Molecular Reaction Dynamics : Applications to Triatomic

Introduction

In this report the molar reaction dynamics is studied by discussing the reaction of a triatomic system. A atom A collide atom B (bonded with C) and from the new AB compound. The surface energy plot was plotted by using MATLAB. The trajectory of the path of the reaction, change in internuclear distance and change in potential energy vs time plot was used in analysis in order to discover the condition for the reaction to proceed.

H+H₂ System

Dynamics from the transition state region

The total gradient of the potential energy surface is zero at a minimum and at a transition structure. According to the definition: transition state is the maximum on the minimum energy path, the transition state in unstable equilibrium, thus the second derivative of potential energy against bond distance is smaller than zero. Whereas the minium of potential energy surface is in stable equilibrium, the second derivative of potential energy against bond distance is larger than zero.

Best transition state position (r_ts)

As explained previously at transition state, the total gradient of the potential energy surface is zero. By plotting a surface plot with r1(0)=r2(1)=0.74 A (bond length of H-H bond), the maximum of minimum energy path gives the transition state distance: 0.9076 A. Internuclear Distance vs. time plot showed AC distance approximate to 1.8 A twice the BC bond distance Thus the bond distance between AB and BC dose not change. The system is in a transition state.

reaction path and calculation

r1=rts+0.01

The dynamics plots gives curved line it includes trasitional and vibrational motion as well as trajectory. This is because the dynamic mode calculation includes interaction between of one atom to another, which take the realistic situation into account. While the MEP mode showed the minimum path as a straight line,just trajectory no atom interaction motion was included in the line. This is because the MEP mode calculation,the velocity was always reset to zero in each time step.

r2=rts+0.01

For the plot in dynamic mode, the r1 = rts+δ plot is symmetrical about y=x with r2=rts+0.01. This shows the same amount of change in energy with one is the transition from reactant to product and the other with transition from product to reactants.

Reactive and Unreactive Trajectories

No.	p₁	p₂	Reactivity	Trajectory	Momentum	Internuclear Disctance	Description
1	-1.25	-2.5	reactive	The surface plot of H+H₂ System under dynamics mode with p1=-1.25 p2=-2.5	The change of momentum vs. time of H+H₂ System under dynamics mode with p1=-1.25 p2=-2.5	The internuclear dis of H+H₂ System under dynamics mode with p1=-1.25 p2=-2.5	The momentum of BC is large, provide enough kinetic energy to overcome the activation barrier to generate the reaction.
2	-1.5	-2.0	unreactive	The surface plot of H+H₂ System under dynamics mode with p1=-1.5 p2=-2.0	The change of momentum vs. time of H+H₂ System under dynamics mode with p1=-1.5 p2=-2.0	The internuclear dis of H+H₂ System under dynamics mode with p1=-1.5 p2=-2.0	The momentum of BC is not enough to overcome the activation barrier to break H-H bond and from the new bond.
3	-1.5	-2.5	reactive	The surface plot of H+H₂ System under dynamics mode with p1=-1.5 p2=-2.5	The change of momentum vs. time of H+H₂ System under dynamics mode with p1=-1.5 p2=-2.5	The internuclear dis of H+H₂ System under dynamics mode with p1=-1.5 p2=-2.5	The momentum of BC is enough to overcome the activation barrier to break H-H bond and from the new bond.
4	-2.5	-5.0	unreactive	The surface plot of H+H₂ System under dynamics mode with p1=-2.5 p2=-5.0	The change of momentum vs. time of H+H₂ System under dynamics mode with p1=-2.5 p2=-5.0	The internuclear dis of H+H₂ System under dynamics mode with p1=-2.5 p2=-5.0	The momentum of BC is enough to overcome the activation barrier to break H-H bond and from the new bond. However, barrier recrossing takes place and there is not enough energy to overcome the activation barrier again to form the product.
5	-2.5	-5.2	reactive	The surface plot of H+H₂ System under dynamics mode with p1=-2.5 p2=-5.2	The change of momentum vs. time of H+H₂ System under dynamics mode with p1=-2.5 p2=-5.2	The internuclear dis of H+H₂ System under dynamics mode with p1=-2.5 p2=-5.2	The momentum of BC is enough to overcome the activation barrier to break H-H bond and from the new bond. Barrier recrossing takes place and there is enough energy to overcome the activation barrier again to form the product.

Transition State Theory states that there is an equilibrium between the reactants and activated transition state complex, as once the system reaches the critical spatical configuration. it will proceed to generate the product.[1] However, in reaction 4, the momentum was big enough to form the products. So the critiacl spatical configuration was generated. Still the reaction was not proceed. This dose not support the transition state theory.

F - H - H system

In this section, instead of three identical atoms. F and H atoms will be involved in the collision.

