cadmium chalcogenides 
 ( cdx , x = s , se , te ) are ii  vi semiconductors , 
 which are used to devise solar energy harvesting solutions like thin - film 
 photovoltaics , photoelectrochemistry , and photocatalysis . over the past 
 decade ,
the interface of water and the cds nanocrystals is not well understood 
 yet , which could be vital in deciphering the near - surface dynamics 
 of water and its influence on surface catalysis .
any theoretical modeling 
 of this interface should include the key interaction motifs at the 
 surface .
some of these key surface motifs could be sought by exhaustively 
 studying the molecular interaction of water on these surfaces , which 
 forms the main focus of this study .
experiments have observed 
 an unusual ferromagnetic - like ( fm ) ordering 
 in nanostructures of semiconductors and insulators , over a wide range 
 of temperatures . this has been a subject of wide scientific interest 
 ( hfo2 , in2o3 , zno , cds ) . 

such an origin of magnetism in materials , having no magnetic host 
 ions or possible magnetic impurities , is also known as d - magnetism .
showed that the bulk counterparts for hfo2 , 
 in2o3 , and tio2 are diamagnetic , 
 and the fm ordering is characteristic for thin films .
later , madhu 
 et al . reported that the saturated fm 
 ordering increases with the decrease in nanoparticle size , suggesting 
 that surface effects may play a direct role in this phenomenon .
similar 
 speculation that the fm mass could be concentrated at the surface 
 was made by studying the magnetization hysteresis loop per volume . in most of these studies ,
it was speculated 
 that surface vacancies ( cationic or anionic ) , or vacancy clusters , 
 are the cause of this widely observed fm - like behavior .
we did 
 not find any direct experimental reports on water adsorption 
 on cds surfaces .
however , in the late 1960s arizumi et al . had already 
 observed electron paramagnetic response ( epr ) signals from powdered 
 cds single crystals .
they also observed 
 a strong interaction of h2o on magnetic centers of powdered 
 cds single crystals , as they found that on exposing the paramagnetic 
 crystals to air ( water moisture ) for 2 weeks , the epr signal vanished . 

this is found to be qualitatively reconsolidated in our molecular 
 study of h2o adsorption ( instead of water moisture ) , where 
 we observe that a water molecule can indeed neutralize the spin polarization 
 of a surface defect center by chemisorption . to make further comparisons 
 with arizumi et al .
we also adsorbed an o2 molecule at 
 the same magnetic defect center . for a continuity in our exposition
, 
 we first discuss in full h2o adsorption on perfect and 
 vacancy defected surfaces , which is then followed by simulation results 
 of this special case of o2 adsorption and a discussion 
 of its correspondence with experimental observations .
theoretical 
 dft calculations using local and semilocal 
 exchange correlational functionals have discussed 
 the possibility of these magnetic cationic vacancies to be responsible 
 for the experimentally observed fm ordering . on inclusion of more 
 accurate theoretical treatments , like hybrid functionals , occupation - dependent potentials , and 
 other self - interaction schemes , it is 
 seen that the coupling strength of such magnetic vacancies is too 
 weak to explain the experimentally observed fm ordering .
it is because 
 they observed that the holes are more localized at the defect sites 
 than predicted by the local and semilocal functionals . apart from 
 vacancy defects as a possible cause , studies have also proposed that 
 it could be undercoordinated polar surfaces that cause the surface 
 magnetism .
coey and co - workers recently 
 made a radically different proposition , suggesting that the magnetic 
 response of ceo2 nanoparticles could be due to giant orbital 
 paramagnetism emerging from the collective response of electrons in 
 the coherent domains due to its interaction with the zero - point fluctuations 
 of the vacuum electromagnetic field .
the 
 validity of this theoretical model is yet to be confirmed by other 
 experiments .
clearly , the understanding regarding the underlying mechanism 
 of this fm - like behavior had shown many twists and turns and is still 
 awaiting new developments . in this study
we do not focus on 
 the macroscopic origin of magnetism 
 but rather on the water - interface effects near these magnetic vacancies 
 ( which are often proposed to explain the fm - like behavior ) .
however , 
 we find that most of the magnetic cationic vacancies on the studied 
 surfaces are energetically unfavorable in comparison to their nonmagnetic 
 counterparts and may not solely be the cause of the poorly understood 
 magnetic response of the nanostructures .
previous theoretical 
 studies investigating the effect on water 
 adsorption at these magnetic vacancies did not find any case of chemisorption . 

ahuja and co - workers studied the water adsorption at te defected zno 
 ( 1010 ) surface ; however , the prevalence 
 of magnetic defect centers was not confirmed .
they had found that 
 the water molecules move away from the zn vacancies and adsorb in 
 a similar manner to the clean surface .
recently , catellani and co - workers 
 found a stable magnetic vacancy on the cds ( 1010 ) surface ; 
 however , its interaction with water or any other ligand was not the 
 focus of that study .
another adsorption 
 study of h2o and o2 molecules on the clean w - cds 
 ( 1010 ) surface was reported by the same group , which we have used to compare with our clean surface adsorption 
 results . in the current study , we investigate all the stable and metastable 
 vacancies on nonpolar wurtzite cds ( w - cds ) surfaces ( 1010 ) 
 and ( 1120 ) , using spin - polarized density functional theory with a semilocal exchange correlational functional . 

