First ionization potentials of Cr, Mo, and W calculated with SHCI

TL;DR

The paper tackles the lack of precise atomic data for tungsten in fusion plasmas by computing the first ionization potentials (IP) of Cr, Mo, and W using semistochastic heat-bath configuration interaction (SHCI) with effective core potentials (ccECP) and basis-set extrapolation. By incorporating orbital optimization and a semi-stochastic perturbative correction, the authors achieve IPs that agree with experimental values within roughly $0.1$ eV for Cr and Mo, and about $0.26$ eV for W, demonstrating SHCI’s efficiency for heavy, multi-electron systems. The work provides a robust workflow capable of delivering improved electron-structure data for ions with many electrons and points to extensions for excited states and state-selective collisional processes relevant to fusion plasmas. This approach offers a path toward more accurate impurity and plasma-impurity modeling, with potential impact on radiative rates and collision cross sections used in fusion reactor design.

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.

Figures (3)

• Figure 1: Summary of key steps in workflow. (Left) A visual network of determinants handled by SHCI, starting from an initial Hartree-Fock determinant and connecting to only the determinants that meet a selection criteria from a variational, then a perturbative subspace. (Middle) Visual of tungsten neutral tungsten atom with Effective Core Potential substituting core electrons, and plot of its energy converging to the limit of an "infinitely large" basis set. (Right) Convergence of variational and perturbatively corrected (total) energies toward the FCI Limit from the HF starting point during SHCI, over increasingly strict thresholds.
• Figure 2: (left) Extrapolation of $E_{tot}$ vs. perturbative correction ($E_{var} - E_{tot}$) for neutral tungsten in aug-cc-pVDZ basis. (right) Basis set extrapolation for neutral tungsten.
• Figure 3: SHCI computation time per $\epsilon_1$ (eps_var) value for an ROHF calculation of neutral chromium in aug-cc-pVQZ basis with (left) and without (right) orbital optimization