Lecture 6: MD2 Flashcards
What happens at a boundary?
It can be a repulsive wall or a periodic boundary
What are periodic boundary conditions?
-they mimic bulk conditions
-as particle goes out the box, it’s periodic image comes in the other side
-system must be large enough that a particle doesn’t interact with its mirror image (as least 2x potential cutoff)
Why are periodic boundary conditions good?
Ensemble properties can be calculated with fewer particles
What ensemble do pure molecular dynamics occur in
The micro canonical (NVE) ensemble
What might be a disadvantage of using a microcanonical ensemble?
Not useful to compare with experiments which are usually at a constant temperature
What can be used to control the temp of the system
Thermostats
What is équipartition theory?
KE total=3N/2kB T
What is a drawback of the Velocity Rescaling Thermostat?
It does not generate the canonical ensemble
Consider a limiting case where we rescale the temp every step, which would lead to zero temp fluctuations
How does the Berendsen thermostat work?
Heats system with heat bath
But this suppresses the KE fluctuations not consistent with ensemble
So a heat decay of Tau is added
What is the Nosé-Hoover thermostat?
Introduces thermal reservoir and friction coefficient into equations of motion and so allows KE changes in the system
Allows canonical ensemble correctly
What is a common approach of thermostats in simulations
Use a weak coupling method to equilibrate the system, then use Nosé-Hoover thermostat for the final simulations
What is a barostat?
Couple the system to a pressure bath
What is the berendsen barostat?
Rescaled coordinates every step
Doesn’t generate proper thermodynamic ensemble
What is the Parrinello-Rahman barostat?
-similar to Nosé-Hoover thermostat where particle equations of motion are updated every step
-correct thermodynamic ensemble generated
How do you know when you’re ready to start sampling?
When the system has reached equilibrium
How do you know a system is at equilibrium?
-minimum free energy
Or
-change in free energy is zero
In NVT ensembles, what will be constant at equilibrium?
Helmholtz free energy (A) is constant
Potential energy is constant
In NPT ensembles, what will be constant at equilibrium?
Gibbs free energy (G) will be constant
Potential energy and volume will be constant
What things need to be considered when seeing if a system has reached equilibrium?
-even if PE isn’t changing it might not be at equilibrium, might be at métastable state it vitrified
To ensure the PES is accurately sampled what needs to happen?
-multiple runs are needed
Why are multiple runs needed?
Allows you to generate more microstates and gain better statistics as well as calculate errors associated with simulations
Also allows for sampling of different regions of the bulk
How is the radial distribution function represented?
g(r)
What info does the radial distribution function give?
-gives info on local density and structure
-can be compared to results from x-ray or neutron scattering experiments
-commonly used to distribution between phases
How is the radial distribution function calculated?
By looking radially from a particle “a” at a shell at distance r and thickness dr, counting the number of “b” particle in this shell and normalising by the shell volume
Then averaged over time and particles
What is the MD simulation checklist?
- Is this simulation sensible to run?
- Am I using right ensemble?
- Is the force field accurate?
- Is my system large enough?
- Is my system charge net neutral?
- Is my time step the right size?
- Is my thermostat/barostat working?
- Is my system statistically accurate?
What are the common rules of thumb for atomistic simulations?
-time step dt 1fs
-total run length 10^6-10^8 dt or 1-10ns
-no. Particles 10^4-10-^6
