The precursor phenomenon of phase transitions is widely present in bulk materials, e.g., shape memory alloys, while it rarely observed in two-dimensional materials, especially in kagome lattice compounds $A{\mathrm{V}}_3{\mathrm{Sb}}_5$ ($A$ = K, Rb, Cs). Our calculations with density-functional theory (DFT) indicated that the most stable structural unit of charge density wave (CDW) phases is a $2\times 2\times 2$ supercell (called ${\mathrm{TT}}_{\mathrm{B}}, {\mathrm{TT}}_{\mathrm{C}}$, or ${\mathrm{TT}}_{\mathrm{D}}$ with local twofold symmetry) staggered inverse star-of-David pattern with interlayer $\pi$-phase shift in $A{\mathrm{V}}_3{\mathrm{Sb}}_5$ ($A$ = K, Rb, Cs) compounds. The most stable ${\mathrm{TT}}_{\mathrm{B}}{\mathrm{T}}_{\mathrm{A}}{\mathrm{T}}_{\mathrm{B}}, {\mathrm{TT}}_{\mathrm{B}}{\mathrm{T}}_{\mathrm{A}}{\mathrm{T}}_{\mathrm{C}}$, and ${\mathrm{TT}}_{\mathrm{B}}{\mathrm{T}}_{\mathrm{A}}{\mathrm{T}}_{\mathrm{D}}$ configurations with pseudo-$2c$ stacking are energy-degenerate states in which every bilayer is an order state while the adjacent bilayers may adopt different orientations that lead to a disorder stacking along the out-of-plane direction. They are followed by the ${\mathrm{TT}}_{\mathrm{B}}{\mathrm{T}}_{\mathrm{A}}{\mathrm{S}}_{\mathrm{A}}$ configuration with $2\times 2\times 4$ stacking. The high-temperature metal phase transforms into $2\times 2\times 4$-stack ${\mathrm{TT}}_{\mathrm{B}}{\mathrm{T}}_{\mathrm{A}}{\mathrm{S}}_{\mathrm{A}}$ CDW phase with order-order type upon cooling (theoretically at 66 K for ${\mathrm{KV}}_3{\mathrm{Sb}}_5$), and then into the mixture of pseudo-$2c$-stacking ${\mathrm{TT}}_{\mathrm{B}}{\mathrm{T}}_{\mathrm{A}}{\mathrm{T}}_{\mathrm{B}}, {\mathrm{TT}}_{\mathrm{B}}{\mathrm{T}}_{\mathrm{A}}{\mathrm{T}}_{\mathrm{C}}$, and ${\mathrm{TT}}_{\mathrm{B}}{\mathrm{T}}_{\mathrm{A}}{\mathrm{T}}_{\mathrm{D}}$ CDW configurations with order-disorder type (theoretically at 48 K for ${\mathrm{KV}}_3{\mathrm{Sb}}_5$). A precursor of first-order phase transition occurs (theoretically at 203 and 175 K for ${\mathrm{KV}}_3{\mathrm{Sb}}_5\text{and}{\mathrm{CsV}}_3{\mathrm{Sb}}_5$) upon cooling in $A{\mathrm{V}}_3{\mathrm{Sb}}_5$ ($A$ = K, Rb, Cs) compounds, which comes from the in-plane contraction of vanadium atoms. The strong Fermi surface nesting effect plays a key role in inducing the formation of an in-plane $2\times 2$ CDW superstructure. Our theoretical calculations can not only reasonably explain the phase transition behaviors, but also predict that there are precursor phenomena for kagome lattice compounds $A{\mathrm{V}}_3{\mathrm{Sb}}_5$ ($A$ = K, Rb, Cs) upon cooling.

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• Charge density waves
• Phase behavior
• Structural phase transition
• Van Hove singularity
• Kagome metal
• Density functional calculations
• Electron diffraction