Electronic flat bands serve as a unique platform to achieve strongly correlated phases. The emergence of a flat band around the Fermi level in $1T\text{−}{\mathrm{TaS}}_2$ accompanied by the development of a $\sqrt{13}\times \sqrt{13}$ charge density wave (CDW) superlattice has long been noticed experimentally, but a transparent theoretical understanding remains elusive. We show that without the CDW order, the primary feature of the $1\times 1$ bands can be fitted by a simple trigonometric function, and physically understood by choosing a rotated $t_{2g}$ basis with the principal axes aligning to the tilted ${\mathrm{TaS}}_6$ octahedron. Using this basis, we trace the band evolution in the $\sqrt{13}\times \sqrt{13}$ superlattice by progressively including different CDW effects. We point out that the CDW order strongly rehybridizes the three ${\tilde{t}}_{2g}$ orbitals, which leads to the formation of a well-localized molecular orbital and the flat band.

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• Charge density waves
• Electronic structure
• Strongly correlated systems
• Transition metal dichalcogenides