Accurate van der Waals coefficients from density functional theory

Abstract

The van der Waals interaction is a weak, long-range correlation, arising from quantum electronic charge fluctuations. This interaction affects many properties of materials. A simple and yet accurate estimate of this effect will facilitate computer simulation of complex molecular materials and drug design. Here we develop a fast approach for accurate evaluation of dynamic multipole polarizabilities and van der Waals (vdW) coefficients of all orders from the electron density and static multipole polarizabilities of each atom or other spherical object, without empirical fitting. Our dynamic polarizabilities (dipole, quadrupole, octupole, etc.) are exact in the zero-and high-frequency limits, and exact at all frequencies for a metallic sphere of uniform density. Our theory predicts dynamic multipole polarizabilities in excellent agreement with more expensive many-body methods, and yields therefrom vdW coefficients C 6 , C 8 , C 10 for atom pairs with a mean absolute relative error of only 3%.T he van der Waals interaction (1) is a long-range attraction between chemical species, arising from instantaneous charge fluctuations on each. This interaction is present even when there is no chemical bond, and even when each species has no permanent multipole moment. Its significance first came to light when van der Waals (vdW) (2) formulated the equation of state for real gases and liquids in 1873 by taking this correlation effect into consideration. The vdW interaction is much weaker in strength than a normal chemical bond, but it has important effects on the properties of materials (3). For example, it is responsible for many phenomena such as sublimation of iodine, naphthalene, dry ice, and other organic molecules, high interlayer mobility of graphite, foldings of long biomolecular chains such as DNA, RNA, proteins, polymers, etc. The vdW interaction has been extensively studied (4, 5) on account of its ubiquity and importance for soft matter relevant to human activity. Many theoretical methods, including CI (6, 7) (configuration interaction), MBPT (8) (manybody perturbation theory), coupled cluster (9) methods, or their combinations such as CI+MBPT (10, 11), have been developed to estimate this effect. These methods are highly accurate (within about 1%) but computationally expensive. A cheap but usefully accurate method is density functional theory (12) (DFT). While this theory has achieved a high level of sophistication and has become the mainstream electronic structure theory, it often fails in practice to describe vdW systems, because the long-range part of the vdW interaction is absent in commonly used DFT approximations [e.g.,[13][14][15]].In the large separation limit of two spherically symmetric interacting densities A and B, second-order perturbation theory yields the (nonretarded) potential energy E vdW , which can be expressed as a power series (16),where R is the separation between centers, C 6 describes the instantaneous dipole-dipole interaction, C 8 the dipole-quadrupole interaction, and C 10 the quadrupol...

First-Principles Models for van der Waals Interactions in Molecules and Materials: Concepts, Theory, and Applications

“…This model was later extended to describe higher-multipole coefficients as well. 222 In the context of general vdW methods, this model is not fully complete, as the C 6 coefficient model is not combined with a damping function, and still requires a prescription for the input static polarizability. However, such a generalization could be obtained in a straightforward manner, for example with the approach used in the XDM or TS methods, and hence we chose to present this model to illustrate the flexibility with which density-functional models for the local effective polarizability can be constructed.…”

On the accuracy of van der Waals inclusive density-functional theory exchange-correlation functionals for ice at ambient and high pressures

“…[45][46][47][48][49][50][51][65][66][67][68][69][70][71][72][73] a) Electronic mail: angelos.michaelides@ucl.ac.uk Understanding the role of vdW forces in water has been greatly helped by the emergence of various approaches which account for vdW forces within the framework of DFT. [74][75][76][77][78][79][80][81][82][83] In the last few years, many of the vdW inclusive DFT xc functionals have been used to investigate the effects of vdW on the structural, energetic, and vibrational properties of liquid water. [65][66][67][68][69][70][71][72][73] Overall, with vdW inclusive xc functionals there are indeed improvements in certain calculated properties of liquid water.…”

van der Waals interactions at the nanoscale: The effects of nonlocality

“…In the classical electrodynamics picture where nonlocality is neglected, the fluctuating surface charges are located precisely on the surface and these infinitely compressed charges result in the unphysically divergent van der Waals force (1,29). In a more realistic framework, considering the inherent quantum nature of electrons, the surface charges are intrinsically smeared across the boundary in a subnanometer layer (7,(20)(21)(22), which dramatically alters the van der Waals energy in the small gap limit (30)(31)(32)(33). Due to the complexity introduced by nonlocality, its influence on the van der Waals force in 3D geometries has never been described appropriately.…”