Beyond Quantum Mechanics Mathematical Modeling for Chemists (and Their Friends) Michelle Francl Bryn Mawr College

Introduction Structure Course Topics Lessons Learned Computers and Chemists Molecular modeling packages Programming languages Spreadsheets Mathematical “environments”

Introduction Structure Course Topics Lessons Learned Physical Chemistry Course “Using molecular modelling software and the computational method of your choice…calculate the fundamental vibrational wavenumber and visualize the vibrational normal modes of SO 2 …” Atkins and dePaula 7th ed

Introduction Structure Course Topics Lessons Learned “The vapor pressure of methanol in bars is given…as a function of temperature. Fit these vapor pressures [to an appropriate equation] using a computer and calculate the heat of vaporization at each of these temperatures…” Silbey and Alberty 3rd ed Physical Chemistry Course

Introduction Structure Course Topics Lessons Learned Physical Chemistry Course “Use mathematical software to integrate the Lotka-Volterra equations and plot the concentration of Y against that of X. Explore the consequences of varying the starting concentration…” Atkins and dePaula 7th ed

Introduction Structure Course Topics Lessons Learned Physical Chemistry Course QM calculation Plotting Fitting Numerical Solutions and Modeling

Introduction Structure Course Topics Lessons Learned Beyond P-Chem “Screening in Short Polyelectrolyte Chains. A Monte Carlo Study”, Chava Brender and Meir Danino J. Phys. Chem., 100 (44), [1996] “Statistical Mechanics of Prion Diseases”, A. Slepoy et al. Phys. Rev. Lett., 87(5) [2001] “Formation of Tethered Nanolayers: Three Regimes of Kinetics”, Lynn Penn et al. Macromol. July 2002 Web release [2002]

Structure Course Topics Lessons Learned Course Development Begin where p-chem left off Open to chemistry majors, math majors, graduate students

Structure Course Topics Lessons Learned Goals Familiarity with modeling approaches Primary literature Create and adapt models

Structure Course Topics Lessons Learned Structure 3 hour time block Lecture/demonstration/”lab”/pres entations 16 students (10 chem majors, 3 math majors, 3 chem grad students) - one/computer

Course Topics Lessons Learned Syllabus Tools What is a model? Random walks Markov chains Monte Carlo Cellular Automata “Chaos” theory

Course Topics Lessons Learned Tools Mathematica Guided self-paced tour “tidbits”

Course Topics Lessons Learned Philosophy of Modeling Increasing complexity When is it right?

Course Topics Lessons Learned Approach Theoretical basis Simple model Model of a physical system Contest!

Course Topics Lessons Learned Random Walks Tiger and the Etymologist 1-D to 3-D Non-reversing walks Self-avoiding walks Radius of gyration predictions

Course Topics Lessons Learned Random Walks

Course Topics Lessons Learned Monte Carlo Deposition on a surface Exploration of packing vs surface structure Packing defects

Course Topics Lessons Learned Monte Carlo

Course Topics Lessons Learned Cellular Automata Epidemiology Prion diseases/drug therapy

Course Topics Lessons Learned Cellular Automata

Lessons Learned Build on skills that exist Move into research Chemical intuition Chemical literature

Lessons Learned Acknowledgements Chemistry 321/521 students Bryn Mawr College Office of the Provost

Lessons Learned Further Information See mfrancl/BostonACS/BeyondQM