Elham Mazarei, Christopher Penschke, Peter Saalfrank

• Graphene is well-knownfor its unique combination of electricaland mechanical properties. However, its vanishing band gap limitsthe use of graphene in microelectronics. Covalent functionalizationof graphene has been a common approach to address this critical issueand introduce a band gap. In this Article, we systematically analyzethe functionalization of single-layer graphene (SLG) and bilayer graphene(BLG) with methyl (CH3) using periodic density functionaltheory (DFT) at the PBE+D3 level of theory. We also include a comparisonof methylated single-layer and bilayer graphene, as well as a discussionof different methylation options (radicalic, cationic, and anionic).For SLG, methyl coverages ranging from 1/8 to 1/1, (i.e.,the fully methylated analogue of graphane) are considered. We findthat up to a coverage theta of 1/2, graphene readily accepts CH3, with neighbor CH3 groups preferring trans positions. Above theta = 1/2, the tendency to accept further CH3 weakens and the lattice constant increases. The band gapbehaves less regularly,Graphene is well-knownfor its unique combination of electricaland mechanical properties. However, its vanishing band gap limitsthe use of graphene in microelectronics. Covalent functionalizationof graphene has been a common approach to address this critical issueand introduce a band gap. In this Article, we systematically analyzethe functionalization of single-layer graphene (SLG) and bilayer graphene(BLG) with methyl (CH3) using periodic density functionaltheory (DFT) at the PBE+D3 level of theory. We also include a comparisonof methylated single-layer and bilayer graphene, as well as a discussionof different methylation options (radicalic, cationic, and anionic).For SLG, methyl coverages ranging from 1/8 to 1/1, (i.e.,the fully methylated analogue of graphane) are considered. We findthat up to a coverage theta of 1/2, graphene readily accepts CH3, with neighbor CH3 groups preferring trans positions. Above theta = 1/2, the tendency to accept further CH3 weakens and the lattice constant increases. The band gapbehaves less regularly, but overall it increases with increasing methylcoverage. Thus, methylated graphene shows potential for developingband gap-tuned microelectronics devices and may offer further functionalizationoptions. To guide in the interpretation of methylation experiments,vibrational signatures of various species are characterized by normal-modeanalysis (NMA), their vibrational density of states (VDOS), and infrared(IR) spectra, the latter two are obtained from ab initio moleculardynamics (AIMD) in combination with a velocity-velocity autocorrelationfunction (VVAF) approach.…