We study Li on graphene using the Vienna ab initio Simulation Package employing the projector-augmented wave method within the generalized gradient approximation for the exchange-correlation potential. We give detailed structural and electronic results for various configurations involving Li on the (1 1), (2 1) and (2 2) two-dimensional unit cells, and we consider the isolated Li dimer on graphene. We consider more detailed configurations than have been studied before, and our results compare
favourably with previously calculated results where such results exist. For 100% coverage, we have new results for Li on the on-top site, which suggests a staggered configuration for the lowest energy structure for which the Li adatoms are alternately pushed into and pulled out of the graphene layer. For 50% coverage, Li favours the hollow site. We have discovered that a careful relaxation of the system also shows a staggered configuration, a result that has not been investigated before.