Computational Domains for Explorations in Nanoscience and Technology

6. COMPUTATIONAL NANOTECHNOLOGY Modeling and theory are becoming vital to designing and improving nanomaterials and nanodevices. One of the challenges: Multi-scale Scale plays a important role in science and engineering.

7. Biology/Bioengineering challenge (from top to bottom)

8. Physical scales (from bottom to top)

9. Common computational methods: Quantum mechanical calculations: First principle calculation Ab initio Molecular methods: Molecular dynamics Monte Carlo methods Multiscale methods: Coupling methods of molecular dynamics and continuum mechanics

10. Quantum mechanical calculations: tight binding method, the method of linear combination of atomic orbitals. Hatree-Fock approximation Density functional theory First principle calculations, solving Schrodinger�s equation. Etc. Computationally Intensive, O(N4) Up to ~ 3000 atoms

11. Molecular Dynamics: Based on the Newtonian classical dynamics Atoms are viewed as mass points Equations of motion can be derived from classical Lagrangian or Hamiltonian mechanics Method has received widespread attention since the 1970 Liquids Defects in crystals Fracture Surface Friction others

12. Molecular mechanics:

13. Molecular mechanics potential:

14. Molecular dynamics simulation:

15. Macroscopic properties: Can be evaluated based on atomic positions and velocities

16. Why molecular dynamics? It is consistent: all results are derived from a classical interatomic potential with a few parameters It is predictive: equilibrium structures, reaction transition states, and dynamical averages are obtained It is cheap: up to ~billions of atoms for nano seconds can be simulated Its downside: Quantum bonding and reactive response are hard to build in Poorly chosen input potentials produce garbage outputs Time step is essentially locked to molecular vibrations

17. Temperature regulation: Velocity scaling: Langevin dynamics: Berendsen thermostat: Nose-Hoover thermostat:

18. Monte Carlo Method A simple example: Evaluation of

19. Why Monte Carlo method? It is consistent: all results are derived from a classical interatomic potential with a few parameters It is predictive: equilibrium structures, reaction transition states, and thermodynamical averages are obtained Random processes simulated � crystal & interface growth, chemical gradients It is cheap: Its downside: Quantum bonding and reactive response are hard to build in Poorly chosen input potentials produce garbage outputs Effective importance sampling are needed

22. Monte Carlo method versus molecular dynamics For some systems in equilibrium state, such as system in canonical ensemble, both molecular dynamics and Monte Carlo method Molecular dynamics allows to study the time-dependent phenomena Grand canonical ensemble simulation is easier to implement with Monte Carlo method than molecular dynamics

23. Kinetic Monte Carlo method The Monte Carlo method, implemented with the standard Metropolis method, which is powerful for phase-space explorations, fails to represent the time evolution of the system. Therefore, it is mainly used for equilibrium description The Kinetic Monte Carlo method provides a tool to simulate a stochastic process with un ambiguous time relationship between Monte Carlo steps and real-time steps.

24. Kinetic Monte Carlo (KMC) method Advantages KMC simulates dynamics of the system in and out of equilibrium with a firm correspondence to real time At every time-step, the system can be recreated. This allows KMC to model dynamics on large time scales Time scale can change automatically Disadvantages KMC gives a coarse-grained picture of time evolution Calculating rates is independent of KMC method Need most efficient data structures for each specific problem

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