Structural, electronic and vibrational properties of methylated single- and bilayer graphene: A density functional theory study

The functionalization of graphene has an immediate effect on its chemical and physical properties. In this paper we systematically study the functionalization of single layer graphene (SLG) with methyl (CH3) radicals, using periodic density functional theory (DFT) at the PBE+D3 level of theory. Special emphasis is on identifying most stable structures and corresponding electronic properties (band gap, electronic density of states, spin polarization) as a function of methyl load. For SLG, methyl coverages ranging from 1/8 to 1/1 (i.e., the fully methylated analog of graphane) are considered. We find that up to a coverage of 1/2, graphene readily accepts CH3, with neighbour CH3 groups prefering trans positions, and band gaps increasing non-monotonically with methyl load. Above coverages of 1/2, the tendency to accept further CH3 weakens, lattice constants widen and the band gap behaves less regular. Besides radicalic methylation, we also study heterolytic methylation by either the methyl anion CH3- (reaction with CH3Li) or the methyl cation CH3+ (reaction with CH3Cl), with counterions also included. Finally, we consider methylation (with CH3 radicals) of bilayer graphene (BLG). To guide in the interpretation of methylation experiments, vibrational signatures of various species are characterized by normal mode analysis (NMA), their vibrational density of states (VDOS), and infrared (IR) spectra, the latter two obtained from ab initio molecular dynamics (AIMD).