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We propose a second version of the van der Waals density functional (vdW-DF2) of Dion et al. [Phys. Rev. Lett. 92, 246401 (2004)], employing a more accurate semilocal exchange functional and the use of a large-N asymptote gradient correction in determining the vdW kernel. The predicted binding energy, equilibrium separation, and potential-energy curve shape are close to those of accurate quantum chemical calculations on 22 duplexes. We anticipate the enabling of chemically accurate calculations in sparse materials of importance for condensed-matter, surface, chemical, and biological physics.
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Large biomolecular systems, whose function may involve thousands of atoms, cannot easily be addressed with parameter-free density functional theory (DFT) calculations. Until recently a central problem was that such systems possess an inherent sparseness, that is, they are formed from components that are mutually separated by low-electron-density regions where dispersive forces contribute significantly to the cohesion and behavior. The introduction of, for example, the van der Waals density functional (vdW-DF) method [PRL 92, 246401 (2004)] has addressed part of this sparse-matter system challenge. However, while a vdW-DF study is often as computationally efficient as a study performed in the generalized gradient approximation, the scope of large-sparse-matter DFT is still limited by computer time and memory. It is costly to self-consistently determine the electron wavefunctions and hence the kinetic-energy repulsion. In this paper we propose and evaluate an adaption of the Harris scheme [PRB 31, 1770 (1985)]. This is done to speed up non-selfconsistent vdW-DF studies of molecular-system interaction energies. Also, the Harris-type analysis establishes a formal link between dispersion-interaction effects on the effective potential for electron dynamics and the impact of including selfconsistency in vdW-DF calculations [PRB 76, 125112 (2007)].
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 [H. Rydberg, et al., 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.
The past few years has brought renewed focus on the physics behind the class of materials characterized by long-range interactions and wide regions of low electron density, sparse matter. There is now much work on developing the appropriate algorithms and codes able to correctly describe this class of materials within a parameter-free quantum physical description. In particular, van der Waals (vdW) forces play a major role in building up material cohesion in sparse matter. This work presents an application to the vanadium pentoxide (V2O5) bulk structure of t
The non-local van der Waals density functional (vdW-DF) has had tremendous success since its inception in 2004 due to its constraint-based formalism that is rigorously derived from a many-body starting point. However, while vdW-DF can describe binding energies and structures for van der Waals complexes and mixed systems with good accuracy, one long-standing criticism---also since its inception---has been that the $C_6$ coefficients that derive from the vdW-DF framework are largely inaccurate and can be wrong by more than a factor of two. It has long been thought that this failure to describe the $C_6$ coefficients is a conceptual flaw of the underlying plasmon framework used to derive vdW-DF. We prove here that this is not the case and that accurate $C_6$ coefficient can be obtained without sacrificing the accuracy at binding separations from a modified framework that is fully consistent with the constraints and design philosophy of the original vdW-DF formulation. Our design exploits a degree of freedom in the plasmon-dispersion model $omega_{mathbf{q}}$, modifying the strength of the long-range van der Waals interaction and the cross-over from long to short separations, with additional parameters tuned_ to reference systems. Testing the new formulation for a range of different systems, we not only confirm the greatly improved description of $C_6$ coefficients, but we also find excellent performance for molecular dimers and other systems. The importance of this development is not necessarily that particular aspects such as $C_6$ coefficients or binding energies are improved, but rather that our finding opens the door for further conceptual developments of an entirely unexplored direction within the exact same constrained-based non-local framework that made vdW-DF so successful in the first place.
The fundamental ideas for a non-local density functional theory -- capable of reliably capturing van der Waals interaction -- were already conceived in the 1990s. In 2004, a seminal paper introduced the first practical non-local exchange-correlation functional called vdW-DF, which has become widely successful and laid the foundation for much further research. However, since then, the functional form of vdW-DF has remained unchanged. Several successful modifications paired the original functional with different (local) exchange functionals to improve performance and the successor vdW-DF2 also updated one internal parameter. Bringing together different insights from almost two decades of development and testing, we present the next-generation non-local correlation functional called vdW-DF3, in which we change the functional form while staying true to the original design philosophy. Although many popular functionals show good performance around the binding separation of van der Waals complexes, they often result in significant errors at larger separations. With vdW-DF3, we address this problem by taking advantage of a recently uncovered and largely unconstrained degree of freedom within the vdW-DF framework that can be constrained through empirical input, making our functional semi-empirical. For two different parameterizations, we benchmark vdW-DF3 against a large set of well-studied test cases and compare our results with the most popular functionals, finding good performance in general for a wide array of systems and a significant improvement in accuracy at larger separations. Finally, we discuss the achievable performance within the current vdW-DF framework, the flexibility in functional design offered by vdW-DF3, as well as possible future directions for non-local van der Waals density functional theory.
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