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Kagome metals AV$_3$Sb$_5$ (A = K, Rb, or Cs) exhibit intriguing chargedensity wave (CDW) instabilities, which interplay with superconductivity andband topology. However, despite firm observations, the nature of the CDW phasesremains elusive. Here, by carrying out first-principles calculations anddeveloping an effective Hamiltonian of CsV$_3$Sb$_5$, we unravel a series ofCDW structures, including the established inverse star of David (ISD) phase anda series of newly discovered D$_{3h}$-n states under mild tensile strains. Withthe first-principles-based effective Hamiltonian, the emergence of the ISD andD$_{3h}$-n states is explained as a result of competition of interactions ofthe first-nearest neighbor V-V and V-Sb$_2$ pairs versus the second-nearestneighbor V-V pairs. Moreover, a possible pattern is proposed for the mysteriousexperimental 4$a_0$ phase. Band structures and scanning tunneling microscopy(STM) images are simulated to help distinguish between different CDW states.Our work thus deepens the understanding of the CDW formation in AV$_3$Sb$_5$and our method should be applicable to other CDW

Nature of Charge Density Wave States in CsV$_3$Sb$_5$