The graphite intercalation compounds(GIC) of lithium is commercially used in lithium ion battery (LIB), then a lot of the experimental and theoretical works on GIC have been reported from the invention of LIB. In our previous study[1] we have shown that first-principles calculation based on the local density approximation(LDA) of Ceperley-Alder(CA) type give us some physic-chemical properties, because the LDA-CA calculation accidentally give us the stable interlayer distance between the graphite layers. The interaction between the layers is believed to be van der Waals (vdW) interaction and this interaction comes from the dynamic properties. In 2004 Dion et al. proposed the approximated method that include the vdW interaction in the density functional framework and some people have shown that the their method works! In this study we have used the vdW-DF2 functional[2] in the VASP code[3] for vdW DFT calculation and compare the results without vdW contribution. The energetics and structure of graphite and LiC₆ are in good agreement with the results by Wang et al.[4] The have shown that energetics and structures for Li, K, Na GIC are in good agreement with the experimental results. In our study the energy barriers of the diffusion for lithium ion in LIC₆ GIC have been calculated. The energy barrier in the parallel direction of the grapheme plane is 0.3 eV per Li ion without vdW interaction, which is in good agreement with out previous calculation[1]. In the vdW-DF2 calculation the energy barrier is increased up to 0.8 eV, the origin of which may be the attractive character of the vdW interaction between the Li and C. If we expand the C-C interplane distance up to 1 nm which corresponds to the distance between the GIC that contains the solvated intercalants, we have found that the calculated energy barrier in plane direction can be neglected.

The dependence of the interlayer distance and the charged state on the diffusion barrier is now evaluating and will be presented.

References [1] M. Yamamoto and H. Imamura, Tanso, 2004 No.212 81-90. [2] K. Lee et al. Phys. Rev. B, 2010, 82 08101 [3] G. Kresse et al. Phys. Rev. B, 1993, 47, 558-561, J. Comput. Mater. Sci. 1996, 6, 15-50. [4] Z. Wang et al. Rsc. Adv. 2014, 4, 4069-4079.