Anisotropic displacement parameters for molecular crystals from periodic Hartree–Fock and density functional theory calculations

Fully periodic Hartree-Fock and density functional theory calculations have been used to compute the anisotropic displacement parameters (ADPs) of molecular crystals at different temperatures by using the CRYSTAL code. Crystalline urea was adopted as a benchmark system to investigate the dependence on basis set and Hamiltonian. The results were compared with ADPs derived from neutron diffraction experiments. The approach can estimate the internal ADPs, corresponding to the contributions of high-frequency intramolecular vibrations, and for these internal contributions the results are almost independent of the basis set and Hamiltonian. Much larger variations and discrepancies from neutron diffraction experiments are seen for the external, low-frequency modes, which become dominant at higher temperatures. The approach was then tested on benzene and urotropine. Finally, ADPs of l-alanine were predicted at the B3LYP/6-31G(d,p) level of theory. The total ADPs, including low-frequency external modes, are underestimated, but can be brought into good agreement with the experimental ADPs by introducing a Grüneisen parameter, which partly accounts for anharmonicity of the potential energy surface, but likely also contains contributions from other deficiencies of the calculations.