Chapter 1: MD Methods

Question 1

Main Uses

(MD Methods: 2 points)

Answer 1

• to obtain dynamic information about the system
• to calculate statistical (i.e. thermodynamic) averages

Question 2

Ergodicity Hypothesis

Answer 2

For significant number of particles, the time average is the same as the ensemble average

Question 3

Ergodicity, MD, MC

Answer 3

Question 4

Overview

(MD Methods)

Answer 4

• approximate solutions to equation of motion using finite difference method

Question 5

Euler Method

(Algorithm)

Answer 5

Derive by Taylor expanding x(t + ∆t )

Question 6

Euler Methods

(Failures)

Answer 6

• Energy grows without bound for oscillatory phenomena
  
  • not symplectic - not compatible with Hamiltonian symmetries

Question 7

Verlet Integrator

(Algorithm)

Answer 7

• derive by Taylor expanding r (t + ∆t ) and r (t - ∆t ) and adding together
• velocity comes from centered finite difference method

Question 8

Verlet Integrator

(Failure)

Answer 8

Not self-starting

Question 9

Velocity-Verlet Integrator

(Algorithm)

Answer 9

1. Initial setup
2. Calculate new position x(t + ∆t )
3. Calculate half-step velocity v(t + 0.5∆t )
4. Calculate new force a(t + ∆t )
5. Claculate final velocity v(t + ∆t )

Question 10

Velocity-Verlet Integrator

(Benefits)

Answer 10

• equivalent to Verlet integrator
• includes velocity explicitly
• self-starting

Question 11

Verlet Integrator

(Benefits)

Answer 11

• more stable than Euler method
• preserves physical properties
• time reversible