  Density-functional calculations of lattice dynamics and high-resolution
synchrotron powder diffraction uncover antiferroelectric distortion in the
kagome francisite Cu$_3$Bi(SeO$_3$)$_2$O$_2$Cl below 115K. Its Br-containing
analogue is stable in the room-temperature crystal structure down to at least
10K, although the Br compound is on the verge of a similar antiferroelectric
instability and reveals local displacements of Cu and Br atoms. The
I-containing compound is stable in its room-temperature structure according to
density-functional calculations. We show that the distortion involves
cooperative displacements of Cu and Cl atoms, and originates from the
optimization of interatomic distances for weakly bonded halogen atoms. The
distortion introduces a tangible deformation of the kagome spin lattice and may
be responsible for the reduced net magnetization of the Cl compound compared to
the Br one. The polar structure of Cu$_3$Bi(SeO$_3$)$_2$O$_2$Cl is only
slightly higher in energy than the non-polar antiferroelectric structure, but
no convincing evidence of its formation could be obtained.
