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the synthesis of monolayer graphite ( i.e. graphene )  @xcite and the experimental observation of dirac charge carriers in this system  @xcite have awakened an enormous interest in this two - dimensional material .
the unusual properties of carriers in graphene are a consequence of the gapless and approximately linear electron dispersion at the vicinity of the fermi level at two inequivalent points of the brillouin zone . in the low - energy limit
the quasiparticles in these systems are described in terms of massless chiral relativistic fermions governed by the dirac equation .
the good sensor properties of carbon nanotubes are already known for some time,@xcite but recently , the possibility to use graphene as a highly sensitive gas sensor was also reported.@xcite it was shown that the increase in graphene charge carrier concentration induced by adsorbed gas molecules can be used to make highly - sensitive sensors , even with the possibility of detecting individual molecules .
the sensor property is based on changes in the resistivity due to molecules adsorbed on the graphene sheet that act as donors or acceptors .
the sensitivity of nh@xmath1 , co , and h@xmath0o up to 1 part per billion was demonstrated , and even the ultimate sensitivity of an individual molecule was suggested for no@xmath0 .
these excellent sensor properties of graphene are due to two important facts : i ) graphene is a two dimensional crystal with only a surface and no volume , which maximizes the effect of surface dopants , and ii ) graphene is highly conductive and shows metallic conductance even in the limit of zero carrier density .    to fully exploit the possibilities of graphene sensors , it is important to understand the interaction between the graphene surface and the adsorbate molecules .
we perform in this letter first principles calculations for the molecules nh@xmath1 , no@xmath0 , no , co , and h@xmath0o adsorbed on graphene .
we determine their exact orientation on the surface and their preferential binding site by calculating their binding energy .
their charge transfer to the graphene surface is investigated in order to determine the donor or acceptor character of the molecular dopant .
the first principles calculations are performed using density funcional theory ( dft ) which has been succesfully used for the study of molecular adsorbates on single - walled ( carbon ) nanotubes ( swnt).@xcite all our dft calculations were carried out with the abinit code,@xcite within the generalized gradient approximation ( gga ) of perdew , burke , and ernzerhof ( pbe).@xcite the advantage of gga over the local density approximation ( lda ) in this work is that the gga will not lead to a strong bonding of the molecules as in lda .
so if the molecules bind in gga , they will definitely bind in a real system ( and in lda ) too .
the distance between adsorbate and the graphene surface , however , will be somewhat overestimated and consequently the binding energy will be underestimated .
+ we use a plane wave basis set with a cutoff energy of 816 ev and pseudopotentials of the troullier - martins type.@xcite for the adsorption of the molecules nh@xmath1 , co , and h@xmath0o we use non - spin - polarized calculations , while for no@xmath0 and no , we use spin - polarized ones .
the total system consists of a @xmath2 graphene supercell ( 32 c atoms ) with a single molecule adsorbed to it ( fig .
[ fig_h2ogr ] ) and with a distance of 16  between adjacant graphene layers .
the sampling of the brillouin zone is done using a @xmath3 monkhorst - pack@xcite grid . for the calculation of the density of states ( dos ) we use a @xmath4 monkhorst - pack grid and a gaussian smearing of 0.14 ev .
charge transfers are calculated based on the hirshfeld charge analysis.@xcite the atomic charge @xmath5 for each atom is obtained by ( with @xmath6 the calculated density and @xmath7 the electron density computed for the isolated atom @xmath8 and taken from ref .  )
@xmath9 from which the charge transfer ( @xmath10 ) is deduced . from this result we determined whether or not the adsorbate acts as an acceptor or a donor .
it should be noted that the size of the charge transfer is slightly dependent on the method used to calculate it .
+ the distance from the adsorbate to the graphene surface is calculated from the difference in weighted averages of the different atoms of the molecule and the carbon atoms of the graphene sheet , where we used the atomic number z of the atoms as the weight factor .
for each adsorbate three adsorption sites are considered , namely on top of a carbon atom ( t ) , the center of a carbon hexagon ( c ) and the center of a carbon - carbon bond ( b ) ( see fig .
1 ) . for these positions , different orientations of the molecules are examined and the adsorption energy is calculated for all of them . the adsorption energy ( e@xmath11 ) is the energy of the isolated graphene sheet and isolated molecule minus the energy of the fully relaxed graphene sheet with the molecule adsorbed to it .
the strength of the molecular doping is discussed in light of the density of states and the highest occupied and lowest unoccupied molecular orbitals ( homo and lumo ) of the adsorbate .
the position of these orbitals , visible as peaks in the dos , is practically independent of the orientation and adsorption site of the molecule , so we only show the total dos for one geometry per molecule . we can now distinguish two charge transfer mechanisms : i )
a charge transfer can occur due to the relative position in the dos of the homo and lumo of the adsorbate .
if the homo is above the fermi level of pure graphene ( the dirac point ) , there is a charge transfer to graphene .
if the lumo is below the dirac point , charge will transfer to the molecule .
ii ) the charge transfer between adsorbate and graphene is also partially determined by the mixing of the homo and lumo with the graphene orbitals ( hybridisation ) . this mixing scales with the overlap of the interacting orbitals and the inverse of their energy difference .
+ it is more difficult to discuss the adsorption energy in this way because of the large amount of possible interacting orbitals present in graphene .
our investigation starts with the non - magnetic molecules h@xmath0o , nh@xmath1 , and co , followed by the paramagnetic ones , no@xmath0 and no .
we discuss the molecules in the order of increasing complexity of their charge transfer mechanism .
we examine the following orientations of the h@xmath0o molecule with respect to the graphene surface : starting from the o atom the h - o bonds pointing up ( u ) , down ( d ) or parallel to the graphene surface ( n ) .
another orientation ( v ) was suggested in a theoretical study , based on an empirical method , of the adsorption of h@xmath0o on graphite.@xcite this orientation has one o - h bond parallel to the surface and the other one pointing to the surface .
all properties were found to be almost invariant with respect to rotations around the axis perpendicular to the surface and through the oxygen atom , and therefore we will not discuss this orientation .
the results of the calculations are given in table  [ tab - h2o ] .
.h@xmath0o on graphene : the adsorption energy ( @xmath12 ) , the distance of h@xmath0o above the graphene surface ( @xmath13 ) , and the charge transfer from the molecule to graphene ( @xmath10 ) for ten different geometries.[tab - h2o ] [ cols="^,^,^,^,^",options="header " , ]     for the considered adsorbates the sign of the charge transfer agrees with what was found experimentally ( see table [ tab - res ] ) in ref . .
our results are also in good agreement with theoretical studies of the adsorption of molecules on large swnt s in e.g. ref . .
this suggests that some of the knowlegde of adsorption on nanotubes should be transferable to graphene .
motivated by the recent realization of graphene sensors to detect individual gas molecules , we investigate the adsorption of h@xmath0o , nh@xmath1 , co , no@xmath0 , and no on a graphene substrate using first principles calculations . the optimal adsorption position and orientation of these molecules on the graphene surface is determined and the adsorption energies are calculated . 
 molecular doping , i.e. charge transfer between the molecules and the graphene surface , is discussed in light of the density of states and the molecular orbitals of the adsorbates . 
 the efficiency of doping of the different molecules is determined and the influence of their magnetic moment is discussed .