  We investigate the lattice dynamics in the spin-1/2 frustrated kagome
compound herbertsmithite ZnCu$_3$(OH)$_6$Cl$_2$ by a combination of infrared
spectroscopy measurements and ab initio density functional theory calculations,
and provide an unambiguous assignment of infrared-active lattice vibrations
involving in-plane and out-of-plane atom displacements in the kagome layers.
Upon cooling, non-thermal red-shifts and broadening appear specifically for
modes that deform the kagome layer or affect the Cu-O-Cu bond angles, thus
creating pronounced modifications of the antiferromagnetic exchange coupling.
Our results indicate the presence of a strong magnetoelastic coupling to the
spin system. We discuss the effects of this coupling and its relation to recent
experiments reporting a global symmetry reduction of the kagome lattice
symmetry.
