Towards reliable theoretical description of molecular solids

Molecular crystals are materials important both in nature and industries. From methane clathrates at the bottom of the sea, over pharmaceuticals in pills, to carbon dioxide ice caps on Mars.

For example, even at the same conditions, many pharmaceuticals can exist in different crystal structures, called polymorphs. One of these polymorphs is the most stable, but the others are usually very close in energy. If we want to reliably predict the energy ordering of different structures from simulation, we clearly need methods which are accurate enough.

However, accuracy is not the only thing to consider. The results of the simulations depend on numerical parameters, such as the basis set size. If we want to benefit from the use of a highly accurate method, we need to converge the desired property with respect to the parameters, that is, the precision needs to be high as well. Doing calculations precisely is important if we want to understand how accurate a given method, such as some density functional theory (DFT) functional, is.

Unfortunately, obtaining tightly converged results can increase the computational requirements substantially and can be even impossible for methods based on perturbation theory. I will show several examples to illustrate some of these issues.First, I will discuss the application of the random phase approximation (RPA) scheme and second-order Moller-Plesset perturbation theory (MP2) to molecular solids. The RPA is the least demanding correlated method available within periodic boundary conditions and, together with the so-called singles corrections, achieves an accuracy that surpasses state-of-the-art DFT functionals [1,2].

However, as correlated schemes, both MP2 and RPA suffer from slow convergence with respect to the basis-set size, or with the simulation cell volume if periodic boundary conditions are used.
Nevertheless, converged results can be obtained. This allows us to understand the precision of an alternative scheme for calculating lattice energies of solids, the many-body expansion.

Second, I will show that weak intermolecular interactions are very suitable to study and understand the precision of computational set-up. Moreover, I will give an example where such test identified a difference in implementation of a widely used DFT functional.

[1] J. Klimes, M. Kaltak, E. Maggio, G. Kresse: J. Chem. Phys. 143, 102816 (2015)
[2] J. Klimes: J. Chem. Phys. 145, 094506 (2016)