these w - cds surfaces are the most stable and abundantly formed crystal 
 facets , owing to their in - plane net charge neutrality .
then , we systematically 
 study the adsorption of a water molecule on these surfaces , identifying 
 the stable and metastable water adsorption sites .
the adsorption geometries 
 on the clean surfaces were tested by a van der waals ( vdw ) functional , 
 thus giving a benchmark for differences between the two exchange - correlational 
 functionals . finally , we focused on the effect of surface vacancies 
 on the adsorption of a water molecule , highlighting the surface motifs 
 which determine surface stability . from our study
, we find that s - dimers 
 and magnetic cationic defect centers are stabilizing surface motifs 
 which could play a role in water adsorption ; on the other hand , anion 
 vacancies do not significantly affect it .
we do not find any case 
 of spontaneous dissociative adsorption for the case of low coverage 
 studied here .
all the calculations 
 were performed by means of density functional 
 theory ( dft ) employing the projector augmented wave ( paw ) method as 
 implemented in the vasp package .
the equilibrium 
 lattice parameters of the cds unit cell were determined using the 
 total energy minimum for a range of unit cell volumes . for each of 
 these fixed volumes , the atoms and
the 
 obtained lattice parameters ( a = 4.205  , c / a = 1.63 , u = 0.376 ) 
 are in agreement with previous theoretical studies and within 2% of the experimental value .
the main exchange - correlation functional used in our study is the 
 generalized gradient approximation ( gga)-pbe , whereas for benchmarking tests of vdw interaction ( on water adsorption ) 
 we used the vdw - optb88 functional . for 
 ii  vi semiconductors it is known that considering d - states 
 in the valence band is important for a reasonable prediction of valence 
 band properties .
however , due to the 
 localized nature of d - electrons , the standard dft can only erroneously 
 predict their binding energies . to correct for this
, we included the 
 dft+u scheme by fitting 
 the binding energies of the d - bands to the ultraviolet and x - ray photoelectron 
 spectroscopy data . using this fit , we 
 use ueff = 6.0 ev for the d - bands of cd 
 ( in cds ) for the rest of the study .
for the bulk supercells and surfaces 
 the cutoff for the kinetic energy of the plane - wave basis was 400 
 ev , and for the augmentation charges , it was 580 ev .
pack k - mesh with an electronic temperature 
 of 0.05 ev for a gaussian smearing at the fermi level .
vacancy - defected 
 bulk calculations were performed in a 128-atom wurtzite supercell 
 with a -centered k - point mesh of 27 irreducible k - points .
we modeled the nonpolar ( 1010 ) and 
 ( 1120 ) surfaces 
 with 96-atom slabs and a vacuum spacing of 20  . the k - point sampling for the ( 1010 ) and ( 1120 ) defected 
 surfaces used 9 and 10 irreducible k - points , respectively . 

the ( 1010 ) surface was comprised of 4  3 unit cells , 
 with a thickness of 4 bilayers ( two bottom layers were fixed ) .
the 
 ( 1120 ) surface was comprised of 2  4 unit cells with 
 a thickness of 6 atomic layers , out of which the bottom four layers 
 were fixed .
such a fixing of bottom layers is suitable to have a physical 
 bulk - like termination .
however , as the fixed layers are chemically 
 noninert , this leads to undesired midgap states . for preventing these 
 states , we passivated the fixed side of the slabs by pseudohydrogens . 

we used h ( z = 1.5 ) and h ( z = 0.5 ) pseudoatoms to passivate the fixed bottom 
 layer of cd and s atoms , respectively . the cd  h and s  h bond lengths were determined by cdh41.5 and sh40.5 in a tetrahedral 
 geometry .
the relaxation of the surface atoms takes place in such 
 a way that the surface anions relax outward and the cations relax 
 inward , with respect to bulk .
this is known to occur to facilitate 
 the giving away of dangling bond electrons from surface cations to 
 anions .
we report and discuss the results 
 in the following order : ( a ) vacancy 
 defects ( vcd and vs ) in bulk - cds , ( b ) vacancies on nonpolar cds surfaces , ( c ) 
 adsorption of a water molecule on clean surfaces , ( d ) water adsorption 
 at the vacancy defects of the surfaces , and ( e ) oxygen molecule adsorption 
 at a particular cation vacancy defect .
depending 
 on the growth conditions , charged and 
 neutral defects occur in the semiconductor nanostructures . in this 
 study
, we restrict our focus to the neutral vacancy defects within 
 spin - polarized calculations , since such an adsorption study on the 
 charged defects would be numerically prohibitive .
the w - cds cell has 
 a lower point group symmetry than td , where one of the tetragonally coordinated cd  s bonds 
 ( along c - axis ) is longer than the other three equivalent 
 bonds ( by 0.007  for gga - pbe ) . for the calculations in bulk 

the most stable state of the cation vacancy has a local magnetic 
 moment of 2 b , due to the localization of the holes 
 at the neighboring s - sites . for this magnetic ( m ) configuration ,
the 
 s - bond parallel to the c - axis is still longer than 
 the other three equivalent s - bonds ( by 0.004  ) , having a c3v point group symmetry .
moreover , 
 we also identified a metastable configuration for the cation vacancy 
 which is nonmagnetic ( nm ) . in this nm case ,
all the four neighboring 
 s atoms relax toward the defect such that they are equidistantly located 
 around the defect site , into a td point group symmetry .
such locally stable symmetric vacancy 
 centers were also reported for cdte and zn - chalcogenides .
the difference in the local structure of the cation vacancy leads 
 to differences in the electronic structures of the neighboring s atoms , 
 at which the hole states localize .
this correlation could also be 
 seen in the ldos of the neighboring s atoms , as shown in figure s1 
 of the supporting information ( si ) .
the 
 occurrence of two such vcd possibilities 
 can be explained with jahn  teller relaxations , where the defect 
 center with the lower symmetry ( c3v , spin - polarized ) is slightly more stable than the higher symmetry 
 complex ( td , nonspin - polarized ) . 

