Layered van der Waals material, $1T-\mathrm{TaS}{\mathrm{e}}_2$ in its star-of-David charge density wave (CDW) phase has attracted significant research interest with several unresolved issues. The current study addresses these issues for monolayer and bilayer $1T-\mathrm{TaS}{\mathrm{e}}_2$ from a perspective of combined intra- and interlayer (quasi)bonding interactions: namely, the $p$-orbital mediated intra- and interlayer d-d orbital interactions, and the interlayer interaction is quasibonding (QB) in nature, mediated by the p-p orbital interaction across adjacent layers. For the CDW phase, within a monolayer, the d-d interaction between supercells is small and leads to the formation of a narrow half-filled single band, in which a small spin-splitting gap of 0.11 eV is exhibited. From monolayer to bilayer, the interlayer interaction gives an energy splitting of 0.5 eV, which is larger than the spin-splitting gap, and hence a transition from spin-polarized insulator to non-spin-polarized insulator occurs. Moreover, we find that the interlayer interaction is multilevel in nature, namely, the bandedge of bilayer is derived from not only the energy level close to Fermi level but also correlated to a deep level with the same orbital character. The interlayer QB interaction also affects the relative stability of different interlayer-stacking configurations. This study provides an intra- and interlayer (quasi)bonding perspective for understanding the electronic structure and stability of the CDW phase monolayer and bilayers, and hence help broaden the understanding of CDW materials.

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• Chemical bonding
• Electronic structure
• Electronic structure of atoms & molecules
• Structural properties
• Surface & interfacial phenomena
• Layered semiconductors
• Surfaces
• Transition metal dichalcogenides
• Band structure methods
• Density functional theory
• First-principles calculations
• Materials modeling