Although amazing progress has been made since the genesis of quantum mechanics in modeling the ground state wave functions and energies of electronic states, modeling the excited electronic states with similar accuracy is still a difficult challenge. In this dissertation orbital optimization of Multi-Slater Jastrow wave functions and its coupling to various Quantum Monte Carlo (QMC) features are used to determine the optical gaps of various systems. The new features being coupled to orbital optimization include: an excited state targeting function, configuration selection for QMC wave functions, a variance matching scheme for optical gaps, and a modified guiding function for sampling within QMC. After a study of the utility of these features, the success of optical gap prediction on both gas phase molecules (aperiodic systems), and condense phase materials (periodic systems) is explored.

For aperiodic systems we found that our QMC optical gap workflow produces predictions on par in terms of accuracy with other standard techniques (e.g. MRCI+Q, CASSCF, CASPT2, EOM-CCSD) for small molecules (e.g. Formaldimine, Thioformaldehyde). In addition, for cases like [C3N2O2H4Cl] in which state-averaged orbitals (between the ground and first excited state) heavily compromises the accuracy of these states, and multiple reasonable active-space choices lead to very different state energies, our workflow can be advantageous to use.

For periodic systems we found that our QMC optical gap workflow produces predictions on par in terms of accuracy with other standard techniques (e.g. DFT, G0W0) for simple bulk materials (e.g. MgO, Trans-Polyaceylene). For more challenging systems, such as bulk transition metal oxides (FeO and MnO) we found that QMC orbital optimization provides the advantage of allowing one to bypass difficult parameterization (e.g. +U value, choice of functional).