Fig. 3. Calculated XES spectrum of Fe(CO)₅ (black line) including error bars (shaded area) giving upper and lower bounds for distortions of the minimum energy reference structure with |ΔR| ≤ 4 pm. The different colors of the shaded area indicate the contributions of the four most influential sensitivity modes (q₁ blue; q₂ green, q₃ red, q₄ cyan). (a) Error bars calculated for the linearized surrogate model and (b) for 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. (c) Spectra calculated for 100 random distortions with |ΔR| = 4 pm (black lines) as well as 20 evenly spaced distortions between Q_i = ±4 pm along each of the four most influential sensitivity modes (red lines). The total error bars from (b) are included as green shaded area for comparison.