Stefano Leoni

Question 1

How is g(r) defined, and how can it be obtained from a molecular dynamics trajectory?

Answer 1

g(x) is the ratio between the average number density ρ(r) at a distance r from
any given atom and the density at a distance r from an atom in an ideal gas at
the same overall density. Distances (within a cutoff) from all configurations of
a MD run can be collected into an histogram and normalised wrt the density of
an ideal gas.

Question 2

Verlet Algorithm - Steps

Answer 2

a) Given positions, velocities and forces
b) new positions can be computed (t + δt).
c) Velocities at t+δt/2 are computed,…
d) and forces at t+δt.
e) Velocities are computed at full step,
f) And the system is advanced to the next time step

Question 3

coordination number from g(x)

Answer 3

Integrate the the g(x) to give the number of neighbours present in distance r

Question 4

Two methods of visiting rare events

Answer 4

• Metadynamics

- Transition path sampling

Question 5

Metadynamics

Answer 5

• Sampling all degrees of freedom is time consuming
• This bundles several degrees of freedom
• calculation can progress quickly towards other energy minima in the system overcoming energy barrier
• Addition of bias to potential energy in order to discourage visiting configurations already explored, favouring the unvisited

Question 6

Transition path sampling

Answer 6

• TPS is able to generate true dynamical trajectories
• Once rare event is observed, system is designed to stay in that region
• Focus here is in the intermediate region only, i.e. TPS is designed to stay in the transition path and explore variations of this path
• Rare events become frequent

Question 7

Why g(x) converges to 1 at high distances

Answer 7

Large distances are more representative of an ideal gas.