Abstract: The design and performance of future fusion power plants will depend on accurate atomic data for plasma-facing material and plasma impurity species. A leading candidate for the plasma-facing material is tungsten due to its high melting point, however, the energy levels and wavefunctions of high-Z atoms with many electrons (e.g. 30 or more), including tungsten, are difficult to calculate with high accuracy. Gaps and large uncertainties in atomic data for tungsten introduce design and performance uncertainties for a fusion power plant. Specifically, improved atomic data for ionization potential, excited state energies, and collisional excitation rates are needed for the low charge states of atomic tungsten. We aim to address these shortcomings by using the semistochastic heat-bath configuration interaction (SHCI) method, which nearly exactly calculates the energies that can be determined at higher cost with the full configuration interaction. Adding well-motivated approximations to SHCI, including orbital optimization and effective core potentials, we demonstrate good agreement between our calculated first ionization potentials and the best available experimental values for chromium, molybdenum, and tungsten. The efficiency and accuracy achieved in calculating these ionization potentials demonstrates that our SHCI workflow can yield improved electron structure data for ions with many electrons, suggesting that the method could also be useful for collisional processes, such as state-selective charge exchange reactions and electron impact ionization.