the magnetization energy of vcd and emag , i.e. , the total energy difference between 
 magnetic and nonmagnetic configurations , is just 85 mev .
figure 1(a ) and ( b ) shows 
 the spin - resolved density of states ( dos ) of the two configurations , 
 indicating that the c3v geometry has a net spin polarization at the fermi - level edge , whereas 
 the td geometry has no 
 net spin .
figure 1(c ) 
 shows the net spin density localized at the s atoms , which is significantly 
 spread through the crystal .
it also shows the c3v nature of the spin - density symmetry and 
 is in agreement with anisotropic spin density seen for analogous semiconductor 
 wurtzite crystals .
the semimetallic character 
 seen in the dos of figure 1(a ) and ( b ) has also been reported in other studies using local or semilocal exchange correlational functionals .
indeed , 
 later more accurate calculations have shown that the holes are more 
 localized than the predictions by local or semilocal functionals ; however , the local magnetic moments 
 of the vacancy defects are often retained .
therefore , we study the 
 adsorption on these defected surfaces within the semilocal , gga - pbe 
 functional level . ( a ) and ( b ) spin - resolved density of states for the vcd in bulk cds and for the two cases of c3v and td configurations , respectively ( m = magnetic , 
 nm = 
 nonmagnetic ) . in ( c ) the net spin density is shown for the c3v case , with an isosurface 
 of 1  10e /  .
the cd atoms are plotted in magenta and s atoms in yellow . the sulfur vacancy in bulk cds 
 is found to be nonmagnetic , where 
 the neighboring cd atoms relax toward the defect site .
the cd - bond 
 parallel to the c - axis is 0.04  longer than 
 the other three equivalent bonds , acquiring a c3v symmetry .
after studying these vacancies 
 in bulk , it is important to know 
 whether they are relatively stable on the surfaces .
the low magnetization 
 energy emag for the cation vacancy in 
 bulk - cds makes it interesting to study these defects on the nonpolar 
 surfaces .
further , as it is believed that the experimentally observed 
 magnetism is a surface effect , we test whether magnetism at these 
 defect sites also persists at the surfaces .
vacancies 
 were created on these surfaces by 
 removing one cation / anion atom .
like in bulk - cds , we find a variety 
 of metastable magnetic and nonmagnetic vacancies on these surfaces . 
 in our study , we test all possibilities by starting with different 
 magnetic configurations as an initial condition for our calculations . 
 apart from the magnetic and nonmagnetic defect possibilities , there 
 are two types of cd and s atoms that can be accessed by an adsorbate 
 ( surface + subsurface ) .
we thus study both such types of vacancies : 
 the surface atoms , i.e. , having coordination three are referred to 
 as vcd1 and vs1 , and the subsurface atoms 
 with coordination of four are referred to as vcd2 and vs2 . for the ( 1010 ) surface 
 the only stable vcd1 configuration 
 is found to exhibit a net local spin , with magnetic moment of 1.62 
 b .
the net spin at this vcd site was also previously reported by giacopetti et al . in our study , this is the only cationic vacancy 
 site where a corresponding nonmagnetic configuration is not found 
 since around this defect site the relaxation of the neighboring s 
 atoms is restricted by surface geometry .
the net spin density of vcd1 is shown in figure 2(a ) . at the subsurface
, the vcd2 converges to two locally stable 
 configurations : a m solution ( 1.96 b , figure 2(a ) ) and a nm solution ( figure 2(b ) ) .
figure 2(a ) and ( b ) show that for m vcd1 and m vcd2 the surface relaxations near the defect sites 
 are insignificant . on the other hand , the nm vcd2 is shown in figure 2(c ) , which is accompanied by the formation 
 of s - dimers .
our results repeatedly show that the surface relaxations 
 of the neighboring anions lead to the formation of s - dimers and stabilize 
 most of the vcd - defected surfaces , resulting 
 into no net spin polarization at the defect site .
such relaxations 
 of the neighboring anions are known to cause rehybridization of the 
 hole states , leading to redistribution of the net spin density .
the vs1 and vs2 on this surface , 
 just like in bulk - cds , are found to be nm . ( a ) , ( b ) , and ( c ) top 
 views of the cation - defected ( 1010 ) 
 surface ( and subsurface ) ; ( d ) , ( e ) , and ( f ) are the same for the ( 1120 ) 
 surface .
the colored isosurfaces are net spin densities with an isosurface 
 of 1  10e /  for the magnetic ( m ) cases . in the nonmagnetic ( nm ) cases
, we can 
 see the formation of s - dimers which stabilize the surface .
the layer 
 below ( in white ) is the atomic layer below the first subsurface . to understand the relative likelihood 
 of formation of the above 
 vacancies we have compared their total energies in figure 3(a ) . here
, our objective is 
 to compare the stability of defects within the same stoichiometry 
 ( i.e. , vcd - type or vs - type ) .
therefore , it should be clear that a comparison of 
 the relative stability of a vcd with a vs is not made since that would require one to 
 calculate chemical potentials of elemental crystals which are not 
 reliable for dft+u calculations . in figure 3(a ) the most stable vcd s and vs s for each of the surfaces are placed 
 lowest .
other vacancies ( with the same stoichiometry ) are placed in 
 the same quadrant , with increasing energy difference from the most 
 stable one .
the m defect configurations are marked in green and the 
 nm in black . in figure 3(a ) , we observe that the magnetic vcd2 is 0.59 ev less stable than its nm counterpart vcd2 . moreover ,
this subsurface cd - vacancy ( vcd2 ) is even more stable than the 
 surface cd - vacancy ( vcd1 ) by 
 85 mev , thus highlighting the stabilizing role of s - dimers formed 
 on nonmagnetic vcd2 .
it should 
 be noted that according to figure 3(a ) vcd1 is 
 the only magnetic defect site which is relatively stable on these 
 surfaces .
the vs1 on ( 1010 ) 
 is easier to be formed by 0.6 ev than the subsurface vs2 , which is in accordance with their coordination 
 number . since vs does not occur in a variety 
 of magnetic states and do not interact strongly with water , their 
 surface geometries are discussed in their respective section of water 
 adsorption .
( a ) and ( b ) summarize the relative stability for the vacancies 
 with the same stoichiometry on the ( 1010 ) and ( 1120 ) 
 surfaces .
the most stable cd - type and s - type defects are placed lowest 
 ( set to zero on the vertical axis ) . magnetic vacancies are displayed 
 in green and nonmagnetic vacancies in black . as the ( 1120 ) surface 
 is more open for relaxations , it favors nm ground states for cation 
 vacancies .
the stable nm configurations are shown in figure 2(e ) and ( f ) for vcd1 and vcd2 .
a magnetic vcd1 was 
 also observed which is shown in figure 2(d ) , with its net spin - density ( 2 b ) .
as shown in figure 2(e ) and ( f ) , in the case of nm vcd1 the dimer is formed with the surface s atoms , while for nm vcd2 it forms with the next subsurface 
 atomic layer .
these dimer - s states have ds  s = 2.12  , which is shorter in comparison 
 to dcd 
a relative thermodynamical stability 
 of these defects is shown in figure 3(b ) , where the m vcd1 is 0.57 ev less stable than nm vcd1 .
figure 3(b ) shows that the likelihood of formation 
 for vs s are again in accordance 
 with their coordination number , where the vs1 is 0.79 ev more stable than vs2 . in summary
, we observed that magnetic 
 vacancies do not form stable ground states on these nonpolar surfaces , 
 except for vcd1 on the ( 1010 ) 
 surface , which is relatively stable .
this is because the neighboring 
 anion relaxations are easier to occur for the nonpolar surfaces , leading 
 to rehybridization of the orbitals localizing the defect states , and 
 cause the vanishing of the local spin polarization . in the following 
 section , we present results of water adsorption on all the vacancy 
 defects at these surfaces to understand all the possible interactions 
 with water .
first , we focus on the adsorption at the clean surface , 
 followed by adsorption at the vacancy - defected surfaces .
we began 
 by investigating possible adsorption sites of a single water molecule 
 on the clean ( 1010 ) and ( 1120 ) surfaces . since these 
 surfaces are nonpolar they have more than one adsorption motif .
we 
 report below the most stable and metastable adsorption configurations 
 on the two surfaces .
after spanning 
 several initial 
 geometries of h2o adsorption on this surface , four configurations 
 were found to be ( meta-)stable . among these , the most stable adsorption 
 configuration is at the hollow site as shown in figure 4(a ) , with eads = 0.62 ev . when the input water geometry 
 was altered by orienting the h  o  h planes parallel or 
 perpendicular to the surface , the adsorbed molecule relaxed to the 
 same geometry , within a difference of 5 mev in eads .
at this site both possible bonding interactions ( dcd  o  2.4  , ds  h  2.3  ) took place .
the inset 
 shows the ldos for the h2o molecule , where the molecular 
 orbitals of water have remained intact and the 1b1 o - states 
 have become dispersed , indicating a physical adsorption at this surface . 

