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since hydrogen is one of the best clean fuels in the future , looking for an ideal storage material has become an important task for experimental and theoretical researchers . among all the candidates , magnesium ( mg ) based materials are widely concerned because they are relatively inexpensive and can hold a high weight percentage of hydrogen @xcite .
so the interaction between hydrogen and mg has been extensively studied @xcite .
the main disadvantage that prevents the vast applications of mg for hydrogen storage lies in that the corresponding hydrogenation and dehydrogenation temperatures are large @xcite .
recently , it is found that the aluminum ( al ) doped mgal thin films have much lower hydrogenation temperatures than pure mg films @xcite .
however , the specific reason for the improvement as well as the influence of al doping on the electronic properties of mg films , remains unclear .
so , in order to advance the searches for ideal hydrogen storage materials and applications of hydrogen fuels , it become quite important to make clear the influence of al doping on the electronic structure of mg and the the interaction between hydrogen and mg .
apart from the potential usages in hydrogen storage , mgal alloys are also important industrial materials used in aerospace applications @xcite .
it is always believed that the al doping makes mg more resistent to being corrupted by air .
so lots of efforts have been applied to upgrade the manufacturing techniques to dope al in mg materials , and now the technology has become quite mature .
studying the interactions between small molecules and al - doped mg surfaces can give us critical information about the mechanisms for al doping to improve the resistance of mg to corruption , and thus are very meaningful and necessary .
based on this background and the requirements of hydrogen storage materials , we here perform first principles calculations to systematically study the influence of al doping on the electronic properties of the mg(0001 ) surface and the adsorption behavior of hydrogen molecules .
previous studies have revealed that the mg(0001 ) surface has both considerable @xmath1 and @xmath2 electronic states distributing around the fermi energy , because of the @xmath3 hybridizations @xcite .
here we further find that after doping of an al atom , the electronic structures around the fermi energy mainly distribute around the doping layer .
for the dissociation of hydrogen molecules on the clean mg(0001 ) surface , it has been found that the most energetically favored site is the surface bridge site @xcite , with the corresponding minimum energy barrier of 0.85 ev @xcite . through our present first - principles calculations , we find that al - doping will not change the most energetically favored dissociation channel .
however , the minimum energy barrier for dissociation of hydrogen is critically dependent on the doping depth of al , and the values are all larger than that on the clean mg(0001 ) surface .
the rest of this paper is organized as follows : in sec .
ii , we describe our fist - principles calculation method and the models used in this paper . in sec .
iii , we present in detail our calculated results , including the comparisons of the electronic structures of the mg(0001 ) surface before and after al doping , and the dissociation of hydrogen molecules on the al - doped mg(0001 ) surface . at
last , the conclusion is given in sec .
our calculations are performed within density functional theory ( dft ) using the vienna _ ab - initio _ simulation package ( vasp ) @xcite .
the pw91 @xcite generalized gradient approximation and the projector - augmented wave potential @xcite are employed to describe the exchange - correlation energy and the electron - ion interaction , respectively .
the cutoff energy for the plane wave expansion is set to 250 ev , which is large enough to make the calculational error of the adsorption energy below 0.01 ev .
the clean and al - doped mg(0001 ) surface are modeled by a slab composing of five atomic layers and a vacuum region of 20  .
the @xmath4 supercell in which each monolayer contains four mg atoms are adopted in the study of the h@xmath0 adsorption .
our test calculations have shown that the @xmath4 supercell is sufficiently large to avoid the interaction between adjacent hydrogen molecules .
integration over the brillouin zone is done using the monkhorst - pack scheme @xcite with @xmath5 grid points .
a fermi broadening @xcite of 0.1 ev is chosen to smear the occupation of the bands around the fermi energy ( e@xmath6 ) by a finite-@xmath7 fermi function and extrapolating to @xmath8 k. during geometry optimizations , the bottom layer of the clean and al - doped mg(0001 ) surface is fixed while other mg and al atoms are free to relax until the forces on them are less than 0.01 ev /  .
