We now need to determine how to estimate the sharpness of the C6 AB vs CN plots. A natural approach is to analyze the behavior of the first derivative d(C6 AA )/d(CN A ). An example of this function for a C-C pair is shown in Figure . From this plot, we can identify which CN transitions might be problematic. Specifically, the sharpest peaks are the second (CN C ≈ 1.4) and the fourth (CN C ≈ 3.4). For the formal definition of sharpness, we considered two metrics. The first one (μ1) is computed as the ratio of the peak height to the peak width, where larger values correspond to sharper peaks. The second criterion (μ2) is the second derivative d 2 (C6 AA )/d(CN A ) 2 computed at the peak position, with larger values indicating sharper peaks. As seen in Figure , both criteria correlate well with our identification of the sharpest peaks, assigning the largest values to peaks 2 and 4. In our k3 optimization procedure, we used the μ2 criteria, as it is less arbitrarily defined and does not encounter issues with cases where two peaks overlap significantly.