Quantitative statistical metrics for the uncertainty of the calculated XES spectrum of Fe(CO)₅ at the maxima of the three considered peaks (E_j, indicated by vertical lines in the spectra in Fig. 4) assuming a normal distribution with standard deviation s_Q = 2 pm and s_Q = 4 pm for the distortions of the underlying molecular structure. Listed are the intensity for the undistorted structure σ(E_j;R₀), the mean of the intensity 〈σ(E_j)〉, its variance Var[σ(E_j)], its standard deviation s[σ(E_j)], and the coefficient of variance COV[σ(E_j)]. All metrics refer to the non-linear surrogate model based on a 3rd order Taylor expansion for the one-mode contributions and neglecting two-mode and higher-order contributions.

E j /eV	σ(Ej;R0)	〈σ(Ej)〉	Var[σ(Ej)]	s[σ(Ej)]	COV[σ(Ej)]
7099.8	4.06	4.06	0.16	0.40	0.10
7103.1	9.36	9.41	0.12	0.35	0.04
7107.9	4.23	4.23	0.02	0.15	0.04
7099.8	4.06	4.06	0.74	0.86	0.21
7103.1	9.36	9.54	0.47	0.69	0.07
7107.9	4.23	4.23	0.09	0.30	0.07