Lattice-Driven Electronic Structure Reconstruction in the Commensurate CDW Phase of 1T-Ta$S_2$

We investigate the structural and electronic reconstruction associated with the commensurate charge-density-wave (CCDW) phase in bulk and monolayer 1T-TaS2 using density functional theory (DFT) and Wannier-based tight-binding modeling. Structural relaxation of a sqrt(13) x sqrt(13) supercell leads spontaneously to the formation of the Star-of-David (SoD) distortion, consistent with phonon softening of the undistorted phase. We focus on establishing a direct connection between real-space lattice distortion and momentum-space electronic reconstruction. Using Wannier interpolation, we demonstrate how the CCDW-induced Brillouin zone reduction leads to band folding, narrowing of Ta 5d bands, and reconstruction of the Fermi surface. Our analysis shows that features often interpreted as Fermi surface nesting emerge naturally from band folding associated with lattice distortion. We compare our calculated electronic structure with previously reported angle-resolved photoemission spectroscopy (ARPES) results at a qualitative level. While we do not explicitly compute electronic susceptibility or electron-phonon coupling matrix elements, the results provide a consistent microscopic framework linking lattice instability and electronic structure reconstruction in 1T-TaS2.