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We compute the phonon dispersion, density of states, and the Gr\"uneisenparameters of bulk palladium in the combined density functional theory (DFT)and dynamical mean-field theory (DMFT). We find good agreement withexperimental results for ground state properties (equilibrium lattice parameterand bulk modulus) and the experimentally measured phonon spectra. Wedemonstrate that at temperatures $T \lesssim 20~K$ the phonon frequency in thevicinity of the Kohn anomaly, $\omega_{T1}({\bf q}_{K})$, strongly decreases.This is in contrast to DFT where this frequency remains essentially constant inthe whole temperature range. Apparently correlation effects reduce therestoring force of the ionic displacements at low temperatures, leading to amode softening.

Lattice dynamics of palladium in the presence of electronic correlations