How critical are the van der Waals interactions in polymer crystals?

van der Waals (vdW) interactions play a prominent role in polymer crystallization. However, density functional theory (DFT) computations that utilize conventional (semi)local exchange-correlation functionals are unable to account for vdW interactions adequately and hence lead to poor predictions of equilibrium structures, densities, cohesive energies, and bulk moduli of polymeric crystals. This study therefore applies two forms of dispersion corrections to DFT, using either the Grimme (DFT-D3/D2) or the Tkatchenko and Scheffler (DFT-TS) approaches. We critically evaluate the relative performance of these two approaches in predicting structural, energetic, and elastic properties for a wide range of polymer crystals and also compare it with conventional electron exchange-correlation functionals (LDA, PBE, and PW91). Our results show that although the conventional functionals either systematically underestimate (e.g., LDA) or overestimate (e.g., PBE and PW91) the lattice parameters that control the polymer interchain interactions in a crystal, the dispersion-corrected functionals consistently provide a better prediction of the structural parameters. In a relative sense, however, the D3 and TS schemes are superior to the D2 approach owing to the environment-dependent atomic dispersion coefficients implicit in the D3 and TS treatments (we do note though that the D2 scheme already constitutes a significant improvement over the (semi)local functionals). Our results not only elucidate the importance of dispersion corrections in the accurate determination of the structural properties of the prototypical polymers considered but also provide a benchmark for comparing other procedures that might be used for including vdW interactions in such systems.