The method of dispersion correction as an add-on to standard Kohn-Sham density functional theory (DFT-D) has been refined regarding higher accuracy, broader range of applicability, and less empiricism. The main new ingredients are atom-pairwise specific dispersion coefficients and cutoff radii that are both computed from first principles. The coefficients for new eighth-order dispersion terms are computed using established recursion relations. System (geometry) dependent information is used for the first time in a DFT-D type approach by employing the new concept of fractional coordination numbers (CN). They are used to interpolate between dispersion coefficients of atoms in different chemical environments. The method only requires adjustment of two global parameters for each density functional, is asymptotically exact for a gas of weakly interacting neutral atoms, and easily allows the computation of atomic forces. Three-body nonadditivity terms are considered. The method has been assessed on standard benchmark sets for inter- and intramolecular noncovalent interactions with a particular emphasis on a consistent description of light and heavy element systems. The mean absolute deviations for the S22 benchmark set of noncovalent interactions for 11 standard density functionals decrease by 15%-40% compared to the previous (already accurate) DFT-D version. Spectacular improvements are found for a tripeptide-folding model and all tested metallic systems. The rectification of the long-range behavior and the use of more accurate C(6) coefficients also lead to a much better description of large (infinite) systems as shown for graphene sheets and the adsorption of benzene on an Ag(111) surface. For graphene it is found that the inclusion of three-body terms substantially (by about 10%) weakens the interlayer binding. We propose the revised DFT-D method as a general tool for the computation of the dispersion energy in molecules and solids of any kind with DFT and related (low-cost) electronic structure methods for large systems.

http://dns2.asia.edu.tw/~ysho/YSHO-English/1000%20WC/PDF/J%20Che%20Phy132,%20154104.pdf

A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu

This article reviews the basic theoretical aspects of graphene, a one-atom-thick allotrope of carbon, with unusual two-dimensional Dirac-like electronic excitations. The Dirac electrons can be controlled by application of external electric and magnetic fields, or by altering sample geometry and/or topology. The Dirac electrons behave in unusual ways in tunneling, confinement, and the integer quantum Hall effect. The electronic properties of graphene stacks are discussed and vary with stacking order and number of layers. Edge (surface) states in graphene depend on the edge termination (zigzag or armchair) and affect the physical properties of nanoribbons. Different types of disorder modify the Dirac equation leading to unusual spectroscopic and transport properties. The effects of electron-electron and electron-phonon interactions in single layer and multilayer graphene are also presented.

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The electronic properties of graphene

It is shown by an extensive benchmark on molecular energy data that the mathematical form of the damping function in DFT-D methods has only a minor impact on the quality of the results. For 12 different functionals, a standard "zero-damping" formula and rational damping to finite values for small interatomic distances according to Becke and Johnson (BJ-damping) has been tested. The same (DFT-D3) scheme for the computation of the dispersion coefficients is used. The BJ-damping requires one fit parameter more for each functional (three instead of two) but has the advantage of avoiding repulsive interatomic forces at shorter distances. With BJ-damping better results for nonbonded distances and more clear effects of intramolecular dispersion in four representative molecular structures are found. For the noncovalently-bonded structures in the S22 set, both schemes lead to very similar intermolecular distances. For noncovalent interaction energies BJ-damping performs slightly better but both variants can be recommended in general. The exception to this is Hartree-Fock that can be recommended only in the BJ-variant and which is then close to the accuracy of corrected GGAs for non-covalent interactions. According to the thermodynamic benchmarks BJ-damping is more accurate especially for medium-range electron correlation problems and only small and practically insignificant double-counting effects are observed. It seems to provide a physically correct short-range behavior of correlation/dispersion even with unmodified standard functionals. In any case, the differences between the two methods are much smaller than the overall dispersion effect and often also smaller than the influence of the underlying density functional.

Effect of the damping function in dispersion corrected density functional theory

CASTEP Computer program / Density functional theory / Pseudopotentials / ab initio study / Plane-wave method / Computational crystallography Abstract. The CASTEP code for first principles electro- nic structure calculations will be described. A brief, non- technical overview will be given and some of the features and capabilities highlighted. Some features which are un- ique to CASTEP will be described and near-future devel- opment plans outlined.

