Chemical Kinetics
Stat. Mech. 576
Outline
Rare events
Potential Energy Surfaces
Quasi-equilibrium
Rare Events
In many systems, characterization
of stable intermediates is common
Direct
conversion?
Classical Limits to
Quantum Mechanics
Stat. Mech. 576
Outline
Particle in a box
Harmonic oscillator
Rigid rotor
Electronic energy levels
Connection of QM to CM
Schrodingers Cat
Most are familiar
Probability and
Mathematical Background
Stat. Mech. 576
Outline for Probability
Definition, averages, variance
Discrete vs. continuous probabilities
Binomial distribution
Multinomial distribution
Introduction to
Statistical Mechanics
Chemistry 576
Applied Physics 576
Professor Paul Zimmerman
Outline
What statistical mechanics does
Why it is useful
Stat. mech. principles
Examples
!
What is
Model System
Partition Functions
Stat. Mech. 576
Outline
Model system: Independent particles
Translational partition function
Rotational partition function
Vibrational partition function
Electron
Ising Model
Stat. Mech. 576
Outline
Spin Lattices and definitions
Partition function for non-interacting spins
Partition function for interacting spins
Spontaneous magnetization
2D Ising Model
R
Non-Hamiltonian Systems
Hamiltons equations of motion provide a basis for
describing the time evolution of systems that conserve
energy
Forces must be internal to the system
Therefore: an isolated
Grand Canonical
Ensemble
Stat. Mech. 576
Previously
Canonical ensemble constructed based on the principles of
equal a priori probabilities for all accessible microstates in the
overall ensemble
Conn
Liouville Theorem
Stat. Mech. 576
Outline
Macroscopic observables as time averages
Can a Hamiltonian describe time-averaged
properties?
Liouville Theorem
Time Averages
Say one were to sample micro
Monte Carlo
Stat. Mech. 576
Outline
Random sampling
Central Limit Theorem
Ensemble sampling
MC Method
Evaluating an Integral
Imagine being unable to analytically evaluate the integral:
1
I=
1
dx
Fluctuations
Stat. Mech. 576
Outline
Why fluctuations?
Derivations for the canonical, grand canonical, and isobaricisothermal ensembles
Equivalence of ensembles
Reading: Chapter 3 McQuarrie
Why i
Lattice Models
Stat. Mech. 576
Outline
Lattice models are a preview to the Ising model, and share
many of the same characteristics
Surface Adsorption
Canonical and Grand Canonical Ensembles
Lattice
Gibbs Paradox
Stat. Mech. 576
Intro. Gibbs Paradox
The development of the classical partition function came with
an arbitrary factor 1/N!
1/N! is added to avoid a disagreement between stat. mech. an
Thermodynamics
Stat. Mech. 576
Office Hours
Friday 3-4, or by appointment ([email protected])
Chemistry 2000E
I am available via email if you have (shorter) questions
or concerns
Outline
Definitio