Van der Waals Interactions in Density Functional Theory

Andersson, Ylva; Hult, Erika; Rydberg, Henrik; Apell, P.; Lundqvist, Bengt I.; Langreth, David C.

doi:10.1007/978-1-4899-0316-7_17

Cited by 38 publications

(59 citation statements)

References 62 publications

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“…(9) provides a route to van der Waals forces for separated pieces of matter, and so is being much studied by developers. In particular, the coefficient in the decay of the energy between two such pieces (C 6 in E → −C 6 /R 6 , where R is their separation) can be accurately (within about 20%) evaluated using a local approximation to the frequencydependent polarizability [21,120,121,122]. Recent work shows that the response functions of TDDFT can yield extremely accurate dispersion energies of monomers [123].…”

Section: Where ∆ (Acc)mentioning

confidence: 99%

“…Just as in the ground-state case, it has the advantage in computational speed, allowing study of larger systems than with traditional methods, and the usual disadvantage (or excitement) of being unsystematic and artful. A final application is to write the ground-state XC energy in terms of the frequency-dependent response function, and so linear response TDDFT yields approximate treatments of the ground-state problem [20,21,22,23].…”

mentioning

confidence: 99%

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Time-dependent density functional theory: Past, present, and future

Burke

Werschnik

Gross

2005

The Journal of Chemical Physics

861

586

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Time-dependent density functional theory (TDDFT) is presently enjoying enormous popularity in quantum chemistry, as a useful tool for extracting electronic excited state energies. This article discusses how TDDFT is much broader in scope, and yields predictions for many more properties. We discuss some of the challenges involved in making accurate predictions for these properties.Kohn-Sham density functional theory [1,2,3] is the method of choice to calculate ground-state properties of large molecules, because it replaces the interacting manyelectron problem with an effective single-particle problem that can be solved much faster. Time-dependent density functional theory (TDDFT) applies the same philosophy to time-dependent problems. We replace the complicated many-body time-dependent Schrödinger equation by a set of time-dependent single-particle equations whose orbitals yield the same time-dependent density n(r, t). We can do this because the Runge-Gross theorem [4] proves that, for a given initial wavefunction, particle statistics and interaction, a given time-dependent density n(r, t) can arise from at most one time-dependent external potential v ext (r, t). We define time-dependent Kohn-Sham (TDKS) equations that describe N non-interacting electrons that evolve in v S (r, t), but produce the same n(r, t) as that of the interacting system of interest. Development and applications of TDDFT have enjoyed exponential growth in the last few years [5,6,7,8], and we hope this merry trend will continue.The scheme yields predictions for a huge variety of phenomena, that can largely be classified into three groups: (i) the non-perturbative regime, with systems in laser fields so intense that perturbation theory fails, (ii) the linear (and higher-order) regime, which yields the usual optical response and electronic transitions, and (iii) back to the ground-state, where the fluctuation-dissipation theorem produces ground-state approximations from TDDFT treatments of excitations.In the first, non-perturbative regime, we have systems in intense laser fields with electric field strengths that are comparable to or even exceed the attractive Coulomb field of the nuclei [5]. The time-dependent field cannot be treated perturbatively, and even solving the time-dependent Schrödinger equation for the evolution of two interacting electrons is barely feasible with present-day computer technology [9]. For more electrons in a time-dependent field, wavefunction methods are prohibitive, and in the regime of (not too high) laser intensities, where the electron-electron interaction is still of importance TDDFT is essentially the only practical scheme available. With the recent advent of atto-second laser pulses, the electronic time-scale has become accessible. Theoretical tools to analyze the dynamics of excitation processes on the attosecond time scale will become more and more important. An example of such a tool is the time-dependent electron localization function (TDELF) [10,11]. This quantity allows the time-resolved observation of ...

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Section: Where ∆ (Acc)mentioning

confidence: 99%

mentioning

confidence: 99%

Time-dependent density functional theory: Past, present, and future

Burke

Werschnik

Gross

2005

The Journal of Chemical Physics

861

586

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“…The metallic sphere has a natural sharp cutoff of all integrals over r , which we extend even to the diffuse density of an atom ( † ). Unbiased sharp cutoffs are also used in the construction of nonempirical density functionals for the exchange-correlation energy (35-37) and a model dynamic dipole polarizability (38). The parameter a l and the cutoff radius R l are determined by the two imposed constraints.…”

Section: Nonempirical Model For the Dynamic Multipole Polarizabilitymentioning

confidence: 99%

Accurate van der Waals coefficients from density functional theory

Tao

Perdew

Ruzsinszky

2011

Proc. Natl. Acad. Sci. U.S.A.

104

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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...

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“…In order to correctly describe a larger number of properties and, more generally, to better describe long-range electron correlation, density-functionals including an explicit dependence on virtual KS orbitals were more recently developed. [9][10][11] Actually, early attempts devoted to include self-consistently a dependence on virtual KS orbitals via Perturbation Theory (PT), firstly introduced by Levy and Görling, 12 were computationally demanding while providing no substantial improvement with respect to standard approaches, at least in the case of benchmark cases. 13 Nonetheless, pioneering works 14,15 allowed to foresee more efficient ways of including the PT contribution, leading to a new class of functionals belonging to the fifth rung of the Perdew ladder: 1 the so called double-hybrid (DH) density-functionals.…”

Section: Introductionmentioning

confidence: 99%

Nonempirical Double-Hybrid Functionals: An Effective Tool for Chemists

et al. 2016

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ConspectusDensity Functional Theory (DFT) emerged in the last two decades as the most reliable tool the description and prediction of properties of molecular systems and extended materials, coupling in an unprecedented way high accuracy and reasonable computational cost. This success rests also on the development of more and more performing Density Functional Approximations (DFAs).Indeed, the Achilles' heel of DFT is represented by the exchange-correlation contribution to the total energy, which, being unknown, must be approximated. Since the beginning of the '90s, global hybrids (GH) functionals, where an explicit dependence of the exchange-correlation energy on model. In such a way, a whole family of non-empirical functionals, spanning on the highest rungs of the Perdew's quality scale, is now available and competitive with other -more empirical-DFAs. This is a previous version of the article published in Accounts of Chemical Research. 2016Research. , 49(8): 1503Research. -1513Research. . doi:10.1021 2 Discussion of selected cases, ranging from thermochemistry and reactions to weak interactions and excitations energies, not only show the large range of applicability of non-empirical DFAs, but also underline how increasing the number of theoretical constrains parallel with an improvement of the DFA's numerical performances. This fact further consolidates the strong theoretical framework of non-empirical DFAs.Finally, even if non-empirical DH approaches are still computationally expensive, relying on the fact that they can benefit of all technical enhancements developed for speeding-up post-HartreeFock methods, there is a substantial hope for their near future routine application to the description and prediction of complex chemical systems and reactions.

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Van der Waals Interactions in Density Functional Theory

Cited by 38 publications

References 62 publications

Time-dependent density functional theory: Past, present, and future

Time-dependent density functional theory: Past, present, and future

Accurate van der Waals coefficients from density functional theory

Nonempirical Double-Hybrid Functionals: An Effective Tool for Chemists

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