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

physical review. b./physical review. b

Lattice vibrations of the charge-transfer salt  $\kappa$-(BEDT-TTF)$_2$Cu$_2$(CN)$_{3}$: novel interpretation of the  electrodynamic response in a spin-liquid compound