the calculation of the potential energy surface for molecular h@xmath0 is interpolated to 209 points with different bond length ( @xmath9 ) and height ( @xmath10 ) of h@xmath11 at each surface site . the calculated lattice constant of bulk mg ( @xmath12 , @xmath13 ) and the bond length of a free h@xmath11 molecule are 3.21  , 5.15    and 0.75  , respectively , in good agreement with the experimental values of 3.21  , 5.20   @xcite and 0.74   @xcite .
as shown in fig . 1 , we have employed 3 different doping depths for al in the mg(0001 ) surface , with the al atom respectively in the first ( mgal1 ) , second ( mgal2 ) and third monolayer ( mgal3 ) .
for the clean mg(0001 ) surface , our calculations reveal that the distances between the three topmost atomic layers are expanded from their bulk values , in accordance with previous theoretical @xcite and experimental reports @xcite .
it is because that due to its special surface charge redistribution , the topmost three layers of the mg(0001 ) surface are negatively charged and hence repel each other .
in fact , the surface expansion is a special phenomena for the mg(0001 ) surface , which is not seen for other surfaces of mg @xcite . and instead of expansions , the surface relaxations of many metals show contractions @xcite . the relaxation calculation for the clean mg(0001 ) surface also confirms the precise of our methods .
however , after the doping of an al atom , the surface relaxation is changed . to describe more clearly the changes , here
we define the surface relaxation as @xmath14 where @xmath15 and @xmath16 are respectively the distance between the @xmath17th and @xmath18th layer of the relaxed surface , and the lattice spacing along the ( 0001 ) direction of bulk mg .
table i summarizes the calculated relaxations for the clean mg(0001 ) , mgal1 , mgal2 , and mgal3 surfaces .
we can easily see from table i that the results critically depend on the doping length of the al atom .
if the al atom is doped at the first ( i.e. the topmost ) layer , then the distance between the first and second layers is contracted by 3.00 % . and
if the al atom is doped at the second layer , then @xmath19 and @xmath20 respectively decreases by 2.60 % and 2.12 % .
one can see that for the layer containing the doped al atom , the lattice spacings with its nearest mg layers are decreased a lot from that of bulk mg .
this result is confirmed by the relaxation results of the mgal3 surface , where @xmath20 and @xmath21 are decreased by 2.25 % and 2.12 % . by analyzing the atomic charges , we find that the neighboring mg atoms always lose electrons to the doped al atom .
so the charging state of the doping layer and its neighboring mg layers are respectively negative and positive , and the interactions between them become attracting forces . thus the surface relaxation changes from expansion of the clean mg(0001 ) surface to the contraction after al doping .
.surface relaxations ( @xmath22 , @xmath23 , and @xmath24 and work function ( @xmath25 ) of the mg(0001 ) , mgal1 , mgal2 , and mgal3 surfaces .
[ cols="^,^,^,^,^,^ " , ]     [ tableii ]    for the dissociation of h@xmath0 molecules on most metal surfaces , it has been revealed that two different interactions exist , which are respectively the orthogonalizations between molecular orbitals of h@xmath0 and electronic states of metal , and the charge transfer from metal atoms to hydrogen atoms @xcite . as shown in fig .
2(b ) , we find that the al - doping did not change the metallic properties of the mg(0001 ) surface .
so such two different interactions still exist for the dissociation of h@xmath0 on the mgal1 surface .    /mgal1
system with the height of h@xmath0 to be 2.00 ( a ) and 0.92    ( b ) .
mg , al , and h atoms are shown in grey , dark grey , and red balls respectively .
all the values are in unit of electrons per @xmath26.,scaledwidth=80.0% ]    figures 6(a ) and ( b ) respectively show the difference electron density for the adsorption system of h@xmath0/mgal1 before ( @xmath27=2.00  ) and after ( @xmath10=0.92  ) the transition state along the bri-@xmath28 channel , namely , @xmath29,\ ] ] where @xmath30 , @xmath31 and @xmath32 are respectively the electron density of the adsorption system , the h@xmath0 molecule and the mgal1 surface . to calculate @xmath33 , the atomic positions in the last two terms in eq .
