Improving the efficiency of computation of free energy differences

Abstract

There has been a recent focus on investigating the properties of semi-conductors at the nanoscale as it is well known that the band-gap of semi-conducting materials is altered due to quantum confinement effects. The potential to fine-tune a material's properties based solely on particle size has raised significant interest both in experimental and computational studies. Zinc sulfide is one of the most studied metal sulfide semi-conductor minerals, due to its potential technological applications.Computational studies of the structural and thermodynamic properties of zinc sulfide nanoparticles and bulk structures have been performed throughout this work. A variety of computational methods have been employed, including molecular dynamics, lattice dynamics, first principles calculations, and free energy techniques, such as metadynamics and free energy perturbation. The thermodynamic stability of zinc sulfide nanoparticles as a function of size and shape has been studied. Investigation of the phase space of these systems required the use of enhanced sampling methods. The metadynamics method was specifically utilised to explore as many structures as possible in combination with extensive simulations. The use of first principles methods for these exploratory simulations was found to be prohibitively expensive, and so force field methods were primarily utilised. Throughout this investigation several force fields were used to compare and contrast their accuracy, while first principles calculations were performed, where possible, to assist in the interpretation and validation of the results.In the present study, two different collective variables, the trace of the inertia tensor and the Steinhardt bond order parameters, have been implemented and their performance in metadynamics compared. The trace of the inertia tensor was found to be useful for exploring clusters of small sizes, while the Q4 Steinhardt parameter, which describes the crystalline order of a solid, is more applicable to larger clusters. Both of these metadynamics studies resulted in clusters displaying zeolite structural motifs, including the zeolite framework `BCT'. This led us to investigate more thoroughly the stability of different zinc sulfide zeolite analogues, thereby highlighting the strengths and weaknesses of all the force fields employed. Many force fields are found to be unable to accurately represent the order of stability for bulk polymorphs.First principles calculations also highlighted that the BCT phase is less stable than either of the bulk polymorphs of zinc sulfide, in contrast to the order of stability obtained by force fields lacking a torsional term, both from literature and the rigid ion model developed during the current study. The larger nanoparticles cleaved from wurtzite exhibited internal strain upon relaxation. A new hypothetical zeolite framework was constructed from the distorted core of these clusters, and was found to possess structural similarities with the `APC' framework. The APC framework is composed of double crankshaft-chains with ”ABCABC…” stacking, while the hypothetical framework identified is formed by the same composite building unit with `ABAB: : : ' type stacking. For all the force fields used the new hypothetical framework was lower in energy than the APC framework, but higher in energy than sphalerite, wurtzite or the BCT phase.Free energy differences between small ZnS clusters in vacuum were calculated using the path variable technique, and also using static methods within the quasi-harmonic approximation. Similar values were obtained using both of these methods, validating the path collective variables used with metadynamics as an effective means of obtaining free energy differences for clusters in vacuum.In addition to clusters in vacuum, a number of studies of ZnS clusters in water were also performed. Both force field and first principles studies were employed to validate the ZnS-water interactions used for the binding energies of water to small clusters. As a further validation, the free energies of solvation of Zn2+ and S2?? in aqueous solution were calculated. The free energy of solvation for the sulfide anion was found to be close to the experimental value, while the parameters for Zn2+-water were found to require substantial modification as the solvation free energy was in error by 500 kJ/mol. While newly derived ZnS-water parameters may prove to be superior for describing ZnS clusters in bulk water, a repetition of the binding energy calculations for individual water molecules bound to ZnS clusters gave energies 2-3 times greater than those obtained via first principles methods and using the five other force fields investigated. These results highlight the issues present when attempting to transfer a model fitted in a certain way to a different application. In particular, the many-body and polarisation effects present when modelling water need to be considered when parameterising ZnS-water interactions.