this adsorbed configuration was also seen in an earlier study ; however , their value of eads = 0.33 ev is significantly lower than in our calculations
. 
 this could be the result of small supercell sizes ( 2  1 ) used 
 for their study .
( a ) charge difference density plot of the most stable 
 h2o adsorption configuration on the clean ( 1010 ) 
 surface and 
 the ( b ) same for the ( 1120 ) surface . an isosurface of charge 
 density of 4.7  10e / 
is used where the blue color indicates charge depletion and 
 green indicates charge accumulation .
the inset shows the ldos for 
 the h2o molecule , which indicates the case of physical 
 adsorption .
the other three metastable 
 adsorption configurations are shown 
 in figure 5(a ) , ( b ) , 
 and ( c ) .
these locally converged configurations were obtained through a rotation 
 of the h  o  h plane of the molecule , about the neighboring 
 s atom . by doing this , the cd  o bonding interaction increases 
 only slightly ( as shown by the charge difference density plots ) , leading 
 to a difference in eads of 50 mev .
this 
 indicates that the potential energy surface for the ( 1010 ) 
 is very flat around these geometries .
the strength of the s  h 
 interactions in physisorption could be estimated to be 0.1 
 ev since the configuration ( a ) is bonded only through these interactions 
 ( 2s  h bonds ) .
( a ) , ( b ) , ( c ) are the charge density difference 
 plots for metastable 
 geometries of adsorption of the h2o molecule on ( 1010 ) 
 surface , and ( d ) and ( e ) are the same for the ( 1120 ) surface . 

