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Taking the prototypical high-T_c superconductor HgBa₂CuO₄ as an example, I will compare ab-initio density-functional-theory (DFT) calculations of the phonon dispersions to inelastic neutron scattering results that exhibit an anomaly in the Cu-O bond stretching branch. We have performed a series of calculations using several codes at different levels of approximation. Our results show good qualitative agreement for all codes, but only one gave a good quantitative agreement (better than 10%). All DFT calculations fail to reproduce the experimentally observed anomalous dispersion of the bond-stretching phonon branch. I will conclude my talk by mentioning other computational methods that may improve the agreement between the calculations and measurement.