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two - dimensional crystals have been given a large amount of attention since the isolation of one - atom - thick materials by novosolov _
et al_.  in 2004.@xcite graphene , a single layer of graphite , has attracted by far the most attention because of the high crystal quality of the graphene samples and its fascinating electronic properties.@xcite these properties make it a promising candidate to use as a basic material for future electronics applications.@xcite however , the use of graphene for applications in electronics suffers from a major drawback : graphene is , in its pristine state , a zero - bandgap semiconductor and this gapless state appears to be rather robust .
several ways have been explored to induce a finite band gap in graphene .
it was found experimentally that a band gap can be opened by confining the electrons in nanoribbons @xcite or by applying a potential difference over a graphene bilayer.@xcite    the chemical modification of graphene is another promising way to create a band gap .
@xcite when radicals such as oxygen , hydrogen , or fluorine atoms are adsorbed on the graphene surface they form covalent bonds with the carbon atoms .
these carbon atoms change their hybridization from @xmath0 to @xmath1 , which leads to the opening of a band gap ( similar as in diamond ) .
the adsorbed radicals can attach to the graphene layer in a random way , as is the case in graphene oxide ( go),@xcite or they can form ordered patterns . in the last case , new graphene - based 2d crystals are formed with properties that can vary greatly from their parent material .
this has been found to be the case for hydrogen and fluorine adsorbates .
the new 2d crystals that are expected to form in those cases@xcite have been named graphane @xcite and graphene fluoride ( or fluorographene)@xcite , respectively .    following this route ,
multi - layer graphene fluoride was recently synthesized , @xcite and its structural and electronic properties were studied .
a strongly insulating behavior was found with a room temperature resistance larger than 10g@xmath2 , which is consistent with the existence of a large band gap in this new material.@xcite only a partial fluorine coverage of the graphene multi - layer samples was achieved in these experiments .
the f / c ratio was estimated to be 0.7 in ref . and 0.24 in ref . , according to weight gain measurements .
an important step forward in creating fully covered two - dimensional graphene fluoride samples was recently achieved in ref . .
the obtained single - layer graphene fluoride exhibits a strong insulating behavior with a room temperature resistance larger than 1t@xmath2 , a strong temperature stability up to 400 @xmath3 , and almost a complete disappearance of the graphene raman peaks associated with regions that are not fully fluorinated.@xcite the graphene raman peaks do not disappear completely , however , which could be an indication of the presence of defects in the sample , such as a small portion of carbon atoms not bonded to fluorine atoms .
it was also found experimentally that fluorographene has a young s modulus of @xmath4 100 n / m , and the optical measurements suggest a band gap of @xmath4 3ev .    in ref .
it was demonstrated that single - side adsorption is also possible and that it probably results in a crystalline c@xmath5f structure with a large band gap .    on the theoretical side ,
first - principles studies on graphene monofluoride started in 1993 , motivated by available experiments on graphite monofluoride . using density functional theory ( dft ) calculations ,
it was shown in ref . that the chair configuration of graphene fluoride is energetically more favorable than the boat configuration by 0.145 ev per cf unit ( 0.073 ev / atom ) , while a transition barrier of the order of 2.72 ev was found between both structures . due to the small difference in formation energy and the large energy barrier between both configurations
, it was argued that the kinematics of the intercalation could selectively determine the configuration , or that there could also be a mixing of both configurations in the available experiments . by using the local density approximation ( lda ) for the exchange - correlation functional a direct band gap of 3.5 ev
was calculated for the chair configuration in ref . .
however , it is well known that dft generally underestimates the band gap .
recent calculations used the more accurate gw approximation and found a much larger band gap of 7.4 ev for the chair configuration of graphene monofluoride ( ref . ) .
this theoretical value is twice as large as the one obtained experimentally for graphene fluoride in ref .
, which is @xmath4 3ev .
the experimental value for the young s modulus as found in ref .
( @xmath4 100 n / m ) is also half the value obtained recently from first - principles calculations in ref .
( @xmath4 228 n / m ) for the chair configuration of graphene fluoride .
it is worth noting that the experimental @xcite and theoretical @xcite values of the young s modulus of graphene only differ in a small percentage .
possible reasons for the disagreement between the experimental values and the ab initio results for the young s modulus and the band gap of graphene fluorine could be : i ) the presence of a different configuration or a mixture of them in the experimental samples , or ii ) the presence of defects , which could decrease the size of both the young s modulus and the band gap from the expected theoretical values .    in this paper , we investigate various possible crystal configurations for both graphene - based two - dimensional crystals , graphene fluoride and graphane , and we examine their structural , electronic , and mechanical properties . in the case of graphene fluorine , we found a new configuration not considered before that has a lower energy than the boat configuration .
this new configuration , which we call the zigzag configuration , is energetically less favorable than the chair configuration by only 0.073 ev per cf unit ( 0.036 ev / atom ) .
we calculated the young s modulus and the band gap ( both with gga and in the gw approximation ) for the different configurations .
the disagreements between experimental and ab initio calculations for graphene fluoride persist independently of the considered configuration .
these results imply that the available experimental samples probably contain a large number of defects , such as a portion of carbon atoms not bonded to fluorine atoms , that decrease the value of both the young s modulus and the band gap from the expected theoretical values .
the paper is organized as follows : first we describe the computational details of our first - principles calculations
. then we investigate the stability and structural properties of the different configurations of both graphene derivatives . to conclude ,
the elastic and electronic properties of the different structures are discussed .
we examine different graphane and graphene fluoride configurations with the use of _ ab initio _ calculations performed within the density functional theory ( dft ) formalism .
