Chemistry has been a primarily laboratory science since its beginning. However, with thanks to powerful modern high performance computer hardware and decades of theoretical chemistry research, the critical role of computational chemistry in today's chemical research enterprise is undeniable. Computational tools serve as a bridge between chemical theory and computer hardware, helping scientists with nearly all aspects of chemistry research. Indeed, it has been a significant driving force that pushes the chemical science forward. This thesis expands the computational toolkit for theoretical chemistry studies, with an emphasis on potential energy surface related studies and transition metal systems.

Proposing a theoretical mechanism for a newly discovered chemical reaction is a difficult job that requires extensive work from well-trained computational chemists. An automatic mechanism generator is proposed to automate this process. Given a reactant and a product, the methodology described expands the chemical space between them, finds the optimal reaction pathway, and reports the most probable mechanisms. The reaction network expands by enumerating all possible elementary reactions based on an electron pushing model. Each generated intermediate is filtered by user-defined atom configuration rules, in order to reduce the complexity of the algorithm.

Spin crossover, or intersystem crossing, happens in many important chemical processes. It takes place at the minimum energy on the crossing seam of two potential energy surfaces of different spins. In this work we developed an efficient optimizer to find the minimum energy crossing point in a spin crossover event. Finding this geometry will facilitate kinetic and thermodynamic studies on spin crossover events. This optimizer is integrated with highly efficient geometry optimization schemes that were published recently.

Zirconium oxide is found to have potential applications as catalyst in water splitting reactions. The work described in chapter 5 aimed to interpret a spectrum obtained from photodetachment spectroscopy on the adduct of ZrO2 and H2O by an experimental collaborator. Employing two-dimensional DVR (Discrete Variable Representation) method, we were able to account for the anharmonicity of the umbrella mode of the adduct, and interpret most of the peaks in a dense vibronic spectra, thus shedding some light on the structure of the adduct.

Spin contamination is a well-documented error of single-determinant DFT methods. The work described in chapter 3 employed Approximate Projection (AP), a simple and efficient spin-projection method to treat spin contamination in DFT calculations, to test its effect in predicting exchange coupling constant and spin crossover gap. In summary, AP greatly reduced error in predicted spin crossover gaps caused by spin contamination. In terms of predicting exchange coupling constants, AP did not perform better than a non-projection method, which was due to statistical reasons. In addition, AP's effect on geometry optimization and subsequent effects on the two physical constants were tested as well, and were found to be significant for exchange coupling constants, and otherwise for spin crossover gaps.

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