1. [3+2] versus [2+2] Addition of Metal Oxides Across C=C Double Bonds Dirk V. Deubel and Gernot Frenking University of Calgary, Canada University of Marburg, Germany ACS National Meeting, Chicago August 26, 2001

2. Outline Objective Methods Metal oxide additions to ethylene Metal oxide additions to activated double bonds Summary

3. Visualization of MD Results: Movie Chaotic nature of molecular motion High-frequency motions such as C-H vibrations often uninteresting Remove unwanted high-frequency motions: -Constrained dynamics: Freeze interatomic distance to equilibrium value, MM chapter 6.5, or -Restrained dynamics: Add penalty terms to the force field for deviations from the reference value, MM chapter 8.7, or -Filter trajectory using Fourier analysis techniques

4. Filter Trajectory Using Fourier Analysis Techniques Convert trajectory x(t) to frequency function X( ) Remove high frequencies from frequency function X( ) Convert modified frequency function X’( ) to modified trajectory x’(t) Use discrete Fourier transform for discontinuous trajectory

5. Chain Amphiphiles Biological interest: Cell membranes Industrial interest: Insulators in semiconductors, filtration devices, anti-reflective coatings, fabric softeners Consist of polar head group and lipophilic hydrocarbon tail Many degrees of conformational freedom in the hydrocarbon tail Example: Palmitic acid

6. Chain Amphiphiles Form Various Phases Mono-, bi-, and multiple layers: Langmuir-Blodgett films: layers adsorbed on solid: Micelles: Dynamic properties of layers: - perpendicular - lateral - conformational changes

7. MD Simulation of Chain Amphiphiles I Energy E of a chain in the mean field consists of the following contributions: E = E int + E vdw + E rep + E spc + E lb E int : internal energy of the chain, Calculated using standard force fields E vdw : van-der-Waals interactions between chains, Calculated using Maier-Saupe potential

8. MD Simulation of Chain Amphiphiles II E = E int + E vdw + E rep + E spc + E lb E rep : repulsive contribution due to lateral pressure Calculated from cross-sectional area A of the chain and the lateral pressure  E rep = A  The approach using the first three terms is denoted mean- field approach (Marcelja) E = E int + E vdw + E rep

9. MD Simulation of Chain Amphiphiles III E = E int + E vdw + E rep + E spc + E lb E spc : specific intermolecular interactions, e.g., hydrogen bridges in head-to-head arrangements, Calculated using force field methods E lb : interaction between lipid and solid in Langmuir- Blodgett films, Calculated, e.g., using a Lennard-Jones potential

10. Summary MD simulations of conformationally flexible molecules such as peptides or chain amphiphiles are important in biochemistry and in the chemical industry High-frequency motions such as C-H vibrations can be removed from trajectories for visualization purposes, using Fourier analysis techniques MD simulations of lipid layers can be performed using the mean-field approach (E = E int + E vdw + E rep ) MD simulations of Langmuir-Blodgett films require additional concepts to model the interactions between lipid and solid