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First principles methods using CASTEP

We report re-optimization of a recently proposed long-range corrected (LC) hybrid density functional [J.-D. Chai and M. Head-Gordon, J. Chem. Phys., 2008, 128, 084106] to include empirical atom–atom dispersion corrections. The resulting functional, ωB97X-D yields satisfactory accuracy for thermochemistry, kinetics, and non-covalent interactions. Tests show that for non-covalent systems, ωB97X-D shows slight improvement over other empirical dispersion-corrected density functionals, while for covalent systems and kinetics it performs noticeably better. Relative to our previous functionals, such as ωB97X, the new functional is significantly superior for non-bonded interactions, and very similar in performance for bonded interactions.

/pdf/long-range-corrected-hybrid-density-functionals-with-damped-44ti6za9f3.pdf

Long-range corrected hybrid density functionals with damped atom–atom dispersion corrections

A scheme within density functional theory is proposed that provides a practical way to generalize to unrestricted geometries the method applied with some success to layered geometries [Phys. Rev. Lett. 91, 126402 (2003)]]. It includes van der Waals forces in a seamless fashion. By expansion to second order in a carefully chosen quantity contained in the long-range part of the correlation functional, the nonlocal correlations are expressed in terms of a density-density interaction formula. It contains a relatively simple parametrized kernel, with parameters determined by the local density and its gradient. The proposed functional is applied to rare gas and benzene dimers, where it is shown to give a realistic description.

Van der Waals Density Functional for General Geometries

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 [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.

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Van der Waals density functional for layered structures.

Sparse matter is abundant and has both strong local bonds and weak nonbonding forces, in particular nonlocal van der Waals (vdW) forces between atoms separated by empty space. It encompasses a broad spectrum of systems, like soft matter, adsorption systems and biostructures. Density-functional theory (DFT), long since proven successful for dense matter, seems now to have come to a point, where useful extensions to sparse matter are available. In particular, a functional form, vdW-DF (Dion et al 2004 Phys. Rev. Lett. 92 246401; Thonhauser et al 2007 Phys. Rev. B 76 125112), has been proposed for the nonlocal correlations between electrons and applied to various relevant molecules and materials, including to those layered systems like graphite, boron nitride and molybdenum sulfide, to dimers of benzene, polycyclic aromatic hydrocarbons (PAHs), doped benzene, cytosine and DNA base pairs, to nonbonding forces in molecules, to adsorbed molecules, like benzene, naphthalene, phenol and adenine on graphite, alumina and metals, to polymer and carbon nanotube (CNT) crystals, and hydrogen storage in graphite and metal–organic frameworks (MOFs), and to the structure of DNA and of DNA with intercalators. Comparison with results from wavefunction calculations for the smaller systems and with experimental data for the extended ones show the vdW-DF path to be promising. This could have great ramifications.

http://iopscience.iop.org/article/10.1088/0953-8984/21/8/084203/pdf

A density functional for sparse matter

There was an error in transcribing Fig. 1 into the variables andD. These variables were not contained in the code used in the calculations, and our results were not affected. A corrected version of Fig. 1 is included with this erratum. We thank Jesper Kleis for discovering this error. The new figure also contains small corrections resulting from an improved integration method for evaluating Eq. (14), also suggested by Jesper Kleis.

Erratum: Van der Waals Density Functional for General Geometries [Phys. Rev. Lett. 92, 246401 (2004)]

The details of a density functional that includes van der Waals (vdW) interactions are presented. In particular we give some key steps of the transition from a form for fully planar systems to a procedure for realistic layered compounds that have planar symmetry only on large-distance scales, and which have strong covalent bonds within the layers. It is shown that the random-phase approximation of that original functional can be replaced by an approximation that is exact at large separation between vdW interacting fragments and seamless as the fragments merge. An approximation to the latter which renders the functional easily applicable and which preserves useful accuracy in both limits and in between is given. We report additional data from applications to forms of graphite, boron nitride, and molybdenum sulfide not reported in our previous communication.(C) 2004 Wiley Periodicals, Inc.

/pdf/van-der-waals-density-functional-theory-with-applications-1oo400wfvw.pdf

Henrik Rydberg

Papers

Van der Waals Density Functional for General Geometries

Van der Waals density functional for layered structures.

A density functional for sparse matter

Erratum: Van der Waals Density Functional for General Geometries [Phys. Rev. Lett. 92, 246401 (2004)]

Van der Waals Density Functional Theory with Applications