Harmonic and Anharmonic Dynamics in Crystals from Classical Simulations

Harmonic atomic displacement parameters (ADPs) provide useful information about the magnitudes and the directions of average atomic vibrations. However, anharmonic effects may be far from negligible, especially above cryogenic temperatures. Even estimating the relative weight of anharmonic and harmonic displacements is experimentally challenging, as it requires diffraction data at very high resolution, which are seldom available at room temperature, precisely where anharmonic effects are expected to be least negligible. Here, we leverage classical Molecular Dynamics (MD) methods available MiCMoSv2.4 to sample atomic probability density functions (pdfs) in form I of crystalline urea as a function of temperature and pressure with the LJC Force Field. We provide approximate yet quantitatively consistent estimates of the harmonic Debye-Waller parameters, comparable with those derived from X-ray and neutron diffraction, and periodic DFT simulations. The anharmonic effects, quantified by the Grüneisen parameter and by explicit temperature-dependent evaluation of Gram–Charlier tensors, are in excellent agreement with available experimental data. Our results confirm that anharmonic effects may be non-negligible even at cryogenic temperatures in molecular materials. Overall, we provide a cheap semi-quantitative method to estimate the relative weight of harmonic and anharmonic displacement amplitudes as a function of temperature, as well as their mutual interplay in describing the crystal dynamics in the real space. Implications on accuracy of X-ray datasets are also discussed.