The spectral emission of hot ${\mathrm{C}}_{60}$ has been experimentally shown to be broad and continuous, in apparent contradiction with the discrete and narrow absorption spectrum associated with the high symmetry of buckminsterfullerene. In the present work we computationally model the emission spectrum of isolated carbon clusters, assuming a broad distribution of isomers that are likely populated under the experimental conditions. The contributions of individual structures to the global spectrum correspond to the relaxation via recurrent fluorescence and vibrational emission, electronic and vibrational structures being described by a simple but efficient density-functional-based tight-binding scheme. The model predicts a blackbody-like emission spectrum that is naturally broad and correctly accounts for the experimental measurements, except for a maximum that is quantitatively shifted with respect to Wien's displacement law. To quantify such differences, we introduce an emissivity parameter $\varepsilon$ as the ratio between the spectral emittance and the corresponding exact blackbody spectrum; $\varepsilon$ is numerically found to scale as ${\left(\lambda T\right)}^{-2}$ at leading order with increasing temperature $T$ and for wavelengths $\lambda >350$ nm, and we provide a theoretical justification for this behavior. Our results are discussed in the light of the astrophysical detection of interstellar fullerenes, as well as in combustion environments where carbon clusters are relevant in the context of nascent soot particle formation.

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• Atomic & molecular clusters
• Electronic excitation & ionization
• Electronic transitions
• Laser-cluster interaction
• Molecular spectra
• Photoemission
• Vibrational states
• Clusters
• Semiclassical methods