the 
 diamond material possesses very attractive properties , such 
 as high transparency and high thermal conductivity at room temperature . 
 however , diamond material with it s intrinsic band gap of 5.5 
 ev and low electronic conductivity will limit applications based on 
 electronic devices . when introducing boron into diamond during thin 
 film deposition , the b dopant will increase the electronic conductivity , 
 which gives a material with extraordinary electrochemical properties . boron - doped diamond is a semiconducting material 
 with very promising properties like ( i ) a wider potential window in 
 aqueous solution ( approximately 1.35 to + 2.3 v versus the 
 normal hydrogen electrode ) , ( ii ) low background 
 current , and ( iii ) corrosion stability in aggressive environments . thus , boron - doped diamond surfaces are nowadays used for a variety 
 of electronic applications . during the process of diamond 
 synthesis , the resulting chemical 
 properties will mainly depend on the number of surface radical c sites 
 ( i.e. , dangling bonds ) and the adsorbed ( especially chemisorbed ) species . the sp hybridization of the carbon atoms , leading to strong 
 and directional  bonds , is decisive for the extreme physical 
 properties of the material . moreover , the 
 chemisorbed adsorbates may prevent the diamond surface from being 
 graphitized ( go from sp toward sp hybridization ) . this is partially why a supersaturation of hydrogen is used in the 
 reaction chamber during growth of diamond . in addition , the chemisorbed species will have the ability to influence 
 the chemical and electronic properties of diamond , such 
 as field emission characteristics , surface 
 wettability , and electrochemical properties of the diamond surface . surface termination is the general notation 
 when a species ( e.g. , 
 h , o , f ) is used with the purpose to uphold the cubic structure or 
 to change the surface properties . the phenomena of diamond surface 
 termination have experimentally been observed to significantly influence 
 the broad - band infrared reflectivity and conductivity . hydrogen - terminated diamond surfaces have been 
 found to be hydrophobic and to show electron 
 transfer across the interface . on the 
 other hand , oxygen - terminated diamond surfaces generally show hydrophilic 
 properties and exhibit fast heterogeneous 
 electron transfer while maintaining low background signals with the 
 wide extended solvent window properties . in addition , oh - terminated surfaces can be formed during etching 
 in a mixture of oxygen and water vapor . this type of surface termination is often desired ; different chemical 
 routes can be used to link functional groups to these oh adsorbates , 
 for further use in , for example , electroanalytical applications . fluorine termination will , compared to h termination , 
 result in even more strongly hydrophobic diamond surfaces . all of these interesting properties 
 of terminated diamond surfaces make it clear that surface termination 
 is very important for especially those applications in which diamond 
 can function as an electrode material . the relative reactivity for 
 the various diamond surface planes , terminated with either h , o , oh , 
 or f , are therefore very important to study from an atomic - level point 
 of view . theoretical modeling has , during the last decades , 
 been proven 
 to become highly valuable in the explanation and prediction of experimental 
 results . the simulation of surface reactivity can aid important information 
 about thin film growth mechanisms , as well as about surface reconstruction , 
 modification , and functionalization . the low - index ( 111 ) plane is 
 one of the most frequently obtained surface planes in cvd - grown crystalline 
 diamond . the origin of surface reactivity for nonterminated diamond 
 surfaces , as well as the energetic stability of the 
 terminated ( 111 ) surfaces , was earlier 
 studied by the present group using density functional theory ( dft ) . what is missing today is the corresponding study for also boron - doped 
 diamond ( 111 ) surfaces . the purpose of the present study has therefore 
 been to theoretically investigate the energetic stability and surface 
 reactivity for b - doped and variously terminated diamond ( 111 ) surfaces 
 using dft under periodic boundary conditions . the models used in the 
 calculations include h , oh , f , oon - top , and obridge terminations , as well as nonterminated diamond surfaces . both b - doped and nondoped diamond ( 111 ) surfaces were used in the 
 study , with the main goal to make a structural and energetic investigation 
 of the combined effect of b doping and termination type . only 100% 
 surface coverage ( for all types of terminating species ) was considered 
 in the present study . all 
 calculations in the present study have been performed using 
 dft under periodic boundary conditions . more 
 specifically , an ultrasoft pseudopotential plane wave approach was used , using the perdew wang ( pw91 ) 
 generalized gradient approximation ( gga ) for the exchange  correlation functional . the gga method usually 
 gives a better overall description of the electronic subsystem , compared 
 to the more simple lda ( local density approximation ) corrections . correlation 
 energy of a uniform electron gas , is inclined to overbind atoms and 
 to overestimate the cohesive energy in the system under study . on 
 the contrary , gga takes into account the gradient of the electron 
 density , which gives a much better energy evaluation . all of the calculations in the present work were carried 
 out using the cambridge sequential total energy package ( castep ) program 
 from accelrys , inc . all individual 
 models consisted of more than 200 atoms in the supercell , 
 and thus , the value of the energy cutoff for the plane wave basis 
 sets was comparably small and set to 380.00 ev . due to the large size 
 of the model , this numerical value should be adequate for the present 
