[3+2] versus [2+2] Addition of Metal Oxides Across C=C Double Bonds

1. ACS National Meeting, Chicago August 26, 2001 [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

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 = Eint + Evdw + Erep+ Espc + Elb • Eint: internal energy of the chain, Calculated using standard force fields • Evdw: van-der-Waals interactions between chains, Calculated using Maier-Saupe potential

8. MD Simulation of Chain Amphiphiles II • E = Eint + Evdw + Erep+ Espc + Elb • Erep: repulsive contribution due to lateral pressure Calculated from cross-sectional area A of the chain and the lateral pressure  Erep = A  • The approach using the first three terms is denoted mean-field approach (Marcelja) E = Eint + Evdw + Erep

9. MD Simulation of Chain Amphiphiles III • E = Eint + Evdw + Erep+ Espc + Elb • Espc: specific intermolecular interactions, e.g., hydrogen bridges in head-to-head arrangements, Calculated using force field methods • Elb: 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 = Eint + Evdw + Erep) • MD simulations of Langmuir-Blodgett films require additional concepts to model the interactions between lipid and solid