The debate over whether the charge density wave (CDW) in ${\mathrm{TiSe}}_2$ originates from spontaneous exciton condensation or the Jahn-Teller effect persists. Although this material has been extensively studied as a candidate excitonic insulator, few investigations have focused on whether spontaneous excitons exist within its CDW phase. In this work, we employ first-principles calculations combined with effective exciton models to systematically investigate the single-electron band gap and exciton binding energy in the CDW phase of monolayer ${\mathrm{TiSe}}_2$, comparing these results with experimentally observed band gaps. Our findings indicate that the single-electron band gap provides a reasonable experimental explanation, while spontaneous exciton condensation alone cannot account for the magnitude of the experimentally observed band gap. Notably, we find that ionic screening plays a pivotal role here, in contrast to the nearly negligible effect in many transition-metal dichalcogenides. While neglecting ionic screening is physically reasonable when calculating photoexcited excitons, we argue that it should be included when considering spontaneously condensed excitons. Based on these findings, we conclude that spontaneously generated and condensed excitons do not exist in the CDW ${\mathrm{TiSe}}_2$ monolayer.

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• Excitons
• 2-dimensional systems
• Transition metal dichalcogenides
• First-principles calculations
• GW method