Lecture Notes CHEM 430b/530b Statistical Methods and Thermodynamics Prerequisites: CHEM 130 or 330 or 332, or equivalents Instructor: Prof. Victor S. Batista Room: SCL 18 Schedule: MWF 9.00-10.20

Introduction

(Chapter 3) January 11-Feb 5

o Pure States

o Statistical Mixture of States

o Density Operator

o Time-Evolution of Ensembles

o Classical Analogue

o Entropy

o Maximum-Entropy Density Operator

o Internal Energy and Helmholtz Free Energy

o Temperature

o Canonical and Microcanonical Ensembles

o Equivalency of Ensembles

§ Example

o Thermal Fluctuations

o Grand Canonical Ensemble

o Density Fluctuations

o Quiz 1

o Postulates of Statistical Mechanics

§ Example: Ensemble Averages

Practice Exam Exam 1 FIRST EXAM February 8th

(Chapter 4) Febr. 8-25 February 10 don't meet February 12, 15 meet at 9:00am

o Bose-Einstein and Fermi-Dirac Distributions

o Classical limit of Quantum Statistical Distributions

o Example 1: Ideal Gas of Structureless Quantum Particles

o Example 2: Dilute Gas of Diatomic Molecules

o Example 3: Phonons in a Solid Lattice

§ Einstein Model

§ Debye Model

o Example 4: Electrons in Metals

§ Continuous Approximation

§ Joint Probabilities

o Chemical Equilibrium

§ Minimum Energy Principle

o Practice Exam 2 Practice Quiz 2

(Chapter 5) Febr. 25- March 5

February 22,24 don't meet February 26, March 1, 3 and 5 meet at 9:00am

o Ising Model

o Lattice Gas

o Mean Field Theory

§ Variational Mean Field Theory

o Renormalization Group Theory

SECOND EXAM March 5

Spring Break March 6-21

(Chapter 6)

March 22-April 2

March 22, 31 don't meet

March 24, 26, 29 April 2 meet at 9:00am

o Metropolis Monte Carlo Method

o Variance-Reducing Techniques

§ Importance Sampling

§ Correlated Sampling

§ Control Variates

§ Stratified Sampling

§ Simulated Annealing

o Practice Exam 3

o Kinetic Monte Carlo

(Chapters 7 and 8)

April 7-16 April 9 don't meet

April 12, 14 meet at 9:00am

o Classical Fluids

§ Radial Distribution Function

o Reversible Work Theorem

o Thermodynamic Properties of Fluids

o Solvation Free Energy

Quiz 3 April 18: Computer assignments deadline

DEADLINE COMPUTER ASSIGNMENTS April 16

(Chapter 8)

April 19-30

April 26-30 (reading period) meet

THIRD EXAM April 30

FINAL EXAMINATION PERIOD MAY 4-11

OPTIONAL COMPREHENSIVE MAKEUP EXAM, May 7