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In order to explore the driving mechanism of the concomitant metal-insulatorand structural transitions in quasi-one-dimensional hollanditeK$_{2}$Cr$_{8}$O$_{16}$, electronic structures and phonon properties areinvestigated by employing the {\it ab initio} density functional theory (DFT)calculations. We have found that the imaginary phonon frequency reflecting thestructural instability appears only in the DFT+$U$ ($U$: Coulomb correlation)calculation, which indicates that the Coulomb correlation plays an essentialrole in the structural transition. The lattice displacements of the softenedphonon at X explain the observed lattice distortions in K$_{2}$Cr$_{8}$O$_{16}$perfectly well, suggesting the Peierls distortion vector {\bf Q} of X (0, 0,1/2). The combined study of electronic and phonon properties reveals thathalf-metallic K$_{2}$Cr$_{8}$O$_{16}$, upon cooling, undergoes thecorrelation-assisted Peierls transition to become a Mott-Peierls ferromagneticinsulator at low temperature.

Structural instability and the Mott-Peierls transition in a half-metallic hollandite : K$_{2}$Cr$_{8}$O$_{16}$