Specific heat of molecular crystals from atomic mean square displacements with the Einstein, Debye, and Nernst-Lindemann models

Analysis of atomic displacement parameters (ADPs) from multitemperature diffraction data provides mean-field molecular translation and libration frequencies. These quantities have been combined with molecular deformation frequencies calculated ab initio, e.g. by DFT methods, to calculate the specific heat C-v of molecular crystals of naphthalene, anthracene, and hexamethylenetetramine. If the difference C-p - C-v is represented by the Nernst-Lindemann relation, C-p curves from diffraction experiments and ab initio calculations agree well with those based on calorimetry. Agreement is better if the Debye rather than the Einstein model is chosen to represent the contribution of the translational vibrations. Compressibilities estimated from the differences C-p - C-v are 2-5 times higher than those obtained from compressibility measurements at 298 K and GrUneisen constants derived from the temperature dependence of ADPs.