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since its discovery in 2004 graphene  @xcite draws much attention because of unique features of this two - dimensional system . graphene is composed of a sp@xmath2-bonded carbon atoms forming honeycomb structure . it became famous for its very interesting electronic structure with characteristic , linear energy dispersion near k point of brillouin zone and many other features  @xcite . shortly after , experimental techniques allowed fabrication of other new two - dimensional materials , like bn and mos@xmath3 honeycomb structures  @xcite . the discovery of such stable two - dimensional materials triggered search for similar structures made from different compounds . up to now many of these hypothetical structures constructed from silanene ( 2d si ) and germanene ( 2d ge )  @xcite , iii - v compounds  @xcite , sic  @xcite or zno  @xcite have been studied theoretically . also , calculations show  @xcite , that graphene - like type of structure is not the only one possible for two - dimensional material . this new class of boron sheets , composed of triangular and hexagonal motifs can be stabilized by interplay of three- and two - center bonding scheme  @xcite . another example of triangular sheet could be found in already known material , which is li@xmath4n in its @xmath5 phase . li@xmath6n is a bulk material known to be a fast ion conductor  @xcite . li@xmath6n is also known as a candidate for hydrogen storage material due its high theoretical h@xmath0 capacity  @xcite . bulk li@xmath4n crystallizes in hexagonal structure which is characterized by @xmath7 symmetry group , each nitrogen atom is surrounded by eight lithium atoms . it has layered structure , one layer is li@xmath0n and the other is of li atoms only . previous theoretical studies confirm ionic nature of bonding in this compound  @xcite . since n - containing layer is rather weakly bound with two li - only layers , it would be interesting to study electronic properties of such two - dimensional structure ( 2dli@xmath0n ) - fig [ fig0]a . since this structure would have n atoms with dangling bonds , it would give opportunity to study influence of different atoms addition on them . for example addition of hydrogen atoms in case of graphene resulted in new material which is graphane  @xcite . graphene and other nano - scale materials are recognized as future building blocks of new electronics technologies  @xcite , including spintronics  @xcite . in the case of low ( one- and two- ) dimensional structures problem arises because of famous mermin - wagner theorem  @xcite , which prevents ferro- or antiferromagnetic order to occur in finite temperatures , which is essential for practical application . this started the theoretical and experimental search for magnetism in graphene and other two - dimensional structures . one of the most promising directions is emergence of magnetism in such structures as an effect of presence of local defects  @xcite . according to works of palacios et al . @xcite and , independently , of yazyev  @xcite single - atom defects can induce ferromagnetism in graphene based materials . in both cases , the magnetic order arises as an effect of presence of single - atom defects in combination with a sublattice discriminating mechanism . in the case of @xmath8role of such defect could play non - hydrogenated n atom in hydrogenated structure . it would be then instructive to check influence of hydrogenation level on magnetic moment of the structure . in this paper electronic and magnetic structure of pure and hydrogenated 2dli@xmath0n have been analyzed by means of @xmath9-@xmath10 calculations . to investigate electronic and magnetic properties of two - dimensional li@xmath4n structures a series of @xmath9-@xmath10 calculations have been conducted with use of dft vasp code  @xcite with paw potentials  @xcite . for both spin - unpolarized and spin - polarized cases exchange - correlation potential has been approximated by generalized gradient approximation ( gga ) using pw91 functional  @xcite . kinetic energy cutoff of 500 ev for plane - wave basis set has been used . in all cases for self - consistent structure optimizations , the brillouin zone ( bz ) was sampled by @xmath11 special k points . all structures have been optimized for both , spin - unpolarized and spin - polarized cases unless feynman - hellman forces acting on each atom become smaller than 10@xmath12 ev/@xmath13 . a vacuum spacing of 12   was applied to hinder the interactions between @xmath8monolayers in adjacent cells . kiedy supercell i jak liczone magn . ) bandstructure and density of states ( dos ) calculations have been confirmed by use of wien2k code  @xcite which implements the full - potential linearized augmented plane wave ( flapw ) method @xcite . in this case for exchange and correlation generalized gradient approximation was used in the perdew - burke - ernzerhoff ( pbe ) parameterization @xcite . to study electronic properties of @xmath8 , at first comparison has been made with bulk material . for both cases lattice constants have been determined by total energy calculations and are found to be equal to 3.65   for bulk ( experimental value 3.63  ) and 3.57   for @xmath8 . in agreement with  @xcite bulk li@xmath4n is a semiconductor with non - direct bandgap equal to 1.15 ev between a ( valence band ) and @xmath14 ( conduction band ) points . in contradiction to this , @xmath8  has metallic nature . two - dimensional structure is rather weakly bound - binding energy ( defined as @xmath15 where @xmath16 is the