Examiners: Hünenberger, Riniker 

Comments: 15min with each examiner, an assistant is present and takes notes  throughout. Relaxed, friendly atmosphere, but quite fast-paced; Hünenberger  provides hints when needed, don’t know about Riniker (didn’t come up). Exam  conducted via Zoom due to COVID pandemic situation. 

Hünenberger 

• Why do we not exclusively simulate at the QM level?
  (unfavourable scaling)

• How dow QM methods scale?
  (n^3 or worse) 

• What can’t we do with MD?
  (covalent chemistry, spectroscopy etc.)

• How do we do MD?
  (integrate Newton’s equations of motion) 

• Can you write down the Hamiltonian of our system?
  ( H = K(q,p) + V(q) )

• Can you write down the Hamiltonian equations of motion?
  ( *write them down* )

• Do you know which one corresponds to F = ma?
  (the one with (del H/ del q) )

• What does the force-field term for electrostatics look like generally?
  (*write down*)

• What about van der Waals?
  (*write down*) 

• Where do we get those C6/C12 from?
  (parametrise against rare gases, draw a little  sketch of curve, explain ε, σ etc.) 

• And if you had two different atom types?
  (*write down combination rule for C6/C12*,  mention some alternatives) 

• What ensemble do we sample with plain MD?
  (NVE) 

• And with MC?
  (NVT)  

• Can you explain how Monte Carlo works?
  (*do it*) 

• Do you remember what the move acceptance criterion is?
  (*write it down*, mention  it’s meant to keep the ensemble Boltzmann) 

• Could you preferentially pick moves along the direction of current force to enhance  sampling?
  (Technically no, the choice of a candidate next state has to be unbiased.  He mentions that biased MC exists, but you have to correct for the bias.)

• Do you remember the definition of the instantaneous temperature?
  (*write down*)

• A system of 100 diatomic molecules with bond constraints has how many degrees  of freedom?
  (200*3 - 100 = 500) 

• What about the instantaneous pressure?
  (*write down*) 

• And the virial?
  (*write down*) 

• How do thermostating and barostating work conceptually?
  (*scale the things*)

• Why would someone want to supply the compressibility to …?
  (My memory is a bit  fuzzy here, it was either a thermostat or a barostat. He wanted me to connect it to the instantaneous pressure expression somehow, but I didn’t quite get it in the  moment. Something about controlling temperature and pressure simultaneously. I  couldn’t answer the question and he said “don’t worry”, and we moved on to the  second part of the exam)

Riniker 

• You talked about MC. How does Temperature Replica Exchange work?
  (*explain*)

• What is the exchange acceptance criterion?
  (*write down*) 

• How does Umbrella Sampling work?
  (*explain*) 

• How would you do the reweighing?
  (*write down formula*) 

• What about accelerated MD, how is that different?
  (*explain, write down formula,  draw a little picture*) 

• How would you get a conformational free energy difference from Umbrella  Sampling?
  (*formula*, explain what the binary assignment functions do, how they  could be defined in terms of RMSD) 

• Would these assignment functions change if your states of interest or the system  were to change?
  (*Yes. Not necessarily the functional form, but yes.*)

• How would you go about getting a relative binding free energy of two ligands to a  protein?
  (*draw the thermodynamic cycle, say which transitions you simulate*)