs. T
Formaldehyde Vibrational Analysis with Formulas
Ab Initio SCF Atomic Energies Table (.pdf)    SCF Atomic Energies Table (Excel)
Equilibrium Constants and Statistical Mechanics
Equilibrium Constants and Statistical Mechanics Example
Statistical Mechanical Equilibrium Constants- Cl + H2 -> HCl + H

Reaction Dynamics

Average Molecular Speed
Collision Theory
Thermodynamic Transition State Theory- Eyring Equation
Thermodynamic Transition State Theory- Gibbs Free Energy
Energy Demand and PE Surfaces
Energy Disposal and PE Surfaces
Statistical Mechanics and Reaction Dynamics Formulas

For more information or corrections contact Tom Shattuck at [email protected]

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Last modified: 4/24/13