Geometry-Optimisation

Question 1

How many degrees of freedom are there?

Answer 1

3N-6
3N-5 linear

Question 2

What is the Newton-Raphson formula?

Answer 2

ΔR = -k^-1 δE/δR
force constant k=secound derivative

Question 3

What is the steepest descent formula?

Answer 3

ΔR = -δE/δR
i.e the negative gradient

Question 4

What are the advantages and diadvantages of steepest descent?

Answer 4

adv: good starting point when far from minima
dis: inefficient as it tends to ‘bounce’ around the minima

Question 5

What are the advantages and disadvantages of Newton Raphson?

Answer 5

adv: effective when close to minima, takes into account curvature to improve the step size

dis: espensive, assumes PES is harmonic at each point so requires curvature k at each point

Question 6

Describe finding the Transition state structure

Answer 6

-Need the co-ordinates where the gradient is 0 wrt all co-ordinates
-Need a very accurate starting structure and k estimate
ΔX = +|Kx|^-1 δE/δX
ΔR = -k^-1 δΕ/δR
must compute the step hill along reaction co-ordinate whilst simultaneously calculating downhill for all other co-ordinates