the insets in ( a ) , 
 ( d ) , and ( e ) show the change in geometry upon relaxing with the vdw - optb88 
 functional ; ( b ) and ( c ) do not show any changes in their geometry .
unlike the ( 1010 ) surface , 
 the ( 1120 ) is ridged and far from being flat .
the most stable 
 adsorption configuration on this surface is also at the hollow position as shown in figure 4(b ) , with an eads = 0.53 ev .
the 
 inset shows the ldos for the adsorbed water molecule , indicating intact 
 molecular orbitals of water and dispersed 1b1 levels of 
 the o atom .
other metastable configurations at this surface are shown 
 with their charge difference density plots in figure 5(d ) with eads = 0.40 ev and ( e ) with eads = 0.09 ev . 

owing to the ridged surface , the difference in their eads is also significant . since the h2o 
 molecule and the nonpolar surfaces are likely to have dipole interactions , 
 it is important to estimate the strength of vdw interactions . for 
 this purpose , in addition to the gga - pbe functional , we also used 
 the vdw - optb88 functional for all the adsorption 
 geometries on the clean surface . to investigate the effect of vdw 
 interaction on eads and relaxed geometries
, 
 we performed the vdw calculations on the same input geometries that 
 were used for pbe calculations , keeping the dimensions of the cell 
 constant ( while allowing the relaxation of atoms that were also free 
 to relax in the pbe calculations ) .
table 1 shows the eads for the vdw and pbe functionals for the geometries shown in figure 4 and figure 5 .
we found that there is no 
 significant change in geometry for the most stable configurations 
 of both the surfaces , i.e. , configurations figure 4(a ) and ( b ) . when vdw interactions are taken 
 into account ,
the eads increases for both 
 these cases by 0.17 ev . converged to the same geometry . on including dispersion interaction 

