Here we describe the fitting and testing, via molecular dynamics simulation, of a bond-order potential for water with a unique force field parameterization. Most potentials for water, including some bond-order (reactive) potentials, are based on a traditional, many-body decomposition to describe water's structure with bond stretch, angle bend, electrostatics, and non-bonded terms. Our model uses an expanded version of the Bond Valence Model, the Valence Multipole Model, to describe all aspects of molecular structure using multibody, bond-order terms. Prior work successfully related these multibody, bond order terms to energy, provided the structures were close to equilibrium. The success of this equilibrium energy model demonstrated the plausibility of adapting its parameterization to a molecular dynamics force field. Further, we present extensive testing of ab initio methods to show that the ab initio data we obtained, using the CCSD(t)/cc-pwCVTZ level of theory, to augment the fitting set of our parameters is of the highest quality currently available for the OH system. While the force field is not yet finished, the model has demonstrated remarkable improvement since its initial testing. The test results and the insights gleaned from them have brought us significantly closer to adapting our unique parametrization to a fully functional molecular dynamics force field. Once the water potential is finished, it is our intent to develop and expand the Valence Multipole Model into a fully reactive alternative to CLAYFF, a non-reactive potential typically used to simulate fluid interfaces with clays and other minerals.

Silicon nitride is a bulk and a coating material exhibiting excellent mechanical properties. The understanding of the complex processes at the nanometre scale gained through experimental research will be enhanced by the existence of a computationally efficient and accurate model that is able to describe the mechanical properties of silicon nitride. Such a model has yet to be proposed. In this thesis we present a transferable reduced tight-binding (TB) model for the silicon nitride system. More precisely, this model consists of a reduced TB model for elemental silicon, a reduced TB model for elemental nitrogen, and a reduced TB model for silicon nitride. These models are developed within the framework of coarse-graining the electronic structure from density functional theory (DFT) to tight binding (TB) to bond-order potentials (BOPs), and can therefore be used in the future as the stepping stone to develop BOPs for the application in large scale simulations. The bond integrals employed in the reduced TB models are obtained directly from mixed-basis DFT projections of wave functions onto a minimal basis of atom-centred orbitals. This approach reduces the number of overall parameters to be fitted and provides models which are transferable through the different coarse-graining levels. We provide an example by using the same bond integrals in the reduced TB model for silicon and the preliminary bond-based BOP for silicon. DFT binding energies of ground state and metastable crystal structures are used as the benchmark to which the TB and BOP repulsive parameters are fitted. In addition to model development, we present an improved methodology when going from TB to reduced TB. By weighting all four σ TB bond integrals equally, we provide a new parameterisation (Eqs. (2.73) and (2.74)) and show that the quality of the silicon reduced TB model can be increased by choosing one of the reduced TB parameters to be distance invariant. The ingredients, the development methodology, and the quality of each of the four models are discussed in a separate chapter. The quality of the reduced TB models and BOP is demonstrated by comparing their predictions for the binding energies, heats of formation, elastic constants, and defect energies with DFT and experimental values.