energy of isolated atom(s ) and @xmath17 is the total energy of two - dimensional structure ) is equal to 10.36 ev , while binding energy of bulk structure is equal to 14.25 ev . also , two dimensional sheet would have n atoms with dangling bonds , such structure would be then rather unstable with respect to foreign atoms addition . graphane case suggests that it would be instructive to examine influenece of hydrogenation on electronic structure in such cases as well as addition of lithium atoms . the nature of li - n bond is ionic , as it can be seen from fig . [ fig1 ] showing charge density projected on [ 110 ] plane . since every bond has both ionic and covalent character the level of ionicity can be estimated using difference between electronegativities of bonded atoms  @xcite . in the case of li - n bond this difference equal to 2 suggests , that the bond is about 65@xmath18 ionic and 35@xmath18covalent . this fact together with rather large lattice constant suggest that the structure of two - dimensional @xmath8  can be low - buckled ( lb ) rather than plane ( pl ) , according to puckering mechanism described in  @xcite . to check this the series of calculations has been done , each with different distance in z direction between li atoms and the plane on which n atoms lie ( @xmath19 ) . the structure with minimal energy has been then optimized . calculations show , that the buckled structure with @xmath19 = x lies 0.54 ev lower that the plane , which means that indeed the puckering mechanism stabilizes the structure . both , plane and low - buckled structures can be seen on fig [ fig0 ] . four structures have been then studied in two conformations , plane and low - buckled  two ( pl and lb ) with single h atom attached on top of each n atom ( 2dli@xmath0n+h ) , two with two h atoms attached on both sides of n ( 2dli@xmath0n+2h ) , two with single li atom attached on top of each n atom ( 2dli@xmath0n+li ) , and two with two li atoms attached on both sides of n ( 2dli@xmath0n+2li ) .    [ cols="^,^ " , ] @xmath20-@xmath10 calculations have been conducted for hypothetical two - dimensional material @xmath8  to investigate electronic and magnetic properties . calculations show , that structure is much more stable when dangling bonds of nitrogen atoms are functionalized with hydrogen atoms . this hydrogenation has very strong influence on on bandstructure , changing it from wide - gap semiconductor to metal . magnetic properties are also interesting . in analogy to graphene and other two - dimensional materials it is possible to generate non - zero magnetic moment by introduction of distorsion . in the case of @xmath8 the distorsion would be a two - hydrogen or hydrohen - lithium vacancy around the same nitrogen atom . this generates magnetic moment of 1 @xmath1 . since bulk li@xmath4n material has ususally 1 - 2% li vacancies in li@xmath0n layers  @xcite such two - dimensional hydrogenated sheet would be almost naturally magnetic . these results may give a hint for experimentalists seeking for two - dimensional ( magnetic ) materials , which would be interesitng addition to growing family of two - dimensional materials . 99 k. s. novoselov et al . , science 306 , 666 ( 2004 ) . k. s. novoselov et al . , proc . usa , 102 , 10451 ( 2005 ) . a. h. castro neto et al . , rev . 81 , 109 ( 2009 ) . s. lebegue et al . , phys . rev . b 79 , 115409 ( 2009 ) . s. cahangirov et al . , phys . 102 , 236804 ( 2009 ) . h. sahin et al . b 80 , 155453 ( 2009 ) . e. bakaroglu et al . , phys . rev . b 81 , 075433 ( 2010 ) . m. topsakal et al . , phys rev . b 80 , 235119 ( 2009 ) . j. kunstmann et al . , phys rev . b 74 , 035413 ( 2006 ) . h. tang et al . , phys . 99 , 115501 ( 2007 ) . g. kerker , phys rev . b , 23 , 12 ( 1981 ) . t. t. fister et al . , phys . , 129 , 044702 ( 2008 ) . h. m. jin et al . , app . lett . , 90 , 084101 ( 2007 ) . s. wu et al . , j. phys . chem , 114 , 16706 ( 2010 ) . j. sofo et al . , phys rev . b 75 , 153401 ( 2007 ) . p. avouris et al . , nat . nanotech . 2 , 605 ( 2007 ) . i. zutic et al . , rev . 76 , 323 ( 2004 ) . n. d. mermin , h. wagner phys . 17 , 1133 ( 1966 ) . p. esquinazi , phys . 91 , 227201 ( 2003 ) . j. j. palacios et al . , phys . rev . b 77 , 195428 ( 2008 ) . o. yazyev , phys . rev . lett . 101 , 037203 ( 2008 ) . o. yazyev et al . , phys . b 75 , 125408 ( 2007 ) . e. h. lieb , phys . 62 , 1201 ( 1989 ) ; 62 , 1927(e ) ( 1989 ) . c. ataca et al . , phys . rev . b 82 , 165402 ( 2010 ) . g. kresse , j. hafner , phys . b 47 , 558 ( 1993 ) . g. kresse , j. furthmuller , phys . rev . b 54 , 11169 ( 1996 ) . e. blochl , phys . b 50 , 17953 ( 1994 ) . j. p. perdew , et al . , phys . rev . b 46 , 6671 ( 1992 ) . p. blaha , k. schwarz , g. k. h. madsen , d. kvasnicka , and j.luitz , in wien2k , an augmented plane wave plus local orbitals program for calculating crystal properties , edited by k. schwarz , techn . universitt wien , austria , 2001 . e. wimmer et al . , b 24 , 864 ( 1981 ) . j. p. perdew , k. burke , and m. ernzerhof , phys . 77 , 3865 ( 1996 ) . ref . needed l. pauling `` the nature of covalent bond '' , ?
using first - principles plane - wave calculations study of electronic and magnetic properties of hypothetical two - dimensional structure of li@xmath0n compound have been conducted . 
 calculations show , that electronic properties of this this structure can be inflenced by hydrogenation , which may change the system from wide - gap semiconductor to metal . 
 also , non - zero magnetic moment , equal to 1 @xmath1 can be generated by intruduction of h vacanies in hydrogenated structure .