Signatures of van der Waals binding: A coupling-constant scaling analysis

Abstract

The van der Waals (vdW) density functional (vdW-DF) method [ROPP 78, 066501 (2015)] describes dispersion or vdW binding by tracking the effects of an electrodynamic coupling among pairs of electrons and their associated exchange-correlation holes. This is done in a nonlocal-correlation energy term E nl c , which permits density functional theory calculation in the Kohn-Sham scheme. However, to map the nature of vdW forces in a fully interacting materials system, it is necessary to also account for associated kinetic-correlation energy effects. Here, we present a coupling-constant scaling analysis which permits us to compute the kinetic-correlation energy T nl c that is specific to the vdW-DF account of nonlocal correlations. We thus provide a more complete spatially-resolved analysis of the electrodynamical-coupling nature of nonlocal-correlation binding, including vdW attraction, in both covalently and non-covalently bonded systems. We find that kinetic-correlation energy effects play a significant role in the account of vdW or dispersion interactions among molecules. Furthermore, our mapping shows that the total nonlocal-correlation binding is concentrated to pockets in the sparse electron distribution located between the material fragments.

van der Waals density functional with corrected C6 coefficients

“…However, at binding separations such higher-order terms are generally less crucial, at least within vdW-DF, 30,57 as multipole effects are described to second order in S. Moreover, vdW-DF includes non-additive effects originating from changes in the electronic density. 58 Drawing attention to the possibility of adjusting h(y) within vdW-DF introduces a measure of flexibility that so far has been missing in standard vdW-DF. In fact, since the release of vdW-DF1 in 2004, 14 a number of exchange functionals have been proposed that aim both to improve binding energies and remedy the notorious overestimation of binding separations present in vdW-DF1 and to some extent in vdW-DF2.…”

First-principles study of the binding energy between nanostructures and its scaling with system size

“…The vdW-DF-cx description of the fullerene crystals gives an example: Appendix A shows that vdW-DF-cx does give an accurate description of structural motifs in fullerene crystals at binding separation even if vdW-DF-cx is not accurate for (and does not give nonadditive) C 6 coefficients, Table VII. We also note that the vdW-DFcx is nonadditive in a different sense, namely in its description of the nonlocal correlation interaction at binding separations [69].…”

Comparison of dispersion-corrected exchange-correlation functionals using atomic orbitals

“…Both VV10 and rVV10 have two adjustable parameters b and c assuring the compatibility between the semilocal XC functional and E nl c [n]. Recently, several variations of these vdW functionals have been proposed: AM05-VV10sol [40], SCAN+rVV10 [41], PBE+rVV10L [42], SG4+rVV10m [43], C09-vdW-DF [44], vdW-DF-cx [45][46][47][48], PBEsol+rVV10s [49], and rev-vdW-DF2 [50,51]. All these variations have been tested for many vdW systems, such as layered materials [33,[39][40][41][42]45,49,[51][52][53][54][55][56][57][58][59][60][61][62], rare-gas (RG) solids [43,49,62,63], and molecular solids [43,62].…”

“…In the case of SIESTA, we combine SG4 and PBEsol with VV10 (instead of rVV10), keeping the same dispersion parameters b and c. The SIESTA method, which uses localized numerical atomic orbitals (NAOs), has a number of advantages with respect to a plane-wave basis set: SIESTA is typically more efficient, as the number of required basis functions is usually smaller, and SIESTA's localized basis set gives a better description of systems where the orbitals are strictly localized in real space, as in the case of adsorption of atoms/molecules on surfaces and in the case of interfaces with different materials. Here we investigate, in the framework of the SIESTA method, new dispersion-corrected functionals that we call PBEsol+VV10s and SG4+VV10m, and we compare to the results one obtains with other functionals such as PBE+VV10L [42] and vdW-DF-cx [45][46][47][48].…”