Lecture 1

Question 1

• There exist many computational methods that are available depending on the length/time scale we are interested in.
• Classes in order of increasing … scale and decreasing … scale they investigate
• Quantum/… … : includes atoms, electrons in an explicit solvent using … … (Schrodinger). Accurate but computationally unfeasible for >… atoms.
• … -…: all/most atoms included in an explicit solvent but instead uses…as a method of reference, which describe atoms via….
• Coarse-grained: group 4-5 heavy atoms into beads, in an explicit or … solvent using MD. Far less interactions to compute but at the cost of accuracy.
• … -…-… : interaction sites grouped, comprising of many atoms, generally proteins/peptides, using an implicit solvent with … dynamics.
• … : Materials represented as a continuous mass in an implicit solvent, using … … (instead of QM/EOM).

Answer 1

• There exist many computational methods that are available depending on the length/time scale we are interested in.
• Classes in order of increasing length scale and decreasing time scale they investigate
• Quantum/Ab initio: includes atoms, electrons in an explicit solvent using quantum mechanics (Schrodinger). Accurate but computationally unfeasible for >3 atoms.
• All-atom: all/most atoms included in an explicit solvent but instead uses MD as a method of reference, which describe atoms via EOMs.
• Coarse-grained: group 4-5 heavy atoms into beads, in an explicit or implicit solvent using MD. Far less interactions to compute but at the cost of accuracy.
• Supra-coarse-grained: interaction sites grouped, comprising of many atoms, generally proteins/peptides, using an implicit solvent with stochastic dynamics.
• Continuum: Materials represented as a continuous mass in an implicit solvent, using continuous dynamics (instead of QM/EOM).

Question 2

Give 3 example of rare events in chemistry

Answer 2

• A protein folding mechanism would contain many different intermediate specific states, occurring on the µs-s scale. Continuum based method ideal for this timescale but cannot describe individual atoms clearly enough
• Phase transitions, e.g. water nucleation to from ice. Process has an extremely low rate, meaning we must simulate for large timescales
• Catalysed reactions occur on the ps scale, which is achievable in QD but involves making/breaking bonds, which is not possible with the non-reactive forcefield used.

Question 3

• Define rare events in the context of molecular simulations.

Answer 3

• Processes that involve time scales much longer than what we can computationally afford.
• Definition relative to our method of choice.

Question 4

What are enhanced sampling techniques

Answer 4

• Computational methods that allow one to overcome the timescale problem by sampling the phase space of our system to a greater extent. We can use MD or MC to do this.

Question 5

• What two variables are measured to find a phase space vector for a given configuration?

Answer 5

• x_λ = r_i=1,…, r_i=N, p_i=1,…, p_i=N
• Where position (defined by PE) and momenta, p (defined by v –> KE) of N particles in x,y,x plane to give us our 6D vector.

Question 6

• (IMP) How is system free energy related to the timescale problem.

Answer 6

• Our phase space if a collection of all configuration’s position and momenta.
• A rare event is likely to be separated from our starting configuration by a high free energy barrier that cannot be overcome using MD/MC alone in a feasible timescale. Instead we are likely to spend all/most of our simulation time trapped in that local minima.

Question 7

• (IMP) Briefly describe the two main methods of enhanced sampling.

Answer 7

• Free energy-based methods: characterize PES of system
• E.g. umbrella sampling, replica exchange MD, metadynamics
• Choice of reaction coordinate/dof important and will affect free E of system.
• No direct info about kinetics of the process
• Path sampling-based methods: explore all possible pathways
• E.g. transition path/interface sampling, forward flux sampling
• More suited for processes with many possible pathways between
• No direct info about the thermodynamics of the system.