Endothermic vs. Exothermic Reaction

The surface plot of F+H₂	The surface plot of F+H₂
The surface plot of H+HF	The surface plot of H+HF

By using the surface plot, the difference of potential energy between the reactant and product can be calculated, as the figure above illustrated. So the F+ H ₂ reaction is exothermic , the potential energy of reactant is smaller than product. The H+HF reaction endothermic as the initial potential energy is larger than the final potential energy.

Transition State and Activation Energy

Position of Transition State

The transition state is discovered at the position where the distance between H atoms as 0.74495 A and the distance between H and F as 1.81073 A. The HH distance is slightly longer than the HH bond distance (0.74) A.

Activation Energy

The reactant potential of H+HF	The product potential energy H+HF reaction
The reactant potential of F+H₂	The product potential of F+H₂

Activation Energy of H + HF reaction is 0.2 kJ/mol
Activation Energy of F + HH reaction is 30.1 kJ/ mol

Reaction Dynaimcs

Mechanism of of F+ H₂

Surfance Plot of Reactive Trajectory of F+ H ₂	Kinetic Energy of Reactive Trajectory of F+ H ₂
Momentum Time Plot of Reactive Trajectory of F+ H ₂	Potential Energy of Reactive Trajectory of F+ H ₂

The condition of the reaction is summarised in the following chart

r _HH=0.74 A
r _FH=2.30 A
p _HH= -1.5 kgm/s
p _FH= 2.87 kgm/s

The mechanism of the reaction is initially the F atom attack the H atom in the middle with generation of the break of H-H bond and forming of H-F bond.
The energy is conserved in the reaction. So the energy of the system is converted from potential energy into kinetic energy. Before the reaction, the reactants vibrated small as both the kinetic energy vs. time plot and potential energy vs. time plot both fluctuated with small value. At the time the reaction was finished, the vibration in the potential energy vs. time graph increased with an increase in small value. The kinetic energy vs. time graph, the vibration of k.e. increase as the reaction proceeded, the value decreased. This is because the reaction is exothermic, so at the end of the reaction kinetic energy is converted into potential energy.
IR or NMR is suggested as a method to check the end of the reaction. The vibration of HF bond is higher than HH bond.

Momentum and Trajectory

No.	p_HH kgm/s	p_FH kgm/s	Reactivity	Internuclear Distance Diagram
1	-0.5	-3.0	unreactive	Internuclear Distance of F+ H ₂ reaction when p_HH=-3 kgm/s
2	-0.5	-2.5	unreactive	Internuclear Distance of F+ H ₂ reaction when p_HH=-2.5 kgm/s
3	-0.5	-2.0	reactive	Internuclear Distance of F+ H ₂ reaction when p_HH=-2.0 kgm/s
4	-0.5	-1.5	unreactive	Internuclear Distance of F+ H ₂ reaction when p_HH=-1.5 kgm/s
5	-0.5	-1.0	unreactive	Internuclear Distance of F+ H ₂ reaction when p_HH=-1.0 kgm/s
6	-0.5	-0.5	unreactive	Internuclear Distance of F+ H ₂ reaction when p_HH=-0.5 kgm/s
7	-0.5	0.0	unreactive	Internuclear Distance of F+ H ₂ reaction when p_HH=0.0 kgm/s
8	-0.5	0.5	unreactive	Internuclear Distance of F+ H ₂ reaction when p_HH=0.5 kgm/s
9	-0.5	1.0	unreactive	Internuclear Distance of F+ H ₂ reaction when p_HH=3.0 kgm/s
10	-0.5	1.5	unreactive	Internuclear Distance of F+ H ₂ reaction when p_HH=1.5 kgm/s
11	-0.5	2.0	unreactive	Internuclear Distance of F+ H ₂ reaction when p_HH=2.0 kgm/s
12	-0.5	2.5	unreactive	Internuclear Distance of F+ H ₂ reaction when p_HH=2.5 kgm/s
13	-0.5	3.0	unreactive	Internuclear Distance of F+ H ₂ reaction when p_HH=3.0 kgm/s

Only the one with p_HF= -2.0 kgm/s is reactive, is showed that initial kinetic energy of the atoms is required to proceed the reaction.

H+HF reaction

Polyanyi's empirical rule generally state that the late barrier is more promoted by vibrational energy rather than translational energy.[2] In this experiment. only the H+HF reaction is endothermic thus, it as a late barrier. The reaction only proceed when the vibration was large enough. In the surface plot of reactive trajectory, the momentum of HF bond is much larger than the momentum of HH bond. Large momentum means large vibrational energy and thus supports the Polyanyi's Rules.

F+H₂. reaction with early barrier, translational barrier is more promoted. The calculation supported this point the vibration increased at the end of the reaction. Thus the reaction trajectories obeys Polanyi's rule.

Reference

1. R. D. Levine Molecular Reaction Dynamics, Cambridge University Press, 2005 2. Guo, H., & Liu, K. (2016). Control of chemical reactivity by transition-state and beyond. Chem. Sci., 7(7), 3992–4003.