the generalized gradient approximation ( gga ) of perdew , burke , and ernzerhof ( pbe)@xcite is used for the exchange - correlation functional and a plane wave basis set with a cutoff energy of 40 hartree is applied .
the sampling of the brillouin zone is done with the equivalent of a @xmath6 monkhorst - pack k - point grid@xcite for a graphene unit cell and we use pseudopotentials of the troullier - martins type.@xcite since periodic boundary conditions are applied in all 3 dimensions a vacuum layer of 20 bohr is included to minimize the ( artificial ) interaction between adjacent layers .
all the calculations were performed with the abinit code.@xcite    the reported quasiparticle corrections for the band gap are obtained using the yambo code.@xcite here the first - order quasiparticle corrections are obtained using hedin s gw approximation  @xcite for the electron self - energy . because we are treating two - dimensional systems ,
the spurious coulomb interaction between a layer and its images should be avoided , as this causes serious convergence problems .
therefore we use a truncation of this interaction in a box layout , following the method of rozzi _
et al._.@xcite the remaining singularity is treated using a random integration method in the region near the gamma point.@xcite nevertheless , a larger separation between the layers is necessary , so a value of @xmath7 bohr is used for these calculations .
we studied four different stoichiometric configurations for both graphane and graphene fluoride in which every carbon atom is covalently bonded to an adsorbate in an equivalent way , i.e.  every carbon / adsorbate pair has the same environment .
these configurations are schematically depicted in fig .
[ fig_conform ] and we will refer to them as the ` chair ' , ` boat ' , ` zigzag ' , and ` armchair ' configuration . the chair and boat configurations have been well investigated before , but the zigzag and armchair configurations are rarely examined for graphane@xcite and we are not aware of any studies for fluorographene .
the names of these last two configurations have been chosen for obvious reasons ( see fig . [
fig_conform](c ) and [ fig_conform](d ) ) .
after relaxation , the different configurations appear greatly distorted when compared with the schematic pictures of fig .
[ fig_conform ] , so these figures should only be regarded as topologically correct ( see fig .
[ fig_superlatt ] ) .      to examine the stability of the different configurations , we make use of the formation energy of the structures and the binding energy between the graphene layer and the adsorbates .
we define the formation energy , e@xmath8 , as the energy per atom of the hydrogenated or fluorinated graphene with respect to intrinsic graphene and the corresponding diatomic molecules h@xmath9 and f@xmath9 .
the binding energy , e@xmath10 , is defined with respect to graphene and the atomic energies of the adsorbates and is calculated per ch or cf pair .
the results are summarized in table [ tab_energies ] .
.the formation energy e@xmath11 , the binding energy e@xmath12 , and the relative binding energy @xmath13e@xmath11 ( with respect to the most stable configuration ) for different hydrogenated and fluorinated graphene configurations . the energies are given in ev.[tab_energies ] [ cols="^,^,^,^,^",options="header " , ]     the electronic band structure and the corresponding density of states of graphane and fluorographene in the chair configuration are shown in fig .
[ fig_bs ] .
both band structures look similar but there are also some clear differences . in the case of fluorographene the parabolic band at the @xmath14-point , corresponding to quasi - free electron states , is at much higher energies which indicates a larger ionization energy for fluorinated graphene .
this ionization energy ( ie ) is defined as the difference between the vacuum level and the valence band maximum and an explicit calculation of this energy indicates a difference of about 3 ev between graphane and fluorographene ( see table [ tab_bg ] ) .
this is a consequence of the negative charges on the fluorine atoms in fluorographene .
we can also compare the ie values with the work function of graphene which is the same as its ionization potential ( because graphene has no band gap ) and has a value of 4.22 ev from gga ( this is somewhat smaller that the experimental value@xcite of 4.57@xmath150.05 ev ) .
it can be seen from table [ tab_bg ] that the ionization energies of both graphene derivatives are higher than that of graphene ( @xmath4 0.5 ev and 3.5 ev , respectively ) , although the ionization energy of graphane is rather similar to graphene .
we investigated different configurations of the graphene derivatives fluorographene and graphane .
the chair configuration is the most stable one in both cases , but the zigzag configuration has only a slightly higher formation energy and is more stable than the much more studied boat configuration .
fluorographene is found to be much more stable than graphane which is mainly due to a much higher desorption energy for f@xmath9 as compared to h@xmath9 .
we also demonstrated that there are structural and electronic differences that are caused by the charged state of the f atoms in fluorographene .
when our results are compared to available experimental data for fluorographene some discrepancies can be noticed : for all the configurations studied we find much larger band gaps in the electronic band structure and the calculated young s modules is much larger .
this might indicate that the experimental samples still contain appreciable amounts of defects .
the nature of these defects requires further investigation , but one can speculate that these defects consist of missing adsorbates , partial h / f coverage , or mixed configurations .
this work was supported by the flemish science foundation ( fwo - vl ) , the noi - bof of the university of antwerp , the belgian science policy ( iap ) and the collaborative project fwo - mincyt ( fw/08/01 ) .
a.d.h . also acknowledges support from anpcyt ( grant no .
pict 2008 - 2236 ) and a fwo - vl senior postdoc fellowship .
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different stoichiometric configurations of graphane and graphene fluoride are investigated within density functional theory . 
 their structural and electronic properties are compared , and we indicate the similarities and differences among the various configurations . 
 large differences between graphane and graphene fluoride are found that are caused by the presence of charges on the fluorine atoms . 
 a new configuration that is more stable than the boat configuration is predicted for graphene fluoride . 
 we also perform gw calculations for the electronic band gap of both graphene derivatives . 
 these band gaps and also the calculated young s moduli are at variance with available experimental data . 
 this might indicate that the experimental samples contain a large number of defects or are only partially covered with h or f.