Chapter 13: ab initio MD

Question 1

Effect on Nuclei Outside BO Approximation

Answer 1

• nuclei move in response to electron cloud

Question 2

Hellman-Feynman Theorem

Answer 2

gives force on nucleus I

Question 3

ab initio MD General Approach

Answer 3

1. Solve SE
2. Get groundstate wavefunction
3. Calculate HF and electrostatic forces
4. Perform MD step with forces on ions

Question 4

Ehrenfest MD

Answer 4

solve EOM for electronic and nuclear subsystems separately for each timestep

• Advantages:
  
  • can capture non-adiabatic effects
• Disadvantages:
  
  • ∆t_E very small (10^-3 - 10^-5 fs)
  • might miss important chemical reactions

Question 5

Born-Oppenheimer MD

Answer 5

similar to Ehrenfest MD, but use TISE

• Advantages:
  
  • electron motion treated implicitly → ∆t_BO = 10² ∆t_E
• electron wavefunction changes because electrons are dragged along with nucleus

Question 6

Car-Parrinello MD

Answer 6

avoid QM calculation at each timestep by treating both subsystems classically

• define Lagrangian
  
  • fictituous mass µ
  • time dependence in Λ
• Advantages:
  
  • if µ is tuned correctly, can get exact results without QM calculation
  • ∆t_CP approx. 10 ps
• Disadvantages:
  
  • bad initial nuclear configuration → potentially miss global minimum

Question 7

Quantum Mechanics/Molecular Mechanics

Answer 7

split system into two parts

1. quantum part
2. classical part

Question 8

QMMM Hamiltonians

Answer 8