the configuration of figure 5(a ) is not the least 
 stable anymore , and it converges to the configuration of figure 5(c ) ( as indicated 
 in the inset ) . as the other two metastable cases of the ( 1010 ) 
 surface ( figure 5(b ) 
 and ( c ) ) do not show any significant change in the adsorption geometry
, 
 we can infer that the vdw effect on the ( 1010 ) surface increases 
 the eads by 0.15 ev . for the ridged 
 ( 1120 ) surface ,
inclusion of dispersion interaction can lead 
 to relaxation of the h2o molecule toward the hollow site 
 of the surface .
in other words , for the configurations on this surface 
 which were metastable with the pbe functional , the inclusion of vdw 
 interaction can lead to adsorption which is nearly as strong as the 
 most stable configuration of the ( 1120 ) surface , i.e. , figure 4(b ) .
this is also 
 what we observe in our findings , where the final geometry upon vdw 
 relaxation is shown in the insets of figure 5(d ) and ( e ) .
the water molecule in figure 5(d ) is altered in 
 its geometry by a rotation of the h  o  h plane over the 
 surface ridge to fall into the hollow site , leading 
 to an enhanced bonding with the surface which explains a larger increase 
 in the eads of 0.28 ev .
the least stable 
 configuration of figure 5(e ) was also no longer locally stable and relaxed to its inset figure , 
 which is similar to the vdw - converged case of the figure 5(d ) configuration .
this 
 benchmarking gives an estimate of the possible effect on geometries 
 and eads due to vdw remarkably interaction , 
 indicating that for the ridged ( 1120 ) surface the metastable 
 configurations converge to the most stable configurations . despite 
 the substantial changes seen in the adsorption on the pristine ( 1120 ) 
 surface
, it should be noted that we have taken into account the vdw 
 interaction for the clean surface adsorption only .
this is because 
 of the fact that most of the currently used vdw functionals consider 
 only the total density ( spin + spin ) of the system 
 and , in this way , are unsuitable for the treatment of spin - polarized 
 systems .
all the results on the defected surfaces 
 discussed below were obtained for the pbe exchange correlational functional .
one of the main objectives of this study is to investigate the 
 effect of vacancies on the surface adsorption of h2o , which 
 are discussed below for both the m and nm vacancies .
in addition to 
 this , we have also studied a case of o2 adsorption at one 
 particularly stable magnetic vacancy site to compare with the observations 
 of arizumi et al . the results and comparison of this set of calculations 
 with experiments
are reported in the last section of results and discussion , while we start with a discussion of 
 the water molecule adsorption results .
the three ( meta-)stable 
 magnetic cation vacancies were found for vcd1 and vcd2 on 
 the ( 1010 ) surface and for vcd1 on the ( 1120 ) surface ( figure 2(a ) , ( b ) , ( d ) ) .
we then initialized the adsorption 
 calculation with the water molecule exactly above these defect sites . at 
 this site we found two cases of h2o adsorption .
the 
 most interesting case was found for an initial guess of a nonmagnetic 
 solution , where the water molecule is chemisorped as shown in figure 6 . here , after relaxation 
 the local magnetic moment of the surface eventually vanished , with 
 significantly higher eads at 1.48 ev .
figure 6 shows that the h2o molecule became a part of the surface , as a new o  s 
 bond was formed with bond length do  s = 1.76  , accompanied by an increase in the water do 
the sulfur monoxide bond in 
 the same settings has a bond length of do 
s = 1.50  , comparable to what we observe for the oh2o  scds bond .
the adsorbed h  o  h 
 is 103 , while the surface s  cd  s is 114.9. 
 the top right inset of figure 6 shows this good match , where h2o fits well with 
 the symmetry of the surface .
the top left inset of figure 6 shows the ldos of h and o 
 from the h2o molecule and of the surface - s bonded to the 
 molecule . here ,
the 1b2 and 3a1 water molecular 
 orbitals undergo splitting , thereby forming new o  s bonds with 
 these states .
new 4a1-like o states are seen at the valence 
 band edge and the conduction band edge , where they bond with the surface - s , 
 clearly establishing new bonding patterns . the above configuration 
 represents the interaction of water with 
 the magnetic cation vacancy site leading to chemisorption ( eads = 1.48 ev ) , where the water molecule becomes 
 a part of the surface .
chemisorption of h2o at the ( 1010 ) vcd1 site leads to neutralizing of 
 the surface magnetic moment .
the inset on the left shows the local 
 dos of the adsorbed h2o and the surface - s site to which 
 the molecule is bonded , which shows the splitting of h2o molecular orbitals ( 1b2 and 3a1 ) and forming 
 of new o  s bonds instead .
the inset at the right shows a top 
 view of the charge density difference plot ( isosurface = 10e /  ) , where it is seen that the 
 symmetry of the surface assists the h2o to bond .
it is interesting that the local 
 spin polarization at the surface 
 can be neutralized by a chemisorption process of a diamagnetic ligand 
 ( like water , in this case ) .
this finding is in qualitative agreement 
 with experimental reports of arizumi et al . , where it was observed that long exposure to moisture in the air 
 can diminish the epr signal from the paramagnetic centers of the cds 
 single crystals .
, we 
 performed additional simulations where an oxygen molecule was adsorbed 
 over this relatively stable magnetic defect center ( vcd1 ) .
an account of our results of o2 adsorption at this stable magnetic defect center are discussed in 
 the last section of the results and discussion .
our results are consistent with the epr reports by arizumi et al . , 
 where we observe that the adsorption strength of the paramagnetic 
 oxygen molecule is lower ( eadso2 = 0.47 ev , figure 9 in the last section ) than 
 that of the diamagnetic water molecule at the magnetic centers .
however , 
 we can not detailedly compare our specific case of water chemisorption 
 to the experimental results since in the latter the interaction with 
 water moisture ( and not the gaseous phase ) is considered . because 
 of this difference , while we find a clear case of chemisorption of 
 a water molecule , in experiments the epr signal gradually appeared 
 on heating at 100 c , indicating lower adsorption energy of water 
 moisture .
this is reasonable since the liquid water phase would certainly 
 have lower bonding strengths with the surface than the isolated chemisorped 
 molecule case which we have studied .
another metastable adsorption 
 configuration at this site was found , 
 whereby the net local spin at the defect site persists and allows 
 a very weak adsorption of the water molecule ( eads = 0.08 ev ) .
apparently , for this metastable solution the 
 interaction between the defect spin density and an overlying water 
 molecule is repulsive since its eads is 
 much smaller than the least stable adsorption configuration of the 
 clean surfaces . to verify this , we rotated the orientation of the 
 h  o  h plane away from the spin densities , where we indeed 
 observed an increase in eads to 0.19 ev . 

