We report on the energetics of intercalation of lithium, sodium and potassium in graphite by density functional theory using recently developed van der Waals density functionals. First stage intercalation compounds are well described by conventional functionals like GGA, but van der Waals functionals is crucial for higher stage intercalation compounds and graphite, where van der Waals interactions are important. The vdW-optPBE functional gave the best agreement with reported structure and

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... tics 10 for graphite and LiC 6 and was further applied for intercalation of Na and K. The enthalpy of formation of LiC 6 and KC 8 were found to be -16.4 and -27.5 kJ/mol respectively. NaC 6 and NaC 8 were unstable with positive enthalpies of formation (+20.8 and +19.9 kJ/mol). The energetics of stacking of graphene and intercalant layers was investigated from first to fifth stage intercalation compounds. Higher stage compounds of Li and K were stable, but with smaller enthalpy of formation with increasing stage order. 15 The higher stage Na compounds possessed positive enthalpy of formation, but less in magnitude than the energy difference of 0.6 kJ/mol between graphite with AB and AA stacking. The abnormal behaviour of the lower stage Na intercalation compounds were rationalized by the lower energy involved in the formation of the chemical bond between carbon Na relative to the corresponding bond with Li or K. The chemical bond between alkali metal and carbon is characterized by charge transfer from the alkali-metal 20 to carbon resulting in ionized alkali-metals. The intercalation induces only a subtle increase in the inplane C-C bond lengths, with longer C-C bonds in the vicinity of the alkali metals but without breaking the hexagonal symmetry. 65 to energetics LDA also severely overestimates the Li-C binding energy [34] . The lack of models for vdW interactions is a fundamental limitation of traditional DFT, and much effort has been devoted to solve this problem. Empirical methods based on 75