Nonlocal van der Waals functionals for solids: Choosing an appropriate one

Abstract

The nonlocal van der Waals (NL-vdW) functionals [Dion et al., Phys. Rev. Lett. 92, 246401 (2004)] are being applied more and more frequently in solid-state physics, since they have shown to be much more reliable than the traditional semilocal functionals for systems where weak interactions play a major role. However, a certain number of NL-vdW functionals have been proposed during the last few years, such that it is not always clear which one should be used. In this work, an assessment of NL-vdW functionals is presented. Our test set consists of weakly bound solids, namely rare gases, layered systems like graphite, and molecular solids, but also strongly bound solids in order to provide a more general conclusion about the accuracy of NL-vdW functionals for extended systems. We found that among the tested functionals, rev-vdW-DF2 [Hamada, Phys. Rev. B 89, 121103(R) (2014)] is very accurate for weakly bound solids, but also quite reliable for strongly bound solids.SL/hybrid xc alone should not already lead to an overbinding, otherwise adding E NL c,disp can only make the results worse. Thus, the combination E SL/hybrid xc + E NL c,disp has to be well-balanced in order to provide accurate geometry and binding energy. 23,25,36,40 Among the NL-vdW functionals that are available in the literature, a certain number of them were selected for the present work. However, we did not consider NL-vdW functionals based on hybrid functionals, 37,38,41,42 since they lead to calculations that are much more expensive, especially for solids. They are therefore less interesting from a practical point of view as long as the electronic structure is of no particular interest. Thus, only semilocal-based NL-vdW functionals are considered and now listed.vdW-DF from Dion et al. (DRSLL), 2 the first proposed NL-vdW functional that can be applied to systems with arbitrary geometry, consists of the GGA exchange revPBE 43 (a reoptimization of PBE 14 ) and LDA correlation 44,45 for the semilocal part. The nonlocal term, Eq. (2), of the vdW-DF functional (DRSLL kernel Φ) has subsequently been used in combination with other semilocal components, and among them, those that are considered in the present work are the following four. C09-vdW from Cooper, 46 which uses a GGA (C09x) for exchange and LDA for correlation. optB88-vdW and optB86b-vdW, which are two of the functionals developed by Klimeš et al.,21,23 and use for the semilocal component, the GGAs optB88 and optB86b for exchange and LDA for correlation. Note that optB88 and optB86b are reoptimizations of B88 47 and B86b, 48 respectively. vdW-DF-cx from Berland and Hyldgaard, 25 which consists of a GGA exchange component, LV-PW86r, that is combined with LDA correlation and was constructed to be more consistent with the DRSLL kernel. vdW-DF2 from Lee et al. (LMKLL) 36 uses the GGA exchange PW86R 36 (a reoptimization of PW86 49 ) and LDA for correlation, while the kernel Φ (called LMKLL) in E NL c,disp has the same analytical form as the original DRSLL kernel, but with a reoptimized parameter Z ...

Unveiling phonons in a molecular qubit with four-dimensional inelastic neutron scattering and density functional theory

“…However, a rescaling of 13% has been uniformly applied to all phonon modes, in order to lower the calculated phonon energies ω j ðqÞ and better reproduce INS data. The observed discrepancies are consistent with other results in literature for molecular crystals [54][55][56] and are mainly due to the limitations of DFT methods in describing vdW interactions in these systems [51][52][53] , especially at low energies. However, the comparison of phonon frequencies alone is not enough to guarantee the accuracy of DFT simulations.…”

“…All the structural optimisation and Hessian calculations were performed with the CP2K software 62 at the level of DFT with the Perdew-Burke-Ernzerhof functional 63 including Grimme's D3 vdW corrections 64,65 . Indeed, the requirement of vdW-corrected functionals for the modelling of molecular crystals is by now confirmed and settled by several results in literature [51][52][53]55 . A double-zeta polarised (DZVP) MOLOPT basis set and a 600 Ry of plane-wave cutoff were used for all the atomic species.…”

“…It is worth noting that calculations of phonons for a generic Brillouin zone point by DFT is a daunting task, as the number of atoms that needs to be included is usually very large and approaches the computational limits of this method. Moreover, the accurate description of molecular crystals is particularly challenging due to the known shortcomings of DFT in describing van der Waals (vdW) interactions [51][52][53] . The latter are expected to be particularly weak in [VO(acac) 2 ], which is highly volatile as are most β-diketonate neutral complexes.…”

Improved Predictive Tools for Structural Properties of Metal–Organic Frameworks

“…We also note the work of Tran et al [48,49], who studied lattice constants, cohesive energies, and bulk moduli of strongly and weakly bound solids and found the best behavior for rev-VDW-DF2 and various meta functionals. The reader is directed to their studies for information complementary to the present study.…”

In Situ Assessment of Intrinsic Strength of X-I⋯OA-Type Halogen Bonds in Molecular Crystals with Periodic Local Vibrational Mode Theory

“…The rev-vdW-DF2 functional is a recently revised version of vdW-DF2 functional [109] with improved accuracy in describing van der Waals interactions (i.e., non-covalent bonding). According to a timely benchmark by Tran and co-workers, the rev-vdW-DF2 functional was shown to be the best choice for describing non-covalent interactions in molecular crystals [110].…”