Comprehensive analysis of the influence of dispersion on group-14 rutile-type solids

Weak van der Waals interactions have a notorious influence on the stability of molecular solids and layered materials. In light of this fact, accurate models have been designed to account for such long-range interactions. Here, we explore the influence of the dispersion on the structural properties of dense rutile-type ${\mathrm{SiO}}_2$, ${\mathrm{GeO}}_2$, ${\mathrm{SnO}}_2$, and ${\mathrm{PbO}}_2$ structures. Several dispersion methods are discussed including pairwise force field and more physically grounded methods such as the so-called many body dispersion and nonlocal correlation functionals. The results clearly show that such methods and functionals have influence on the predicted crystal structure of the investigated solids, usually improving the structural properties with a reduction of the errors with respect to experiment. In particular, Perdew-Burke-Ernzerhof (PBE) coupled with many body dispersion (MBD)@rsSCS emerges as the most suitable method showing the lowest relative errors. Interestingly, this method reproduces similar results to those obtained by the PBEsol generalized gradient approach (GGA) functional designed to reproduce crystal structures without considering dispersion terms. Finally, we want to point out that the present study suggests that the proper inclusion of dispersion allows one to improve the description of the crystal structure and, consequently, due to the sensibility of either electronic and magnetic properties to it, methods coupling a suitable description of dispersion to a standard PBE GGA functional would lead to an improved description of crystalline solids.

Figure 1

Schematic representation of the rutile-type structure where lattice parameters are denoted by $a$ and $c$. The apical and equatorial distances of the octahedron unit $d_{\mathrm{a}}$ and $d_{\mathrm{e}}$ are also shown. Red and light purple spheres stand for oxygen, and metal atom.

Figure 2

Relative errors in % of the calculated lattice parameters ($a$ and $c$) and the $d_{\mathrm{a}}$ and $d_{\mathrm{e}}$ octahedron distances of (a) ${\mathrm{SiO}}_2$, (b), ${\mathrm{GeO}}_2$, (c) ${\mathrm{SnO}}_2$, and (d) ${\mathrm{PbO}}_2$ respect to experimental values compiled in Table 1. All data including the relative errors are listed in Tables SI–SIV of the Supplemental Material [71]. The dashed lines are a guide to the eye separating the results obtained from the no-dispersion, pairwise, TS &MDB, and vdW functionals, respectively.

Figure 3

Relative errors for the unit-cell volume of ${\mathrm{SiO}}_2,{\mathrm{GeO}}_2,{\mathrm{SnO}}_2$, and ${\mathrm{PbO}}_2$ with respect to experimental values complied in Table 1. All volume data including the relative errors are listed in Tables SI–SIV of the Supplemental Material [71]. The dashed lines are a guide to the eye separating the results obtained from the no-dispersion, pairwise, TS &MDB, and vdW functionals, respectively (see Fig. 2).

Figure 4

Plot of the $d_{\mathrm{a}}$/$d_{\mathrm{e}}$ ratio vs the $c$/$a$ ratio. The dashed lines define the linear fittings of each trend listed in Table 2.