such a low eads of the metastable solution , 
 in comparison to the chemisorped geometry , ensures that the former 
 would not be occurring in practice .
the adsorption process 
 at this magnetic site converges to a stable 
 state ( eads = 0.30 ( 1.04 ) ev ) where the 
 neighboring s atoms form dimer - s states with the subsurface layers , 
 as shown in figure 7(a ) .
the calculation of eads = 0.30 ev 
 accounts only for the interaction strength where the eads is comparable with the clean surface .
the value in 
 the parentheses also includes the surface stabilization energy upon 
 relaxation , at 1.04 ev .
the difference in these two values is the 
 surface stabilizing contribution of the stable nm surface in comparison 
 to the initial metastable m configuration . in figure 7(a ) h2o is seen to adsorb with 
 the s - dimer states at the surface .
it is to be noted that in the presence 
 of water it does not converge to the nm vcd2 , as observed earlier in figure 2(c ) , but to a new way of forming s - dimers 
 with the subsurface layer , again neutralizing the locally polarized 
 spin .
this shows that the physical inclusion of water for adsorption 
 induces relaxations at the surface , which drive the metastable m vcd2 to a new nm vcd2 .
( a ) and ( b ) show the adsorption geometries for 
 a water molecule 
 on m and nm in the case of vcd2 on ( 1010 ) .
( c ) and ( d ) show the same for nm cases of vcd1 and vcd2 of the ( 1120 ) surface .
upon adsorption of a water molecule at this site , the only magnetic 
 metastable site at the ( 1120 ) surface ( figure 2(d ) ) relaxed to the nm case of vcd1 on ( 1120 ) , analogous to figure 2(e ) . this will be 
 discussed with the cases of nm defect adsorption in the following 
 section .
another metastable water adsorption solution at this site 
 is observed where the local spin moment persists , leading to another 
 case of very weak adsorption ( eads = 0.12 
 ev ) .
we also adsorbed a water 
 molecule at nm vacancy sites on the two surfaces . for the vcd , these sites were figure 2(c ) , ( e ) , and ( f ) .
their respective adsorption 
 geometries are shown in figure 7(b ) , ( c ) , and ( d ) .
for the ease of comparison between the 
 two figures , we have also shown the m case of vcd2 of the ( 1010 ) surface in figure 7(a ) , which was already discussed 
 in the previous section . in the open cage - like site of figure 2(b ) , the water molecule is trapped as shown in figure 7(b ) , where it is seen to adsorb slightly below the 
 surface atomic layer . the high adsorption strength of this configuration 
 is due to the interaction of h2o with three surface motifs  two 
 s - dimer sites and the subsurface s atom . figure 7(c ) is the converged adsorption geometry 
 for both the m case of figure 2(d ) and the nm case of figure 2(e ) , with an eads = 0.20 
 ( 0.74 ) ev . again , 0.20 ev accounts for the actual adsorption strength , 
 while the value in the parentheses accounts to stabilizing energy 
 of the nm surface .
figure 7(d ) , the adsorption case of figure 2(f ) , shows an adsorption 
 strength of 0.43 ev , with h2o adsorping at the dimer - s 
 site .
the adsorbed 
 geometries at the vs of the ( 1010 ) 
 and ( 1120 ) surfaces are shown in figure 8(a , b ) and ( c , d ) , respectively .
for vs1 on both the surfaces , 
 in figure 8(a ) and 
 ( c ) , the h2o moved away from the sulfur vacancy and converged 
 close to the nearest cd atom or s atom for physical adsorption .
the vs2 in figure 8(b ) and ( d ) forms an open - ring structure 
 where the h2o adsorps .
overall , the eads at the vs sites are similar 
 to those at the clean surfaces , indicating that the s - vacancy has 
 almost no effect on the adsorption of water .
( a ) , ( b ) h2o adsorption geometries on vs1 and vs2 defects of the ( 1010 ) 
 surface , and ( c ) and ( d ) are 
 the same for the ( 1120 ) surface . to make a comparative assessment with the h2o and o2 adsorption , as described in the experimental 
 report of ref ( 9 )
, 
 we also studied the adsorption 
 of an o2 molecule at the stable magnetic defect center 
 ( vcd1 ) of the ( 1010 ) 
 surface .
the same computational settings ( gga - pbe , energy cutoff , k - points ) were used as in the h2o adsorption calculations . 

the isolated o2 molecule ( serving as a reference for calculating eads ) was calculated in a cubic box of 20  
 in length .
the o  o bond length of the o2 molecule 
 was 1.23  , with a magnetic moment of 2 b .
figure 9 briefly summarizes the observed metastable and stable 
 adsorption configurations of the o2 molecule at the vcd1 site on the ( 1010 ) surface . 

the state in column ( a ) is paramagnetic where the oxygen molecule 
 does not interact with the spin density at the defect site .
the electronic 
 levels of atoms o1 and o2 are unaffected by 
 the surface , in the second row of column ( a ) , leading to an eads of 0.01 ev .
also , the net spin densities 
 ( shown in the third row of column ( a ) ) are almost unchanged owing 
 to very little interaction .
, the electronic states of the oxygen molecule ( shown 
 by atoms o1 and o2 ) and the s atom of the surface 
 ( bonded to the molecule ) align with one another , resulting in a considerable 
 interaction with eads = 0.28 ev . in this 
 case , as both the local and overall spin polarizations are zero , the 
 net spin density plot is not shown .
column ( c ) of figure 9 shows the most stable of the 
 oxygen adsorption geometries with eads = 0.47 ev , having the geometry very similar to case ( b ) .
the second 
 row of column ( c ) shows that electronic levels of o1 and 
 surface - s undergo splitting near the valence band and conduction band 
 edges , leading to a stronger adsorption .
the net spin density plot 
 of geometry ( c ) indicates that the spin polarizations at the oxygen 
 molecule and at the defect site are directed opposite to one another . 

