1 / 13

Molecular Dynamics

Learn the basic idea of Molecular Dynamics simulations: solving Newton’s equations of motion, choosing force fields, ensembles, and observables, with examples and insights on implementations and potential used in biomolecular modeling. Discover how to compute transport coefficients and recommended textbooks for further understanding.

jlindahl
Download Presentation

Molecular Dynamics

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Molecular Dynamics

  2. Basic Idea • Solve Newton’s equations of motion • Choose a force field (specified by a potential V) appropriate for the given system under study • Decide a statistical ensemble to use, choice of boundary conditions; collect statistics of observables

  3. Commonly Use Force Fields • Lennard-Jones potential • For noble gas and generic fluids • Tersoff, Brenner, Stillinger-Weber, 3-, 4-body potentials • For C, Si, Ge, … • AMBER, CHARMM, GROMOS, MM4, etc • For biomolecules • GULP, LAMMPS, DFT codes, etc

  4. Example of potential used in biomolecular modeling

  5. Ensembles • Micro-canonical Ensemble • Energy is fixed • Canonical ensemble • Need to use “thermostat” to fix temperature • Langevin dynamics • Nosé-Hoover • Generalized Langevin

  6. Langevin Dynamics How to correctly implement the white noise on computer?

  7. Nosé-Hoover Dynamics

  8. Generalized Langevin Σ is known as self-energy

  9. Observables, Statistics • Equilibrium temperature (in micro-canonical ensemble) by equipartition theorem. • Pressure of a fluid (for pair potential) Where d is dimension, Fij is the force acting on particle i from particle j.

  10. Transport Coefficients • The diffusion constant can be computed through velocity correlation function

  11. Transport Coefficients • Thermal conductivity can be computed through energy-current correlation using Green-Kubo formula; or nonequilibrium simulation by directly computing the energy current

  12. Textbooks on MD • M P Allen & D J Tildesley, “Computer Simulation of Liquids,” (Oxford, 2017) • D Frenkel & B Smit, “Understanding Molecular Simulation,” (Academic Press, 2002) • A R Leach, “Molecular Modeling, principles and applications,” (Pearson, 2001)

  13. Tutorial Problem Set 12 • Prove the pressure formula (required a great deal of knowledge of statistical mechanics).

More Related