Benchmarking Calculated Lattice Parameters and Energies of Molecular Crystals Using van der Waals Density Functionals

The development of new functionals and methods to accurately describe van der Waals forces in density functional theory (DFT) has become popular in recent years, with the vast majority of studies assessing the accuracy of the energetics of collections of molecules, and to a lesser extent molecular crystalline systems. As the energies are a function of the atom positions, we assess the accuracy of DFT calculations from both a geometric and energetics point of view for the C21 reference data set of Otero-de-la-Roza and Johnson for molecular crystals, and a set of monosaccharide molecular crystals. In particular, we examine the performance of exchange-correlation functionals designed to handle van der Waals forces, including the vdW-DF, vdW-DF2, and XDM methods. We also assess the effect of using small and large basis sets, the choice of basis functions (local atomic orbitals using the SIESTA code versus planewaves using the Quantum ESPRESSO code), and the effect of corrections for basis set superposition errors. Finally, we examine the geometries and energies of the S22 reference set of molecular complexes. Overall, the most accurate geometries for both choices of basis functions are obtained with the vdW-DF2 functional, while the most accurate lattice energies are obtained using vdW-DF2 with local atomic orbitals and XDM with planewaves with mean absolute errors of less than 4 kJ/mol.