  The dimer Mott insulator $\kappa$-(BEDT-TTF)$_2$Cu$_2$(CN)$_3$ exhibits
unusual electrodynamic properties. Numerical investigations of the electronic
ground state and the molecular and lattice vibrations reveal the importance of
the Cu$_2$(CN)$_3^-$ anion network coupled to the BEDT-TTF molecules: The
threefold cyanide coordination of copper and linkage isomerism in the anion
structure cause a loss of symmetry, frustration, disorder, and domain
formation. Our findings consistently explain the temperature and
polarization-dependent THz and infrared measurements, reinforce the
understanding of dielectric properties and have important implications for the
quantum spin-liquid state, which should be treated beyond two-dimensional,
purely electronic models.
