Nature of project: **software**, data analysis

Available to students on full-time physics degree schemes or joint students.

Nano-sized clusters of atoms have applications in nano-technology. This project is about predicting the most likely arrangements of atoms in a nano-cluster. More specifically, oxide clusters such as those consisting of silica (SiO2) or titania (TiO2) will be considered. It is assumed that the arrangement of atoms that forms the global minimum of the interaction energy will be the most likely to be formed in an experiment. Hence this project is about structure prediction by global optimisation of the energy with respect to the spatial coordinates of each of the atoms.

The energy of a cluster of atoms can be determined at various levels of precision. Ideally, one would like to incorporate all of quantum mechanics in this calculation. However, with current computers, this is too time-consuming. Various approximations, such as Density Functional Theory (DFT) or semi-empirical methods are faster, but still too slow for all but the smallest numbers of atoms.

Classical force fields, in the form of empirical potentials provide a rough but very quick way of approximating the interaction energy. In order to achieve a reasonable accuracy, the parameters of such a potential need to be chosen with care. The supervisor has developed a potential specifically for silica clusters [1].

There are a number of global optimisation algorithms that can be used for attempting to find the global minimum of the energy. Basin Hopping [2] is a simple, yet powerful global optimisation method. It is the aim of this project to apply the Basin Hopping method to the problem of finding the global minimum of the energy of oxide clusters of varying size and possibly of varying composition. The supervisor has already applied this method to silica clusters in a size range of up to 27 SiO2 units [3]. For this project, larger sizes can be attempted. Alternatively, a different composition (e.g. titania) can be considered, resulting in novel predicted structures for these atomic clusters.

*A successful project will develop beyond the above in one/some of the following directions:*

To develop this project further, the student(s) can perform an analysis of the effect of changing the parameters of the Basin Hopping method (mainly temperature and step size) on the efficiency of finding the global minimum.

When considering where to take your project, please bear in mind the time available. It is preferable to do fewer things well than to try many and not get conclusive results on any of them. However, sometimes it is useful to have a couple of strands of investigation in parallel to work on in case delays occur.

*Additional scope or challenge if taken as a Year-4 project:* If taken as a 4th-year project, the student can refine the structures and energies by using ab-initio methods such as DFT.

Please speak to **Edwin Flikkema** if you consider doing this project.

*Initial literature for students:*

- A new interatomic potential for nanoscale silica, E. Flikkema, S.T. Bromley, Chemical Physics Letters 378 (2003) 622–629
- Global Optimization by Basin-Hopping and the Lowest Energy Structures of Lennard-Jones Clusters Containing up to 110 Atoms, D.J. Wales, J.P.K Doye, J. Phys. Chem. A 1997, 101, 5111-5116
- Columnar-to-Disk Structural Transition in Nanoscale (SiO2)N Clusters, S.T. Bromley, E. Flikkema, Physical Review Letters 95, 185505 (2005)

The Basin Hopping method has already been implemented, e.g. in the form of the GMIN program. The supervisor has already implemented the empirical potential from [1] within the GMIN program. At a very basic level, the student(s) can run this code for different cluster sizes and varying temperature and step size. After some instruction, the student should be able to do this fairly independently. To take the project further, the details of the empirical potential can be changed to model clusters of a different composition. This may include coding to implement a potential of a different mathematical form. This will be more challenging, and this will probably involve a fair amount of assistance by the supervisor.

milestone | to be completed by |
---|---|

Familiarisation with Basin Hopping method at end user level. | Christmas |

Familiarisation with Basin Hopping at coding level. | end of February |

Implementation of new potential (if required). | mid-March |

Production runs finished. Data analysed. | Easter |