The situation is slightly different for the ISP analysis. Here we perform the calculation on the entire set that includes 311 excited states, and track their reference weight deviations ∆w ref with respect to the ground state ones. Recall that for ε = 0, there are 109 states that have a reference weight deviating by more than 10 % from the ground state one. In CASPT2D method have a ∆w ref that is larger than 20 % (note the CDF function at around 0.8 in the top right part of Figure ). Correspondingly, the first series of points shown in the center of Figure -the red pluses -extends beyond the 20 % mark (hence, it is not visible in the plot), resulting in a large average deviation. The real level shift improves this situation, producing a significantly more compact distribution of the ∆w ref and a CDF that grows much faster in the range ∆w ref < 10 %. Nevertheless, several states remain affected by the ISP, which keep the average ∆w ref relatively large. In contrast, the imaginary shift and σ p regularization are much more robust, as evidenced by a CDF curve that reaches the value of 1 for ∆w ref smaller than 15 %. This means that no state of the 311 ones considered has a deviation of the reference weight larger than 15 % with respect to the ground state one. The distributions of the weights is very similar across the three approaches, with the imaginary shift slightly outperforming the regularizers, e.g. displaying a lower mean deviation of about 4 % compared to ≈ 4.5 % for σ p -CASPT2D. Increasing the value of ε to 0.3 E h has a dramatic effect for the real level shift, which becomes the most effective way to fix the ISP, as evidenced by the fastest-growing CDF shown in Figure . All intruder states are removed and the average w ref deviation is as low as ≈ 2 %. The imaginary shift also improves significantly, with no deviation of the reference weights above the 10 % mark. The smallest difference between ε = 0.1 E h and ε = 0.3 E h is obtained with σ p regularization. This result is in agreement with the lower sensitivity with respect to the input parameter observed in the NOISP analysis.