the local magnetic moments at the molecule are m = 0.30 b and m = 0.46 b , while the surface 
 s atoms have magnetic moments with values between 0.2 b and 0.0 b , resulting in a net moment of 
 0.29 b in the cell .
columns ( a ) , ( b ) , and ( c ) represent the 
 characteristics of the 
 converged geometries that were obtained for the o2 molecule 
 adsorption at the vcd1 magnetic 
 site on the ( 1010 ) surface .
the two o atoms of the oxygen molecule 
 are referred to as o1 and o2 atoms of the molecule , 
 as shown in geometry ( a ) .
the second row shows 
 the spin - resolved ldos for the configurations , indicating the two 
 o atoms and surface s atom which bonds to the molecule .
the third 
 row shows the net spin density for these configurations . in the nonmagnetic 
 case of ( b ) the local and the spin densities are zero and
these results of the most stable 
 o2 molecule adsorption 
 geometry on the vcd1 defect 
 site ( column ( c ) ) , along with the case of water chemisorption on the 
 same site , are consistent with the experimental findings of ref ( 9 ) .
first , the surface adsorption 
 of a h2o molecule at the magnetic defect center is 1 
 ev stronger than that of o2 adsorption .
the experiments 
 have shown that water moisture can replace the o2 molecule 
 from surface adsorption .
at least for the case of the isolated water 
 molecule considered here , the difference in adsorption energy is significantly 
 large and consistent with this finding .
second , for both the cases 
 ( b ) and ( c ) , the o2 adsorption geometries result in a decrease 
 of the local spin polarization of the magnetic defect center of the 
 surface . for the most stable case of column ( c ) , the overall magnetic 
 moment of the cell reduced to 0.29 b ( which was 
 initially about 1.62 b for the surface vacancy , 
 before adding o2 ) . for both h2o and o2 , adsorption at this vcd1 defect 
 site
third , the experiment observed 
 a broadening in the magnetic resonance lines , which was shown to be 
 a result of the dipolar interaction between the o2 molecule 
 and the paramagnetic center on the surface . this scenario shown in 
 column ( c ) in figure 9 fits well with this finding , as the ldos and net spin density plots 
 show that the local spin polarizations are directed opposite to one 
 another , leading to dipolar interactions . keeping in mind our 
 prediction of thermodynamic stability leading 
 to a predominance of nonmagnetic cationic vacancies on these surfaces
, 
 we would like to clearly state our inferences in relation to the experiments . 

although our results are recurrently consistent with some of the observations 
 of arizumi et al . , we do not claim that the vcd1 is the source of magnetic signal observed experimentally 
 with powdered cds or the cds nanostructures ( observed in the past 
 decade ) .
such a prediction of the magnetic origin can only be confirmed 
 by a theoretical macroscopic prediction of correlated magnetism , which 
 we have not covered here .
however , we show that simple vacancies like vcd1 could prove to be a suitable 
 testbed for studying localized adsorption interactions at d magnetic centers of the semiconductor surfaces .
we have extensively studied water adsorption at the neutral vacancies 
 of nonpolar w - cds surfaces , with all of their possible magnetic configurations . 

first , we have shown that most of the vacancies on these nonpolar 
 surfaces are nonmagnetic .
the net spin polarization is relatively 
 unstable , owing to possible surface relaxations which result in stable 
 anion dimers .
this finding indicates that whenever the surface geometry 
 is not structurally constrained and relaxations are likely to occur , 
 the stable vacancy configurations would be nm .
hence , most of the 
 cationic vacancies ( i.e. , one out of four ) on the nonpolar cds surfaces 
 do not exhibit a thermodynamically stable magnetic moment , and therefore 
 the vacancies from these surfaces may not solely be the cause of the 
 experimentally observed fm behavior . second , we have shown that for 
 one of the relatively stable vacancy sites , where the neighboring 
 atom relaxations are structurally constrained , a relatively stable 
 magnetic cationic vacancy is the only possibility . upon adsorption 
 of a water molecule on such a stable magnetic site , we found a clear 
 case of chemisorption . in this case , the water molecule strongly interacts 
 with the surface , resulting in no net spin polarization .
for comparison 
 with an experimental report , we also adsorbed 
 an o2 molecule at this interesting surface vacancy .
the 
 o2 adsorption resulted in a decrease in the local magnetic 
 moment , although with lower adsorption energy in comparison to h2o .
these relative adsorption strengths , diminishing of the 
 magnetic signal , and the dipolar interaction of o2 adsorption 
 are all consistent with the epr findings .
for other nonmagnetic cationic 
 vacancy cases , the surface motifs like s - dimers or the subsurface - s 
 atoms can be the main interaction centers for the h2o molecule . 
 for the interaction with the s - dimers , the adsorption energies are 
 comparable to or lower than those of the clean surfaces . unlike the 
 cation vacancies
, the anion vacancies do not significantly affect 
 the h2o adsorption in comparison to clean surface adsorption .
 a detailed understanding 
 of the water  
 semiconductor interface 
 is of major importance for elucidating the molecular interactions 
 at the photocatalyst s surface . here , we studied the effect 
 of vacancy defects on the adsorption of a water molecule on the ( 1010 ) 
 and ( 1120 ) cds surfaces , using spin - polarized density functional 
 theory . 
 we observed that the local spin polarization did not persist 
 for most of the cationic vacancies on the surfaces , unlike in bulk , 
 owing to surface reconstructions caused by displaced s atoms . 
 this 
 result suggests that cationic vacancies on these surfaces may not 
 be the leading cause of the experimentally observed magnetism in cds 
 nanostructures . 
 the surface vacancies are predominantly nonmagnetic 
 except for one case , where a magnetic cationic vacancy is relatively 
 stable due to constraints posed by the ( 1010 ) surface geometry . 
 at this particular magnetic defect site 
 , we found a very strong interaction 
 with the h2o molecule leading to a case of chemisorption , 
 where the local spin polarization vanishes concurrently . at the same 
 defect site , adsorption of an o2 molecule 
 was also simulated , 
 and the results were found to be consistent with experimental electron 
 paramagnetic resonance findings for powdered cds . 
 the anion vacancies 
 on these surfaces were always found to be nonmagnetic and did not 
 affect the water adsorption at these surfaces . 
Introduction
Computational Methods
Results and Discussion
Conclusion