Benchmarking DFT-GGA calculations for the structure optimisation of neutral-framework zeotypes

Abstract

Structure optimisations in the framework of plane-wave density functional theory (DFT) were performed for a set of reference structures of neutral-framework zeotypes and related compounds. The reference set comprised eight all-silica zeolites, four aluminophosphate zeotypes, and two dense polymorphs of SiO2 (α-quartz) and AlPO4 (α-berlinite). The optimisations considered a total of five GGA-type exchange–correlation functionals (GGA = generalised gradient approximation). Along with the very popular PBE functional, which is well-known to overestimate the lattice dimensions, two GGA functionals designed for solids (WC and PBEsol) and two variants of PBE including a pairwise dispersion correction (PBE-D2 and PBE-TS) were included. A detailed analysis of the agreement between DFT-optimised structures and experimental crystal structure data (obtained for calcined systems) showed that the inclusion of a dispersion correction greatly improves the prediction of the lattice parameters, with PBE-TS performing particularly well. On the other hand, WC and PBEsol give T–O bond lengths (T = tetrahedral sites) that are in better agreement with experimental data. The accurate reproduction of the T–O–T angles was found to be particularly challenging, as functionals without dispersion correction tend to overestimate these angles, whereas dispersion-corrected variants underestimate them. For all-silica zeolites, the present results were compared to those of a previous DFT study using the hybrid B3LYP-D2 functional and to results of molecular mechanics calculations employing two popular force fields, with none of these methods performing better than PBE-TS or PBE-D2. In order to better understand some of the shortcomings of the functionals considered, additional results for two outliers that were removed from the set of reference structures were analysed. Finally, the ability to reproduce the relative stability was assessed for those SiO2 frameworks for which experimental enthalpies of transition are available. Here, PBE-D2 outperformed PBE-TS, which showed a systematic tendency to overestimate the energy difference (relative to α-quartz). On the basis of the present work, PBE-TS can be recommended as a reasonable default choice for structure optimisations of neutral-framework zeotypes. While future benchmarking work could address a wider range of functionals and dispersion correction schemes, it needs to be considered that the limited availability of low-temperature crystal structure data limits the accuracy with which the deviations between computation and experiment can be assessed for this group of materials.