Recently, $alpha$-$textrm{RuCl}_3$ has attracted much attention as a possible material realization of the honeycomb Kitaev model, which may stabilize a quantum-spin-liquid state. Compared to extensive studies on its magnetic properties, there is still a lack of understanding on its electronic structure, which is strongly related with its Kitaev physics. Here, the electronic structure of $alpha$-$textrm{RuCl}_3$ is investigated by photoemission (PE) and inverse photoemission (IPE) spectroscopies. The band gap, directly measured from PE/IPE spectra, is found to be 1.9 eV, much larger than previous estimations. The LDA calculations show that the on-site Coulomb interaction $textit{U}$ can open the band gap without spin-orbit coupling (SOC). However, the SOC should also be incorporated to reproduce the proper gap size, indicating that the interplay between $textit{U}$ and SOC plays an essential role in the physics of $alpha$-$textrm{RuCl}_3$. There exist some spectral features in PE/IPE spectra which cannot be explained by the LDA calculations. To explain such discrepancies, we perform the configuration-interaction calculations for a ${textrm{RuCl}}_6^{3-}$ cluster. The experimental data and calculations demonstrate that the 4$textit{d}$ compound $alpha$-$textrm{RuCl}_3$ is a $J_{textrm{eff}}$ = 1/2 Mott insulator rather than a quasimolecular-orbital insulator. Our study also provides important physical parameters, required in verifying the proposed Kitaev physics in $alpha$-$textrm{RuCl}_3$.
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