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Survey of Molecular Dynamics Simulations: Week 2 By Will Welch For Jan Kubelka CHEM 4560/5560 Fall, 2014 University of Wyoming

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Forces on each particle are calculated at time t. The forces provide trajectories, which are propagated for a small duration of time, Δt, producing new particle positions at time t+ Δt. Forces due to new positions are then calculated and the process continues: How do the dynamics happen? The **basic** idea…

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Verlet algorithm (http://www.fisica.uniud.it/~ercolessi/md/md/node21.html) Velocity Verlet algorithm Leap-Frog algorithm (From Wikipedia) How do the dynamics happen?

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What is a suitably short time step? How do the dynamics happen? Adequately Short Time step Time step Too long Must be significantly shorter than the fastest motion in your simulation: What is frequency of C-H stretch. O-H stretch? Constraint algorithms: Settle, Shake, Rattle, LINCS Minimum time step depends on what you are monitoring. At least, simulation must be stable. Normal restoring force Huge restoring force: simulation crashes

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Temperature control The natural ensemble for the most basic MD simulations is the microcanonical (N,V,E) ensemble. Often we want to use the canonical (NVT) isothermal, isobaric (NPT).

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Temperature control The natural ensemble for the most basic MD simulations is the microcanonical (N,V,E) ensemble. Often we want to use the canonical (NVT) isothermal, isobaric (NPT). Stochastic thermostats: Introduce random perturbations to velocities—can be viewed as random reassignment rather than rescaling. Andersen: Randomly select particles and reassigns velocities from a distribution determined by the desired temperature. Langevin or Browninan dynamics: include a stochastic term in dynamics equations that perturbs normal velocities by assigning random forces from within a distribution determined by the temperature. ***These cause drag and slower dynamics. Weak temperature coupling is advised. Non-Equilibrium MD simulations: Does strict temperature control make sense? Is the center of mass moving? (Probably) Must you apply a thermostat to the whole system? Weak temperature coupling is advised!

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Pressure Control If we want to perform a simulation at constant pressure we generally have to let the volume fluctuate (NPT ensemble). The simplest barostat is the Berendsen barostat, which is similar to the Berendsen thermostat such that the volume of the simulation cell is corrected at each (specified) time step by a scaling factor: Where μ is the scaling factor for of one side of the (cubic) simulation cell (and other lengths in the system) and τ is a time coupling constant. Again the Berendsen method does not generate any known statistical ensemble, especially for small systems, but it is stable. For production runs, use the Parinello-Rahman method, which is somewhat analagous to the Nose-Hoover thermostat method. Pressure coupling only works at equilibrium!

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Thermostats and Barostats Recap All types of temperature control alter velocities and therefore disturb dynamics. In Non-stochastic methods, the “flying ice cube” artifact can be circumvented by removing translational and rotational center of mass motion. The Nose-Hoover method produces the correct velocity distributions for a canonical ensemble and maintains smooth trajectories; consequently it is a method of choice for equilibrium NVT and NPT simulations. Stochastic temperature control typically disturbs dynamics more than non-stochastic methods. Velocity reassignment causes significant drag on dynamics and produces discontinuous trajectories. Non-equilibrium simulations should use stochastic temperature control in order to avoid build up of kinetic energy in translational and/or rotational modes. Issues with thermostats may be circumvented by selectively thermostatting different groups (i.e. solvent or an specific area in space). The Rahman-Parrinello and MTTK pressure coupling schemes generate the correct ensemble, but they are sensitive and unstable far from equilibrium, epsecially R-P. A more stable Berendsen scheme can be used initially to reach the correct volume. Pressure coupling only makes sense for equilibrium simulations.

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