Van der Waals Density Functional for Layered Structures

Abstract

To understand sparse systems we must account for both strong local atom bonds and weak nonlocal van der Waals forces between atoms separated by empty space. A fully nonlocal functional form [H. Rydberg, B.I. Lundqvist, D.C. Langreth, and M. Dion, Phys. Rev. B 62, 6997 (2000)] of density-functional theory (DFT) is applied here to the layered systems graphite, boron nitride, and molybdenum sulfide to compute bond lengths, binding energies, and compressibilities. These key examples show that the DFT with the generalized-gradient approximation does not apply for calculating properties of sparse matter, while use of the fully nonlocal version appears to be one way to proceed.PACS numbers: 71.15. Mb, 61.50.Lt, 31.15.Ew, Calculations of structure and other properties of sparse systems must account for both strong local atom bonds and weak nonlocal van der Waals (vdW) forces between atoms separated by empty space. Present methods are unable to describe the true interactions of sparse systems, abundant among materials and molecules. Key systems, like graphite, BN, and MoS 2 , have layered structures. While today's standard tool, density-functional theory (DFT), has broad application, the common local (LDA) and semilocal density approximations (GGA) [1,2,3,4] for exchange and correlation, E xc [n], fail to describe the interactions at sparse electron densities. Here we show that the recently proposed density functional [5] with nonlocal correlations, E nl c [n], gives separations, binding energies, and compressibilities of these layered systems in fair agreement with experiment. This planar case bears on the development of vdW density functionals for general geometries [6,7], as do asymptotic vdW functionals [8].Figure 1 with its 'inner surfaces' defines the problem: voids of ultra-low density, across which electrodynamics leads to vdW coupling. This coupling depends on the polarization properties of the layers themselves, and not on small regions of density overlap between the layers, excluding proper account in LDA or GGA. For large interplanar separation d the vdW interaction energy between planes behaves as −c 4 /d 4 , while LDA or GGA necessarily predicts an exponential falloff. Layers rolled up to form two (i) nanotubes with parallel axes a distance l apart interact as −c 5 /l 5 , or (ii) balls (e.g., C 60 ), a distance r apart, as −c 6 /r 6 . If by fluke an LDA or GGA were to give the correct equilibrium for one shape, it would necessarily fail for the others. The simple expedient of adding the standard asymptotic vdW energies as corrections to the correlation energy of LDA or GGA also fails. The true vdW interaction between two close sheets must be (i) substantially stronger (Fig. 1), (ii) seamless, and (iii) saturate as d shrinks (Fig. 2).Like earlier work directly calculating nonlocal correlations between two jellium slabs [9], the vdW density functional (vdW-DF) theory [5] used here exploits assumed planar symmetry. It divides the correlation energy functional into two pieces,, where E nl c [n] is defined to in...

An ab Initio Study of Solid Nitromethane, HMX, RDX, and CL20: Successes and Failures of DFT

“…To properly describe the electronic structure of the crystals, possible solutions are: (1) new functionals need to be developed which include accurate dispersion forces for non-or nearly-overlapping densities (Rydberg et al, 2003;Dion et al, 2004), (2) employ linear response theory to calculate the frequency dependent susceptibility and use it to obtain the dispersion forces, (3) or use perturbation theory for the intermolecular correlation and DFT for the intramolecular correlation, taking care to avoid doublecounting.…”

Role of van der Waals bonding in the layered oxideV2O5: First-principles density-functional calculations

“…LDA lacks a physical description of the dispersive interactions and has no basis for a transferable account in more general geometries. 17 In other geometries the LDA approach gives results that are not in accordance with experiment or more accurate methods. 26,49 C. Numerical noise and exchange functionals Our DFT calculations are based on a description of the valence-electron wave functions by USPP.…”

“…Previous atomic-scale calculations that were based on densityfunctional theory ͑DFT͒ with the popular semilocal generalized gradient approximations ͑GGAs͒ have often failed in arriving at the experimentally known value of the lattice parameter in the stacking direction of the layers. [8][9][10][11][12][13] This is believed to happen because GGA does not describe the van der Waals ͑vdW͒ forces, 17 and because these are expected to play an important role in binding the layers in V 2 O 5 bulk. 12 In several GGA-based V 2 O 5 surface or vacancy studies this deficiency of GGA was either ignored or worked around by imposing the experimentally obtained lattice parameter or unit-cell volume.…”

The van der Waals interactions of concentric nanotubes

“…1) we define two sets of local cylindrical coordinate systems with origos separated by d, and with indices 1 and 2 referring to the two nanotubes and their local coordinate systems. Within the dipole-dipole approximation we then find the van der Waals energy for R = R (4,4) and R = 3R (4,4) .…”