Assessment of Grouped-Bath Configuration Interaction for Transition-Metal Complexes by L-Edge X-ray Spectra Calculations

We assess the accuracy and limitations of the grouped-bath configuration interaction (GBCI), formerly termed the grouped-bath ansatz for the spin-flip nonorthogonal configuration interaction (SF-GNOCI), by calculating L-edge X-ray absorption spectroscopy (XAS) spectra and 2p3d resonant inelastic X-ray scattering (RIXS) spectra of transition-metal complexes. We compare the computed GBCI spectra with those from the spin-flip complete-active-space (SF-CAS) method and experiment. These comparisons demonstrate that the bath-orbital relaxation in GBCI is crucial for accurately describing both the energies and wave functions of charge-transfer states. For L-edge XAS, GBCI accounts for the core-hole relaxation neglected in SF-CAS, leading to a uniform energy shift across the spectral bands. For 2p3d RIXS, GBCI produces an energy shift in the charge-transfer band that corrects the overestimated energy in SF-CAS. Moreover, GBCI improves the wave functions of charge-transfer states, thereby correcting the RIXS intensities overestimated by SF-CAS. Nevertheless, discrepancies with experiment indicate that additional electronic correlation remains necessary. We expect that the X-ray spectral comparison presented in this study will serve as a useful benchmark for validating electronic-structure theories of transition-metal complexes.