Band Gaps and Optical Spectra of Chlorographene, Fluorographene and Graphane from G 0 W 0 , GW 0 and GW Calculations on Top of PBE and HSE06 Orbitals Frantis ̌ ek Karlicky ́ * and Michal Otyepka* Regional Centre of Advanced Technologies and Materials, Department of Physical Chemistry, Faculty of Science, Palacky ́ University, Tr ̌ . 17. listopadu 12, Olomouc 771 46, Czech Republic * S Supporting Information ABSTRACT: The band structures of three graphene derivatives (chlorographene, fluorographene, and graphane) were analyzed at three levels of many-body GW theory (G 0 W 0 , GW 0 , and GW) constructed over GGA (PBE) and screened hybrid HSE06 orbitals. DFT band gap values obtained with the HSE06 functional were notably larger than those from PBE calculations but were significantly lower than band gaps from all GW calculations. On the other hand, all GW-type calculations gave similar band gaps despite some differences in band structures. The band gap (4.9 eV at the highest GW- HSE06 level) was predicted to be smaller than that of fluorographene (8.3 eV) or graphane (6.2 eV). However, chlorographene can be considered a wide-band gap insulator analogous to fluorographene and graphane. Using the Bethe-Salpeter equation, optical absorptions of graphene derivatives were found to be at significantly lower energies due to large binding energies of excitons (1.3, 1.9, and 1.5 eV for chlorographene, fluorographene, and graphane, respectively). Point defects lowered band gaps and absorption energies. Taking into account the low concentration of defects in this type of material, their effect on the discussed electronic properties was rather small. ■ INTRODUCTION Covalently modified graphene derivatives prepared by attach- ment of hydrogen and halogens have attracted considerable interest over the past few years because of their potential applications (e.g., in electronic devices). 1,2 The attachment of atoms to sp 2 carbons changes its hybrid state to sp 3 , which significantly alters the electronic properties and local structure but preserves the 2D hexagonal symmetry. Such structural changes induce opening of the zero band gap of graphene at the K point and lead to loss of the π-conjugated electron cloud present above and below graphene plane. Recently, fully hydrogenated graphene (graphane, CH) 3,4 and fully fluorinated graphene (fluorographene, also known as graphene fluoride, CF) have been successfully prepared. 5-8 In contrast, the fully chlorinated counterpart has not yet been prepared and partially chlorinated graphene derivatives have only very recently been reported. 9,10 Generally, wide band gap materials, such as CF, CH, or BN, may be useful as 2D insulators for creating semiconductor/insulator interfaces suitable for the develop- ment of nanosized field-effect transistors (FETs). 11 Recently proposed graphene-based ultracapacitors 12 also highlight the importance of 2D insulator research. Despite numerous theoretical and experimental studies, much is still unknown about the electronic structure of these types of materials. Therefore, we investigated the electronic structure and band gaps of 2D halogenated graphene compounds. Standard generalized gradient approximation (GGA) to density functional theory (DFT) gives a band gap value for CF only half that calculated using a high-level many- body GW 13 approximation (GWA; Table 1), 14-18 which includes electron-electron (e-e) interactions beyond DFT. The CH band gap predicted by GWA is also much larger than values obtained by using local density approximation (LDA) or GGA of Perdew-Burke-Ernzerhof (PBE). 14,15,17,19-21 More- Received: March 21, 2013 Published: July 10, 2013 Table 1. Summary of Calculated and Experimental Band Gaps, E g (in eV), for Graphane (CH), and Fluorographene (CF) based on a Literature Survey a method CH CF DFT(PBE) 3.5 3.1 DFT(HSE06) 4.5 5.1 GW 0 ,G 0 W 0 5.4-6.1 7.3-7.5 BSE-G 0 W 0 (optical spectra) 3.8 5.4, 3.8 exp. (optical spectra) >3.8, >3.0 b exp. (density of states) >3.8 c exp. (transport measurement) ∼3 d a For details, see ref 22. b Optical band gaps, refs 7 and 27. c Fundamental band gap, ref 27. d For C 2.1 F, ref 28. Article pubs.acs.org/JCTC © 2013 American Chemical Society 4155 dx.doi.org/10.1021/ct400476r | J. Chem. Theory Comput. 2013, 9, 4155-4164