Figure : Radial pair distribution functions and corresponding vibrational power spectra for the pure carbon system at selected temperatures and pressures. Data from DFT, the 2024 ChIMES carbon model (used by the Hierarchically and Partially-Hierarchically learned models), and the traditionally fit models are given in blue, magenta, and green, respectively. DFT and 2024 ChIMES carbon model data are adapted from 26. slightly better results, just as was seen for the pure C in the previous section. Notable exceptions to this performance include predicted pressure at 8000 K, 4.5 g cm , where DFT and the Hierarch model are in good agreement with P = 204.67 and 202.4 3 GPa respectively, versus the Standard and Partial, which over predict this value by approximately 60 GPa (i.e., with P = 257.20 and 259.4, respectively). The 300 K diffusion coefficient is also significantly underestimated by the Standard and Partial models. Small deficiencies are also observed in RDF and vibrational power spectra for the Standard and Partial Hierarch models. Namely, the 300 K, 1 g cm 3 RDF peak at r ⇡ 3.5 Å is sharper shifted to larger r relative to DFT, and the and 6000 K, 2.5 g cm 3 power spectrum, which is missing the N 2 vibration peak near 2250 cm 1 , and exhibits non-zero vibrations between 1000 and 1500 cm 1 unseen in the DFT data.