  Cuprates are promising candidates for study in developing higher temperature
superconductors. A thorough understanding of a material's phonon modes enables
further investigation of its emergent properties, however, no complete
reference of the phonon modes exists. Here, using density functional theory, we
evaluate the phonon frequencies and atomic displacements for
$\text{La}_2\text{CuO}_4$, $\text{Bi}_2\text{Sr}_2\text{CuO}_6$, and
$\text{Bi}_2\text{Sr}_2\text{CaCu}_2\text{O}_8$ in their tetragonal structures.
The phonon modes for all materials agree with those expected from space group
symmetry and display instabilities corresponding to known low-temperature
structural phase transitions.
