Hy2915:

MRD:everything01095534

2017-05-05T14:03:47Z

Hy2915:

== Molecular Reaction Dynamics of Triatomic systems ==
this wiki page is to explain triatomic interaction dynamic and illustrate it on specific example

=== background Theory ===
The nucleus, is extremely heavy and large compare to electron in the atom. So when an atom moving toward or backward to another atom, the relationship can be shown by the equation below:

<math> {dp_i \over dt} = - { \partial V(r_1,r_2,...)\over \partial r_i}</math>

The force (variation of momentum '''p''') acting on a given intervatomic coordinate '''ri''' will depend on the derivative of the potential energy surface with respect to that coordinate.

In this concept only three atoms on a straight line will be considered.

=== H+H2 System ===
In this context, three hydrogen atoms are aligned on a straight line to use Matlab programming the potential energy change of the atoms under different condition
[[File:Plot1.png|500px|thumb|center|contour plot, r1=0.74A, r2=2.30A, p1=0 p2=-2.70]]

contour graph when the distance between A and B is equal to 0.74 which is just like the normal bond length of a normal H2 molecule. In the H + H2 model, the initial conditions are set as '''r1''' = 0.74 ,'''r2''' = 2.30 and the momenta '''p1'''=0 ''' p2''' = -2.7.

[[File:haiyang2.png|500px|thumb|center|intermolecular distance vs time, r1=0.74A, r2=2.30A, p1=0 p2=-2.70]]

This is the figure which shows when the time goes to 0.38 time units, a repetitive oscillation behavior is happened, showing that the transition state was also suppose to be found at 0.38 time units. So the rts is 0.9148A then. But based on the result of animation, the true rts is 0.90775A but not 0.9148A.
[[File:haiyang3.png|500px|thumb|left|Kinetic Energy vs Time, r1=0.74A, r2=2.30A, p1=0 p2=-2.70]]
[[File:haiyang4.png|520px|thumb|center|Potential Energy vs Time, r1=0.74A, r2=2.30A, p1=0 p2=-2.70]]

The "Potential Energy vs Time" and "Kinetic Energy vs Time" proved that at transition state the potential energy gives rise to the highest value while kinetic energy give rise to the lowest value. As well, an oscillatory behavior rising after the transition state.

The total gradient of the minimum (at the start and the end point in reactant) on the potential energy surface is equal to '''0 as well as '''at the transition state point. But the difference between the minimum and the transition state point is that transition state point has a negative second derivative towards product and a positive second derivative towards reactant; while at the minimum point in the whole system (at the beginning point in the reactant) have a '''zero''' second derivative value.Hence the potential energy difference between minimum energy and transition state is the '''activation eneregy'''

=== Trajectories from r1 = r2 locating the transition state ===
Due to H + H2 potential surface is symmetric(left and right of the transition state), assuming the transition state must have '''r1 = r2''' '''=''' '''0.90775A''' (rts at the transition state position), the relative stationary state of motion is observed. If the approaching proton atom is placed at the ridge of potential surface, there is no gradient in the direction at right angle to the ridge; therefore the proton sphere would oscillate about that region without falling down. As shown in the figures below, one figure shows that the reactant proton is oscillating at the transition state position; while another shows that there is not any relative change in terms of the distance for the three protons against time.

=== Calculating the reaction path by using Trajectories from r1 = rts r2 = rts+ δ ===
This model will favour HA-HB + HC as reactant proton C is very close to the central proton. In this section, a initial system of r1 = 0.91775, r2 = 0.90775. p1 = 0 p2 = 0 is considered.

'''MEP calculation type'''

In this case, there is a little derivation from the transition state position, say 0.01A derivation for a first try, for one of the protons. The MEP calculation type is set so as to simulate the motion for this circumstance. The MEP contour plot is given below.

'''Dynamics calculation type'''

When dynamics calculation type is applied again, the trajectories gained is quite different from MEP calculation type. See the figures below, which show the averaged moment and the final positions.

'''r1''' = 5.281A

'''r2''' = 0.7455A

'''p1''' = 2.481 (Calculated as an average of the maxima 1.564 and minima 0.9109 at a large t)

'''p2''' = 1.237

Because '''MEP''' is considered that there is '''a step-energy down''' where the main difference is, comparing to the '''dynamics calculation type'''. The '''MEP''' just calculate all the minimum energy following the trajectories while '''dynamics calculation type''' includes all the vibrating situation with the trajectories.

=== Calculating the reaction path by using Trajectories from r1 = rts + δ r2 = rts ===
Here, we are going to swap the parameters from what we just did in '''section 1.3''',

'''r1''' = 0.7455A

'''r2''' = 5.281A

'''p1''' =1.237 (Calculated as an average of the maxima 1.564 and minima 0.9109 at a large t)

'''p2''' = 2.481

1.'''What value does the total gradient of the potential energy surface have at a minimum and at a transition structure? Briefly explain how minima and transition structures can be distinguished using the curvature of the potential energy surface.'''

File:Haiyang4.png

2017-05-05T13:54:50Z

Hy2915:

File:Haiyang3.png

2017-05-05T13:52:19Z

Hy2915: