Modelling microscopic clusters of sulphuric acid and water relevant to atmospheric nucleation

Classical nucleation theory has been a useful tool for predicting the phenomena of nucleation for the past seventy years. However the model has several limitations, which in some examples give rise to predicted rates that are several orders of magnitude in error. One such example is that of sulphuric acid and water nucleation which has long been framed as an important source of cloud condensation nuclei and therefore has implications for the climate, both locally and globally. In addition stratospheric aerosol injection of molecules containing sulphur, including sulphuric acid, are of interest as a potential geoengineering technique. The focus for this study is to improve upon our understanding of water and sulphuric acid nucleation. The initial phase of the project concerned performing quantum chemistry calculations which go beyond the macroscopic description employed by classical nucleation theory. Kohn-Sham density functional theory has been successfully employed in the fields of condensed matter, material physics and chemistry. However one of the assumptions of the theory is the classical treatment of the nuclei. The path integral molecular dynamics technique is used here to test this assumption on small clusters of sulphuric acid and water. We find that the introduction of zero point motion has a small effect on the equilibrium properties of certain configurations in line with expected behaviour. An interesting structure is found which serves to emphasise the importance of liquid like behaviour in this cluster at room temperature. The first study demonstrated the computational expense of treating systems at the microscopic scale using quantum chemistry approaches. The second phase of the research focused upon finding a suitable classical potential to employ within a molecular dynamics scheme, which would drastically reduce the computational expensive of performing simulations. This potential would be required to retain the ability for protons to transfer between selected species. The empirical valence bond method was chosen for its straightforward implementation and its similarity to traditional classical schemes. However some modifications were required to implement the scheme. Two algorithms were designed to identify species within the system and treat them in a fashion suitable for use in the empirical valence bond method. In addition the empirical valence bond method also needed to be parametrised for the sulphuric acid and water system. This was achieved by using the particle swarm optimisation technique, which performed force matching parametrisation using the Kohn-Sham density functional theory work from the previous phase of the project. The model was fully programmed in FORTRAN 90/95 and was incorporated into DL-POLY version 4.03. It is tested against the density functional theory data to which it is parametrised to check that the main features of the quantum chemistry are retained within the empirical valence bond technique. A puzzling issue appeared in preliminary molecular dynamics simulations performed with DL-POLY 4.03. The issue arises from a constraint imposed to fix the centre of mass. The solution to the modified Langevin equation introduced by this constraint is derived. The results are then compared to the puzzling DL-POLY simulations and found to be consistent. The constraint is then removed for all further simulations. The developed empirical valence bond potential was used to perform simulations of small clusters of sulphuric acid and water. We test the level of hydration required to ionise the system and find it to be in line with literature values. A thermodynamic integration scheme that was suitable for this system was derived. Preliminary simulations were performed using the model to compute free energies for use with classical nucleation theory in order to calculate nucleation rates.