First-Principles Description of Correlation Effects in Layered Materials

Abstract

We present a first-principles description of anisotropic materials characterized by having both weak (dispersionlike) and strong covalent bonds, based on the adiabatic-connection fluctuation-dissipation theorem with density functional theory. For hexagonal boron nitride the in-plane and out-of-plane bonding as well as vibrational dynamics are well described both at equilibrium and when the layers are pulled apart. Bonding in covalent and ionic solids is also described. The formalism allows us to ping down the deficiencies of common exchange-correlation functionals and provides insight toward the inclusion of dispersion interactions into the correlation functional. DOI: 10.1103/PhysRevLett.96.136404 PACS numbers: 71.15.Mb, 63.20.ÿe, 71.10.ÿw, 71.15.Nc Soft matter, biomolecules, and layered materials are examples of weakly bonded compounds, which constitute stringent tests for ab initio electronic structure calculations. A successful description of such systems requires an accurate treatment of a whole range of interactions, from short-range covalent to long-range van der Waals (vdW) forces. Moreover, their study provides valuable hints about how to devise new approximations that describe at a reasonable computational cost very different bonding regimes. In this realm, layered materials represent a unique case. The Kohn-Sham (KS) method under the simple local density approximation (LDA) [1] is known to give reasonable structural properties near the equilibrium interlayer distance of systems like graphite [2] and hexagonal boron nitride (h-BN) [3,4]. Surprisingly, the more elaborate exchange-correlation (XC) energy functional based on the generalized-gradient approximation (GGA) [5], while providing a good in-plane bonding, fails dramatically in the description of the equilibrium interlayer distance in h-BN and graphite, leading to completely unphysical results [6,7]. The mechanism responsible for this poor performance is not specific to GGA but to all functionals based on exact exchange [8] plus some LDA correlation (EXXc) (as illustrated below).It has been hypothesized that this failure is due to the lack of description of vdW forces, which are the manifestation of long-range correlation effects [7]. However, LDA, without accounting for vdW interactions, does bind the h-BN and graphite layers. More importantly, recently proposed approximate nonlocal prescriptions beyond LDA or GGA in the vdW density functional (vdW-DF) framework [9], while describing vdW forces, result in a large overestimation of the equilibrium layer-layer distance [7]. Thus, available XC functionals cannot describe correctly a layered material at different geometrical configurations. Consequently, there is a basic need to understand this severe breakdown and how to define a stable, successful scheme to calculate such structural properties. This is the goal of the present Letter. We demonstrate that a fully microscopic, parameter-free approach based on the adiabaticconnection fluctuation-dissipation theorem (ACFDT) [10] correctly describes ...

Mechanics and Mechanically Tunable Band Gap in Single-Layer Hexagonal Boron-Nitride

“…Similar to the mechanical properties of graphene, [24,41] we find that the strength and the failure strain in h-BN are strongly anisotropic. The strength and failure strain when pulling along the zigzag direction is much higher than that along the armchair direction.…”

“…[36] Except for the bi-axial loading case, we relax the box in the direction perpendicular to the loading axis in the sheet plane in all other calculations. To obtain the equivalent stress of the single-layer h-BN, an interlayer distance h 0 = 3.3 Å [36][37][38][39][40][41] is used, following reference. [42] We note that current thicknesses for 2D materials are derived based on their three-dimensional counterparts.…”

Recent development of atom‐pairwise van der waals corrections for density functional theory: From molecules to solids

“…The ACFDT-RPA calculations are known to provide accurate binding energy between slabs, [38] and therefore it can provide a reliable reference for the interlayer binding energies of layered materials as shown for graphite. [39] So far, the interlayer binding energies from the ACFDT-RPA calculations have been determined for graphite, [39] h-BN, [40] and various transition metal dichalcogenides (TMDs). [41] In this review, we compare different atom-pairwise methods against various benchmark sets that include intermolecular vdW interactions up to condensed phase many-body interactions, which range from dispersive interactions to ionic ones.…”

Hubbard-Ucorrected Hamiltonians for non-self-consistent random-phase approximation total-energy calculations: A study of ZnS,TiO2, and NiO

“…However, it is important to note that the most well-documented successes of this scheme-for instance, in describing nonlocal correlation in weakly bonded systems, describing chemisorption and bonding in solids, or in the TMC examples above-were performed non-self-consistently [18][19][20][21][22]. That is, the XC potential felt by the noninteracting electrons was not the functional derivative of the XC energy, at variance with the standard Kohn-Sham (KS) formulation of DFT [23].…”