Observables and Structure

Question 1

What are the common thermodynamic observable?

Answer 1

• Common observables are: Particle number, KE, PE, Temperature
• Complicated observables are: Entropy, Gibbs Free energy and Helmholtz Free energy.

Question 2

Describe the Central Limit Theory (CLT) and how it is used for error analysis

Answer 2

• sample number increases, distribution will approach normal distribution regardless of its original distribution
• rule of thumb = more data points = closer to the expected value. Thus, the error would be minimal.

Question 3

How would you average a thermodynamic observable in a simulation?

Answer 3

• Ensemble average [average the observable over all N particles] or
• Time average [average the observable at a specific time step].

Regardless of the values from these two average would be the same as based on “ERGOCITY THEOREM”.

Question 4

What is coordination number?

Answer 4

CN is the no. of nearest neighbor of an atom and is the “first” peak of the RDF

Question 5

What happens during ballistic motion, caging and diffusion?

Answer 5

Three regimes are distinguished:
• ballistic motion: free movement of particles, e.g. ideal gas
• caging regime: atoms are locally trapped in the nearest neighbor shell
• diffusive motion: long-time behavior, dominated by random collisions

Question 6

Differentiate Standard Deviation versus Standard Error

Answer 6

Standard Deviation is a measure for the spread of measurements

Standard Error is the accuracy of measurement

Question 7

Importance of Radial Distribution Function

Answer 7

1. For Pair Potentials: All thermodynamic properties can be calculated from RDF
2. Statistical Theory of Liquids builds upon RDF
3. RDF can be directly measured from neutron scattering experiments and as well as microscopy

Question 8

What is Radial Distribution Function?

Answer 8

• Characterization tool to analyze a structure

* Describes how the density varies with distance in respect to a reference point

Question 9

How can Diffusion coefficient be determined in a simulation?

Answer 9

• Via MSD (Mean square displacement) or how far did the particle moved through time
• described by the Einstein Relation

Question 10

How would you measure thermodynamic observables?

Answer 10

• PE from Lennard Jones Potential
• KE from a known velocity then
• Temperature from MB-Distribution