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Register a new userLi intercalation in graphite: a van der Waals density-functional study
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Modeling layered intercalation compounds from first principles poses a problem, as many of their properties are determined by a subtle balance between van der Waals interactions and chemical or Madelung terms, and a good description of van der Waals interactions is often lacking. Using van der Waals density functionals we study the structures, phonons and energetics of the archetype layered intercalation compound Li-graphite. Intercalation of Li in graphite leads to stable systems with calculated intercalation energies of $-0.2$ to $-0.3$~eV/Li atom, (referred to bulk graphite and Li metal). The fully loaded stage 1 and stage 2 compounds LiC$_6$ and Li$_{1/2}$C$_6$ are stable, corresponding to two-dimensional $sqrt3timessqrt3$ lattices of Li atoms intercalated between two graphene planes. Stage $N>2$ structures are unstable compared to dilute stage 2 compounds with the same concentration. At elevated temperatures dilute stage 2 compounds easily become disordered, but the structure of Li$_{3/16}$C$_6$ is relatively stable, corresponding to a $sqrt7timessqrt7$ in-plane packing of Li atoms. First-principles calculations, along with a Bethe-Peierls model of finite temperature effects, allow for a microscopic description of the observed voltage profiles.
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Potassium intercalation in graphite is investigated by first-principles theory. The bonding in the potassium-graphite compound is reasonably well accounted for by traditional semilocal density functional theory (DFT) calculations. However, to investi
gate the intercalate formation energy from pure potassium atoms and graphite requires use of a description of the graphite interlayer binding and thus a consistent account of the nonlocal dispersive interactions. This is included seamlessly with ordinary DFT by a van der Waals density functional (vdW-DF) approach [Phys. Rev. Lett. 92, 246401 (2004)]. The use of the vdW-DF is found to stabilize the graphite crystal, with crystal parameters in fair agreement with experiments. For graphite and potassium-intercalated graphite structural parameters such as binding separation, layer binding energy, formation energy, and bulk modulus are reported. Also the adsorption and sub-surface potassium absorption energies are reported. The vdW-DF description, compared with the traditional semilocal approach, is found to weakly soften the elastic response.
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
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.
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.
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