Lattice dynamics calculation of infrared active modes of cuprate superconductors

We have calculated the highest-energy infrared active E_u mode for three cuprate compounds with and without apical ions, in order to investigate the experimental energy-difference between T- and T^′-structures. The calculated energies show the similar Cu-O bond length dependence to the experimental results. The calculated spin densities of the T-structure have more electrons in the d_x2 ^{- y}2 orbital than that of the T^′-structure. This means that the CuO₂ plane in the T-structure is compressed, in comparison with the T^′-structure even with the same Cu-O bond length. This compression increases the energy of the E_u mode in the T-structure. This is the clear evidence that the block layer is important for the electronic state on the CuO₂ plane.