There are a large number of materials with mild stiffness, which are not as soft as tissues and not as strong as metals. These semihard materials include energetic materials, molecular crystals, layered materials, and van der Waals crystals. The integrity and mechanical stability are mainly determined by the interactions between instantaneously induced dipoles, the so called London dispersion force or van der Waals force. It is challenging to accurately model the structural and mechanical properties of these semihard materials in the frame of density functional theory where the non-local correlation functionals are not well known. Here, we propose a van der Waals density functional named vdW-DFq to accurately model the density and geometry of semihard materials. Using β -cyclotetramethylene tetranitramine as a prototype, we adjust the enhancement factor of the exchange energy functional with generalized gradient approximations. We find this method to be simple and robust over a wide tuning range when calibrating the functional on-demand with experimental data. With a calibrated value q = 1.05 , the proposed vdW-DFq method shows good performance in predicting the geometries of 11 common energetic material molecular crystals and three typical layered van der Waals crystals. This success could be attributed to the similar electronic charge density gradients, suggesting a wide use in modeling semihard materials. This method could be useful in developing non-empirical density functional theories for semihard and soft materials.
Functional derivative of the zero-point-energy functional from the strong-interaction limit of density-functional theory
