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Multiscale modelling approaches, connecting data from electronic structure calculations all the way towards engineering continuum models, have become an important ingredient in modern materials science. Materials modelling in a broader sense is already amply used to address complex chemical problems in academic science, but also in many industrial sectors. As far as multiscale modelling is concerned, however, many challenges remain, in particular when it comes to coupling and linking the various levels along the multiscale ladder in a seamless and efficient fashion. This thesis focusses on the development of new and efficient linear models to improve the quality and parameterisation processes of the two-body potentials used in empirical and semi-empirical methods within a multiscale materials modelling framework. In this regard, a machinery called curvature constrained splines (CCS) based on cubic splines to approximate general two-body potentials has been developed. The method is linear, and parameters can be easily solved in a least-square sense using a quadratic programming approach. Moreover, the objective function is convex, implying that global minima can be readily found. This makes the optimisation process easy to handle and requires little to no human effort. Initial tests to validate the method were performed on molecular and bulk neon systems. Later, the method was extended to incorporate long-range interactions by including atomic charges. The capability of the method was demonstrated for ZnO polymorphs, and at the same time benchmarked towards the conventional Buckingham potentials applied to the same problem. The results indicate that the CCS+Q method performs on par with the Buckingham approach, but is much faster and easier to parameterise. The merits of the method is further demonstrated with an exploration of size and shape dependent stability of CeO2 nanoparticles. Having established the framework of the CCS methodology, the method was further used to develop repulsive potentials for the semi-empirical self-consistent charge density functional tight binding (SCC-DFTB) method. The generation of the repulsive potentials is normally a tedious and time-consuming task. The CCS methodology makes this process significantly more efficient, and further provides new opportunities to explore the limits of the SCC-DFTB method. The development of repulsive potentials for bulk Si polymorphs showed that it is possible to retrieve a good description of each individual polymorph, but impossible to obtain an acceptable joint description of all polymorphs. The results indicated that a transferable repulsive potential needs to have coordination dependence, and by the use of a many-body artificial neural network representation for the repulsive potential, it was indeed possible to obtain a global transferability. The CCS methodology was finally used to model a system of considerable chemical diversity and complexity, namely reduced CeO2 within the SCC-DFTB formalism. Here, the CCS framework facilitated the development of an efficient workflow that yielded a harmonized description of Ce ions in different oxidation states. In short, the introduced CCS-based workflow proved to extend the applicability of SCC-DFTB to complex oxide systems with correlated electronic states. To conclude, the CCS methodology is demonstrated to be a versatile tool for efficient linking between (and within) electronic and atomistic models. |
