# Thermodynamics of Plutonium Monocarbide from Anharmonic and Relativistic Theory
## 3 Results  
### Electronic Structure  
As mentioned in the introduction, one of the central questions regarding the electronic structure of any actinide compound is the nature of the actinide 5f electrons. For the elemental metals, up to americium, the 5f electrons can be regarded as bonding and itinerant and not localized as they are in americium and the following, heavier, actinides. For plutonium there is still a debate on this, but our view is that the 5f electrons are more delocalized than not and that opinion is based on a wealth of evidence [5]. Specifically, for plutonium monocarbide, it has been argued that the 5f electrons are less correlated than they are in both plutonium oxides and nitrides [11]. No theoretical method is currently able to predict with certainty the nature of the 5f electrons in these systems but model comparisons with experimental data provide clues. In Figure 2 we show the (DFT+SO+OP) total electronic density of states (e-DOS) for PuC. The PuC e-DOS is dominated by 5f states and shows substantial weight and even a peak in the vicinity of the Fermi level (highest occupied energy state that is shifted to zero). This behavior is quantitatively comparable to that of both the \(\alpha\) and \(\delta\) phases of plutonium [5] because these phases also display significant occupation of 5f states at the Fermi level. The degree of 5f itineracy can, however, only be judged knowing how well theory reproduces measured photoelectron spectra. The photoelectron spectra for sub-stoichiometric PuC\({}_{0.85}\) has been measured by [PERSON] et al. [49] and in Figure 3 we compare that result with our e-DOS for PuC that has been broadened and convoluted to simulate instrumental resolution and photon lifetimes [50]. [PERSON] et al. utilized two different photon energies; HeI at 21.22 eV and HeII at 40.81 eV. Here we show the latter (40.81 eV) because it enhances the 5f photoexcitation cross section that makes the 5f contribution dominate the spectra [49]. We also include, for comparison, the corresponding simulated photoemission for \(\delta\)-plutonium [50]. Figure 2: Total electronic density of states, from our best theory (DFT+SO+OP), for PuC at 16.2 Å\({}^{3}\). The vertical dashed line indicates the location of the Fermi level (shifted to zero energy). The experimental PuC\({}_{0.85}\) photoelectron result actually resembles our simulation for PuC quite well. One would not necessarily expect a perfect agreement because the stoichiometries are different and the calculated spectral density do not include photoexcitation matrix elements. Nevertheless, the favorable comparison supports the interpretation that the 5f electrons, that dominate the spectra for the plutonium-carbide system, are indeed delocalized as treated by the theory. We further notice in Figure 3 that the result for \(\delta\)-plutonium is quantitatively comparable to PuC. The estimated 5f-band occupation is marginally lower in PuC (4.95) than in \(\delta\)-plutonium (5.31) [51]. Plutonium monocarbide (PuC\({}_{1-\chi}\)) is known to be anti-ferromagnetic (AF) at temperatures below 100 K, but, to date, the size of the magnetic moments has not been accurately determined but estimated to be \(\sim\)0.7 \(\mu_{\text{B}}\)[52]. Previous DFT calculations within the local-density approximation [53] reproduce the AF configuration for PuC\({}_{0.75}\) but for ideal-stoichiometry PuC, a ferromagnetic (FM) configuration was predicted with considerably larger magnetic moments \(\sim\)2 \(\mu_{\text{B}}\). The present calculations for PuC, that are based on GGA and the aforementioned spin-orbit and orbital-polarization correlations, predict the FM state but it is only weakly stable over the AF configuration (\(\sim\)1 mRyatom\({}^{-1}\)). Both configurations have total magnetic moments that are smaller (\(\sim\)0.1 \(\mu_{\text{B}}\)) because of the effective compensation between the spin and anti-parallel orbital components (both close to 3.7 \(\mu_{\text{B}}\) in absolute magnitude).