The Pu M 5 -edge VB-RIXS data of PuO 2 and Pu 4+ (aq) were fit using the XES Neo program. XES Neo is a data fitting package that uses a genetic algorithm along with least squares fitting to optimize the fit parameters (see also Section S10 of SI). The software is based on the EXAFS Neo package. The error values on the parameters found are calculated using the square root of the diagonal of the covariance matrix. The fitting procedure consisted of assessing the peak locations in the data and running the program 30 times, randomly altering the fitting parameters and their ranges until a fit was found that matched the data set most accurately. An offset to the dataset was subtracted so that the high energy side of the VB-RIXS spectra was equal to zero for both PuO 2 and Pu 4+ (aq). After this offset was applied, the maximum of the data was found for each dataset. The entire dataset was then divided by this value, making the maximum of each dataset equal to 1. Both datasets were then scaled by multiplying the data by 1000 and adding an offset of 1000 to each datapoint, prior to fitting in XES Neo. The fit Pu M 5 -edge VB-RIXS spectra of PuO 2 and Pu 4+ (aq) and the fitting results are shown in Figure and Table (PuO 2 ) and Table S13 (Pu 4+ (aq)). Discussion on influence of self-absorption effects on the VB-RIXS spectrum is given in the SI Section S10.