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Modeling layered intercalation compounds from first principles poses aproblem, as many of their properties are determined by a subtle balance betweenvan der Waals interactions and chemical or Madelung terms, and a gooddescription of van der Waals interactions is often lacking. Using van der Waalsdensity functionals we study the structures, phonons and energetics of thearchetype layered intercalation compound Li-graphite. Intercalation of Li ingraphite leads to stable systems with calculated intercalation energies of$-0.2$ to $-0.3$~eV/Li atom, (referred to bulk graphite and Li metal). Thefully loaded stage 1 and stage 2 compounds LiC$_6$ and Li$_{1/2}$C$_6$ arestable, corresponding to two-dimensional $\sqrt3\times\sqrt3$ lattices of Liatoms intercalated between two graphene planes. Stage $N>2$ structures areunstable compared to dilute stage 2 compounds with the same concentration. Atelevated temperatures dilute stage 2 compounds easily become disordered, butthe structure of Li$_{3/16}$C$_6$ is relatively stable, corresponding to a$\sqrt7\times\sqrt7$ in-plane packing of Li atoms. First-principlescalculations, along with a Bethe-Peierls model of finite temperature effects,allow for a microscopic description of the observed voltage profiles.

Li intercalation in graphite: a van der Waals density-functional study