Ab Initio Molecular Dynamics

All of the dynamics discussed so far have been based on Newton’s equations of motion, while these can be useful for representing systems on the micro-scale, when one wants to study small local interactions between atoms, a more complex model is required. This is where Ab Inito MD (AIMD) comes into effect, this uses the same equations for calculating the movement of the atoms as the classical MD (time steps and integration algorithms), and it is the interaction between the atoms that is calculated using quantum mechanical methods. The first type of AIMD is

Chapter 2 Kinetic Analysis and Modelling in Heterogeneous Catalysis

Born-Oppenheimer molecular dynamics (BOMD) which calculates the forces on the atoms via electronic minimisation using DFT as outlined previously, it then uses those forces in the classical dynamics equations to move the atoms forward in time.

LBO = Ekin− E = 1 2



i

mir²_i − E[ρ(r), ri] (2.146)

The Lagragian describing the system derives from the kinetic energy (left term) from classical mechanics, and the electronic energy as calculated from DFT (right term).

This is a highly accurate approach for calculating the dynamics of a system as the "potential " being used to describe the system is the highly accurate DFT calculation, but the downside is that this is extremely computationally expensive, and is reserved for very small systems for a very small total simulation time. BOMD is available for use in the VASP package, along with the various thermostats and barostats mentioned in the previous sections. Alongside BOMD there is also the option of using Car-Parrinello Molecular Dynamics (CPMD), which is considered to be more efficient, but this is not available in VASP and is considered outside the scope of this thesis.

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3 | Development and Application of TAP Numerical Analysis

The next three chapters will be dedicated to the work that I have undertaken throughout the PhD course. The large majority of the work was performed devel-oping analysis tools (i.e. CCI-TAP and CCI-TPR) and here I will explain explicitly the development and testing procedures, and how they have been applied to real catalytic systems. I will also outline the work performed under the NOVACAM project, both experimental and theoretical.

3.1 Development of Analysis Software

This first section is dedicated to the development of the analysis software, which applies the theory used in Section 2.2 (CCI-TPR) and Section 2.3 (CCI-TAP) and implements it into a graphical user interface outlined in Section 2.1. The develop-ment of a graphical user interface was seen as the best way to present the analysis tools in an easily usable fashion. The development of this user interface - and the underlying MATLAB code is outlined in this section.