CP3MD

Molecular Reaction Dynamics: Applications to Triatomic systems

Part 1 – the H and H₂ system.

Important Note: Your physical chemistry tutors are not expected or required to help you with this material. This is a self-study exercise.

This document contains:

1. Instructions for the exercise – how to use the software and run trajectories pp 1-20
2. Guidance on what to include in the report 20-22
3. A pro-forma (template) which you may use to fill in your data and include discussion etc. pp 22-23

(Page numbers are a rough guide and may alter a bit with formatting)

Introduction

This experiment is computational. The software is available on Chemistry PCs in the computer rooms and can also be downloaded for free from the ICT software shop . For the current year (2014-5) students are expected to complete this exercise on their own time. 

Script revised in Feb 2015 by Pietro Aronica and Paul Wilde.

The Write-up Required

A template/guide to the write-up required and points for discussion are included at the end of the exercise. A (proforma) data sheet is attached. You might find it convenient to enter data and make sketches, or include screenshots, in the data sheet at points indicated in the text by ==> data sheet

Background reading

Note that it is possible to start this exercise and run some trajectories very easily but reference to literature will be needed to understand the more complex examples that you will tackle later in this exercise particularly in part 2.

Atkins and de Paula: Physical Chemistry, 7^th Edition. Topic titles are provided so that you can find the material in later editions of this textbook or in other textbooks.

• Chapter 25: The Rates of Chemical Reactions
• Section 25.5 - T dependence of reaction rates, Arrhenius Parameters their determination and interpretation.
• Chapter 27 Molecular Reaction Dynamics.
• Sections 27.4 Activated Complex Theory, The Eyring Equation.
• 27.5 Thermodynamic aspects of activated complex theory
• 27.6- Dynamics of Molecular Collisions.
• 27.7 Potential Energy (P.E.) Surfaces
• 27.8 Some results from experiments and calculations with P.E. 

Note that many other physical chemistry textbooks will also cover this material. Editions of Atkins will vary in their coverage.

 Objectives

The objectives of this exercise are to study the reactivity of triatomic systems, where an atom and a diatomic molecule collide, through calculations using Molecular Reaction Dynamics.

The gas phase collision and reaction between an atom and a linear diatomic molecule will be studied. If the reaction proceeds it will form a new diatomic molecule and atom. This exercise builds a level of sophistication upon previous kinetic treatments that you have seen by examining other types of energy (e.g. vibrational) that may be needed for reaction or present in products and also by illustrating how certain conditions lead to reaction profiles which simpler models do not predict.

Relevance to other courses

A lot of the background material for this exercise has been covered in courses you have taken in year 1.

Year 1

• States of Matter  (Intermolecular interactions  - Dr. Ian Gould)
• Chemical Kinetics  (Collision Theory – Kinetics  - Dr Oscar Ces)
• Spectroscopy (Foundation Course/Quantum Chemistry – vibrational energy, the vibrating molecule) – Dr McKinley, Dr Bearpark.
• Introduction to Physical Organic Chemistry  (Foundation Course – transition states activation enthalpies and entropies, reaction energy profiles (2D)  Prof I McCulloch).

This exercise now adds an extra layer of subtlety to the basic information presented in year 1 – particularly with regard to making the model of simple reactions more sophisticated as noted on the previous page.

Having completed the exercise you will be better prepared to understand  material in year 3 where the molecular reaction dynamics course in particular builds on the ideas and concepts used here.

Year 3- this material will be explored and developed next year in the following courses:

• Statistical Thermodynamics 
• Molecular Reaction Dynamics 

Note: all distances and velocities are in atomic units for this exercise 

Theory

Introduction

We’re able to simulate a reaction by treating the molecule and atom that are reacting as if they were “billiard balls colliding into each other”. They have masses, positions, accelerations and speeds and using these properties we can analyse how a reaction might proceed. Because nuclei are so much heavier than electrons, we can focus on the nuclei alone.

It is possible to understand much of chemical reactivity using classical Newtonian mechanics for the nuclei. This is because electrons move very rapidly (they have much lower mass) compared to the speed of nuclear motion. You have seen a number of occasions where the separation of nuclear and electronic motion has been used before (e.g. Born Oppenheimer Approximation and the Franck-Condon Principle). In Newton’s notation, a dot over a quantity indicates the first derivative and two dots the second derivative. If r represents position and V(r) potential energy then we have the equations below which are equivalents to the more familiar F= ma etc.

 

m is a column vector that contains the masses of the nuclei, r is a position vector that contains the Cartesian co-ordinates of the atoms and V(r) is the potential energy function. (For a diatomic molecule V(r) is just the usual 2 dimensional potential energy curve that expresses the change in the energy as the two nuclei are displaced from their equilibrium positions by changing the interatomic distance – making the separation too small leads to a rapid rise in potential energy and increasing the bond length also leads to an increase in energy (and eventually to dissociation).

Molecular Dynamics simulation of the system involves solving these equations expressing the changes in the atomic co-ordinates etc. at a time increment ∆t:

The time step (∆t) used is typically 0.1 fs (femtosecond = 10-15 sec). In this way one obtains a classical trajectory r(t) that describes how the system evolves in time. The trajectory represents a path across the potential energy surface (you will see examples shortly). Such simulations have many applications in chemistry and biology and you may well encounter there is higher level lecture courses in year 4. In the computations you will perform, it is convenient to use internal coordinates (bond lengths and angles) rather than Cartesian coordinates of the atoms. The form of the "F=ma" equation changes slightly but this is a detail that does not need to concern us.