Chemical Rate Process Theory: from Electron Transfer to Ion Permeation

Chem. 3490   Spring 2009



Rob Coalson
Eberly 321, (412)624-8261

Course Syllabus


Lecture Notes

1)     Notes, Jan. 11, 2009: Problem of Random Flights, Markoff's method, with applications to polymer extension and swelling; the Central Limit Theorem; the Diffusion Equation.

2)     Notes, Jan. 13, 2009: Langevin Eq.; free particle velocity distribution, Einstein relation between friction and random force; position distribution for free particle: reduction to Diffusion Equation in high friction limit.

3)     Notes, Jan. 15, 2009: Langevin Eq. for particle in a constant force field; stochastic Langevin dynamics algorithm for motion in an arbitrary force field and its reduction in the high-friction limit.

4)     Notes, Jan. 20: Velocity auto-correlation function for a particle undergoing Langevin dynamics; correlation functions of the random force.

5)     Notes, Jan. 22, 2009: Connection of stochastic ordinary differential equations (ODEs) to deterministic particle differential equations (PDEs): equivalence of Langevin Eq. and phase space Fokker Planck Eq.; equivalence of high-friction Langevin Eq. and Smoluchowski Eq.

6)     Notes, Jan. 27, 2009: Thermally Activated Barrier Crossing: Transition State Theory, Kramer's Theory in the high and low friction limits.

7)     Notes, Feb. 5Transformation of the Smoluchowski Eq. to Schrodinger form.

8)     Notes, Feb. 10, 2009: Generalized Langevin Eq. (GLE): Phenomenology and Fluctuation-Dissipation Theorems.

9)     Notes, Feb. 17, 2009: Derivation of the Generalized Langevin Eq. from a microscopic Hamiltonian (a system coordinate coupled blinearly to a bath of harmonic oscillators).

10)     Notes, Feb. 25, 2009: 1-D Drift-Diffusion Equations (steady state of the Smoluchowski Eq.): quadrature formulae for the steady state concentration profile and current; application to ion permeation through channel proteins (GHK theory).

11)     Notes, Mar. 5, 2009: Computing mean first passage times in high-friction Brownian motion via the Adjoint Equation: reduction to quadrature for 1D motion; PDE formulation for multi-dimensional motion.

12)     Notes, Mar. 24, 2009: Fermi's Golden Rule for state-to-state quantum mechanical transition rates: derivation using time-dependent perturbation theory; requirement of a dense manifold of accepting states; counterexample: quantum dynamics of an isolated two-level system.

13)     Notes, Mar. 26, 2009: Decay of a Doorway State: Exact vs. Golden Rule quantum dynamics.

14)     Notes, Apr. 9, 2009: Spectroscopy and the Golden Rule. Time-dependent perturbation theory with a monochromatic driving field: transition probabilities and cross sections for 1-photon absorption and emission; time-independent (sum over states) vs. time-dependent (correlation function) formulations; Application to vibronic absorption spectra: Franck-Condon factors, time-correlation function formulation for pure initial states and finite temperature systems.

15)     Notes, July. 20, 2009: Simple Quantum Relaxation Theory: Population Relaxation of a System Coupled to a Bath. (Golden Rule for System Transitions; Detailed Balance; Pauli Master Equations; Semi-classical Evaluation of Heisenberg Correlation Functions.)


Problem Sets

1)     Problem Set 1, Solution Key

2)     Problem Set 2, Solution Key

3)     Problem Set 3, Solution Key

Guest Lectures

1)     MC_feb09. Dr. Mary Cheng: Brownian Dynamics Simulation of Ion Permeation through Protein Channels.

2)     IK_apr09. Dr. Igor Kurnikov: Non-adiabatic Electron Transfer in Chemistry and Biology.

3)     KW_apr09. Dr. Kim Wong: Approaches for Calculating Non-adiabatic, Energy Transfer, and Chemical Reaction Rates.

Student Presentations

1)     JX_apr09. Jiawei Xu: Linear Response Theory and Its Applications.

2)     AS_apr09. Andrey Sharapov: Debye-Falkenhagen Theory and Its Computer Simulation.

3)     GZ_apr09. Guozhen Zhang: Poisson-Nernst-Planck Theory Approach to the Calculation of Ion Transport through Protein Channels.

4)     FY_apr09. Fangyong Yan: Graphical Rule-Based Modeling of Signal Transduction Systems.