Ensembles

Question 1

Why are ensembles useful

Answer 1

Ensembles set up the condition for simulation

• to directly map to and compare with experiment
• to consider fluctuations that are important in small systems
• to follow simulation protocol, e.g. a temperature or pressure change

Question 2

Give some ensembles

Answer 2

Microcanonical (N,V, E)
Canonical (N,V,T)
Isotherm-Isobaric (N,p,E)
Grandcanonical (u,V,T)

Question 3

What is the challenge for simulation with ensemble of constant Temp?

Answer 3

The need to rescale the temperature since velocity scales with temperature

Solution:
Use of thermostats to rescale the velocity with respect to Temp

Question 4

Give some thermostats

Answer 4

Naive: Draw particle velocities at every time step randomly from the Maxwell-Boltzmann distribution

Anderson: Couple to a heat bath via stochastic collision. If particle performs collision choose another velocity from the MB distribution

Noose Hoover: Use Mass (Q) The parameter Q is a thermal inertia parameter, which determines the rate of the heat transfer. Integral feedback and oscillates depending on the desired system Temp

Berendsen/ Parinello: Uses “friction” force of either negative or positive to bring back the system to the desired Temp.

Question 5

How can MD and MC be combined? Why is this possible?

Answer 5

• It is possible to combine MC/MD since some thermodynamic observables are not necessary to be defined via deterministic or stochastic approach.
• Both MC and MD can work, provided that the assumptions, limits and boundaries are valid [as described in Metropolis Criterion]
• MC generally provides “some” acceptance and rejection criteria that would make MD work faster through skipping the “strict’ time evolution pathway and just considering the ‘working’ criteria set by MC