Unresolved spectral discrepancies between Qlanth and the Lanthanide code when T^(k) terms are included

Ascertain the computational or theoretical reason for the significant differences between spectra produced by the Qlanth implementation and the Edvardsson–Åberg Lanthanide code when nonzero three‑electron configuration‑interaction parameters T^(k) are included in the parametric Hamiltonian, and reconcile the implementations so that identical parameter sets yield consistent spectra.

Background

To validate and cross‑check the revised calculations, the authors compare their open‑source Qlanth code with other available implementations. With T^k=0, Qlanth and the Lanthanide code agree to high numerical precision, indicating consistent handling of the single‑configuration and lower‑order terms.

When T^k three‑electron configuration‑interaction terms are activated, however, the two codes produce significantly different spectra, and the authors were unable to resolve or explain the origin of these differences. Clarifying this mismatch is important for robust, reproducible use of T^k corrections across software implementations.