2 have been kept at those of the first term . through careful wavefunction analysis
, we find that at the beginning of the adsorption process , the molecular orbitals of h@xmath0 orthogonalize with electronic states of the mgal1 surface and are thus broadened .
this orthogonalization is very similar to that has been observed during the interaction of h@xmath0 with the mg(0001 ) @xcite and al(111 ) @xcite surfaces . as shown in fig .
6(a ) , there is an electron - depletion region on top of the al atom , which is formed because electrons around the al atom are repelled by the h@xmath0 bonding electrons due to the orthogonalization . in comparison , on the clean mg(0001 ) surface
, the electrons of mg are repelled from the surface at the beginning of the adsorption of a h@xmath0 molecule .
we can also see from fig .
6(b ) that the h@xmath0 molecule begins to get some electrons from the mg and al atoms , when it gets more closer to the mgal1 surface .    as we have already seen , extra electrons on the mgal1 surface trends to distribute around the al atom .
thus during the initial stage of the adsorption of a h@xmath0 molecule , the molecular orbitals of h@xmath0 orthogonalize only with electronic states around the al atom , while on the clean mg surface , the molecular orbitals orthogonalize with electronic states around the two nearest mg atoms . besides , the ability to lose electrons is stronger for a mg atom than an al atom . therefore , the h@xmath0 molecule is more difficult to get electrons from the mgal1 surface .
and so the dissociation energy barrier is larger on the mgal1 surface .
in summary , the electronic structures of the al - doped mg(0001 ) surfaces and the dissociation behaviors of h@xmath0 molecules on the doped surfaces are systematically studied , using the first - principles calculations .
our calculational results show that after al - doping , the surface electronic structure is largely changed . due to the electrons redistribution , the surface relaxation changes from expansion to contraction around the doping layer . for different doping lengths , the work function of the mg(0001 ) surface
are all enlarged . through careful electronic structure analysis , we further find that the electronic states around the fermi energy mainly distribute around the doping layer for al - doped mg(0001 ) surface . by calculating the potential energy surface of a h@xmath0 molecule on the al - doped mg(0001 ) surfaces , we find that the doping of an al atom does not change the dissociation path with the lowest energy barrier , but enlarges the energy barrier . and
for the first layer doping , the energy barrier is changed by 0.30 ev . from wavefunction and charge - density analysis
, we reveal the two interaction stages during the dissociation of the h@xmath0 molecule , i.e. the first orthogonalization and later charge - transfer stages .
we find that because more surface electrons distribute around the al atom , the orthogonalization mainly happens between the h@xmath0 molecule and the surface al atom .
in addition , since al atom has a weaker ability to lose electrons , the dissociation energy barrier for h@xmath0 is enlarged on the mgal1 surface than on a clean mg(0001 ) surface .
our studies provide a detailed mechanism for explaining the improvement on the resistance to corrosion for the mg(0001 ) surface by doping of al atoms .
by using the density functional theory method , we systematically study the influences of the doping of an al atom on the electronic structures of the mg(0001 ) surface and dissociation behaviors of h@xmath0 molecules . 
 we find that for the al - doped surfaces , the surface relaxation around the doping layer changes from expansion of a clean mg(0001 ) surface to contraction , due to the redistribution of electrons . 
 after doping , the work function is enlarged , and the electronic states around the fermi energy have a major distribution around the doping layer . for the dissociation of h@xmath0 molecules , we find that the energy barrier is enlarged for the doped surfaces . 
 especially , when the al atom is doped at the first layer , the energy barrier is enlarged by 0.30 ev . for different doping lengths , 
 however , the dissociation energy barrier decreases slowly to the value on a clean mg(0001 ) surface when the doping layer is far away from the top surface . 
 our results well describe the electronic changes after al - doping for the mg(0001 ) surface , and reveal some possible mechanisms for improving the resistance to corrosion of the mg(0001 ) surface by doping of al atoms .