High accuracy modeling of chemical species and reactions is limited by the complexity ofthe molecular wavefunction. Balancing the accuracy and efficiency of methods in quantum chemistry is crucial to study systems of interest. This dissertation introduces electronic structure theory and applies it to the high accuracy study of an important chemical species. Then two approaches to pushing the computational limits of modeling molecules with ab initio quantum chemistry methods are explored. The first is utilizes the symmetry of the molecule of interest in order to reduce computational burden. We present analytic formulae for the irreducible representation matrices of all molecular point groups, as well as a program for molecular symmetry detection and usage that can easily be integrated into electronic structure packages. The second approach is to apply machine learning in the approximation of the molecular potential energy surface (PES). Multifidelity models incorporate multiple methods of varying accuracy and computational cost to maximize the coverage and accuracy of a PES. We compare several methods of multifidelity modeling of PESs and implement these models such that they can easily be used by the scientific community.