Chapter 5: Periodic Boundary Conditions Flashcards Preview

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Flashcards in Chapter 5: Periodic Boundary Conditions Deck (6):
1

Periodic Boundary Conditions 
(Motivation)

Using a finite box makes surface effects extremely non-negligible with respect to bulk effects

2

Periodic Boundary Conditions 
(Notes)

  • Use minimum image convention for short-range interactions with xij |< L/2
  • PBC forbids long wavelength fluctuations
    • max correlation length lc = L
  • ​PBC is problematic for long-range interaction
    • use something like Ewald sum or P3M

3

Periodic Boundary Conditions 
(Efficiency)

  • Force calculations very expensive N2
  • Can increase efficiency using cell division and verlet lists

4

Periodic Boundary Conditions 
(Cell Division)

  • divide central box into subboxes with length Lc >| rc
    • ​particle only interact with those in same, or neighboring, box
  • reduces force calcuation to N

5

Periodic Boundary Conditions 
(Verlet Lists)

  • Let rs > rc be skin radius and list li of all particles within sphere of radius rs around particle i
    • choose rs such that some particles can remain rc < r < rs for 10-20 timesteps
  • particle i can only interacts with particles j in li
  • update when max{∆rij} > 1/2(rs-rc)
    • rij = ri - rj

6

MD Observables

  • thermodyanmic properties TP, CV, etc. simplest to measure
    • relevant equations dependent on ensemble
  • virial pressure (see below)
  • thermodyanmic potentials SFG cannot be measure in simulation