 study . in addition , the monkhorst  pack scheme was used for the k - point sampling of the 
 brillouin zone , which generated a uniform mesh of k points in reciprocal space . the 1  1  1 k - point , as well as the cutoff frequency of 380 ev , was earlier found 
 to be adequate to use for the present type of system . due to the presence of unpaired electrons in the systems , the atomic 
 charges and bond electron populations were estimated by using the 
 methods of mulliken analysis , which is performed using a projection 
 of the plane wave states onto the localized basis by a technique described 
 by segall et al . as will be more deeply 
 described in section 3.c , the calculated 
 atomic charges , electron density (  ) , fukui function ( ff ) , and 
 information about bond electron populations ( i.e. , electron densities ) 
 were important tools in the interpretation of the underlying causes 
 to the effects of ( i ) terminating species and ( ii ) b doping . the ffs of the surface area generally have been used in visualizing 
 the surface reactivity . parr and yang improved the 
 frontier orbital theory introduced by fukui , whereby it became possible to calculate the so - called ffs1where n is the total number 
 of electrons in the system and (r ) is the 
 electron density at a certain position and at a fixed external potential , v. there are three ffs defined as f , f , and f , which correspond to a surface reactivity toward radical , 
 electrophilic , and nucleophilic attack , respectively . previous work 
 has shown that this f function can be 
 very useful in studying the surface reactivity of diamond . the atomic charges were also carefully estimated to give information 
 about the degree of ionic bond strengths , while the bond populations 
 contribute with covalent bond strength information . the averaged adsorption energies associated with the chemisorption 
 of the terminating species h , oh , f , oon - top , and 
 obridge , were calculated using eq 22where esurface is the total energy of the 100% terminated surface , ebare - sur is the total energy of a clean ( i.e. , 
 nonterminated ) surface , n is the number of a specific 
 terminating species within the supercell , and en is the total energy of the adsorbing gas - phase 
 species ( i.e. , o , oh , h , and f ) . this averaged value will give information 
 about the more global effect on the b dopant ( i.e. , on the whole surface 
 within the supercell ) . in addition , the adsorption energy eads , last of an individual terminating species 
 in the closest vicinity to the b dopant was also calculated in order 
 to receive information about the more local effect of the b dopant3where esurface is the total energy of the 100% terminated surface , eradical is the total energy of the otherwise terminated 
 surface with a radical bare site in the supercell , and en is the total energy of the adsorbing 
 gas - phase species ( i.e. , o , oh , h , and f ) . as a result of chemical 
 vapor - phase deposition ( cvd ) of diamond 
 thin films , there are usually different low miller index planes that 
 will dominate on the surface ; ( 111 ) and the 2  1-reconstructed 
 ( 100 ) surfaces are the most frequently observed ones . the ( 111 ) surface 
 has in the present investigation been chosen for studying diamond 
 surface properties and reactivity tendencies ( see figure 1 ) . a six carbon layer thick diamond slab , with the 
 cell dimensions of 5  5 , was used for all surface models , with 
 the purpose to properly simulate the reconstruction and relaxation 
 of the various types of diamond planes . this model size was proven 
 by earlier investigations to be adequate to use for the present type 
 of study . the diamond surfaces were terminated 
 to 100% with any of the following species : ( a ) f , ( b ) h , ( c ) oh , ( d ) 
 o in the ketone position ( oon - top ) , and ( e ) o in 
 ether positions ( obridge ) . in addition , one boron atom 
 was substitutionally positioned within the second c layer . this position 
 will render an appreciable effect on the diamond growth rate and especially 
 on the rate - determining h - abstraction step . the energy barrier for 
 this abstraction step was found to be reduced to zero for the diamond 
 surfaces ( 111 ) , ( 100)-21 , and ( 110 ) . to suppress the artificial 
 charge transfer between the two polar ends of the slabs , the dangling 
 bonds on the lower surfaces of the slabs were saturated with h atoms , 
 and a large vacuum distance between the slabs was used ( > 7  ) . the reason to saturate the lower c atoms with hydrogen atoms was 
 also to saturate the dangling bonds and to simulate the continuation 
 of bulk diamond . these h atoms were therefore , together with the lowest 
 c layer , kept fixed during the geometry optimization process . the 
 rest of the atoms in the model systems were allowed to freely relax 
 using the bfgs algorithm ( broyden  fletcher ( a ) five different types of surface - terminating species , 
 chemisorbed 
 onto a diamond ( 111 ) surface : ( a ) f , ( b ) h , ( c ) oh , ( d ) oon - top , and ( e ) obridge . ( b ) model of the h - terminated diamond 
 ( 111 ) surface . the h , b , and c atoms are shown in white , pink , and 
 gray . the surface reactivity of a certain material is generally determined 
 by the number of fermi level electrons and can be estimated by different 
 means . one way is to calculate the chemisorption energy for some specific 
 model adsorbates . within the present study , the chemisorption of h , 
 f , and o onto b - doped diamond ( 111 ) surfaces each 
 of them is most frequently used in the growth process , during surface 
 functionalization , and for surface modifications ( as presented in 
 the introduction ) . it is therefore of largest 
 interest to investigate in more detail the effect of each of these 
 termination scenarios on the surface reactivity of the diamond ( 111 ) 
 planes , being one of the most common low - index planes in micro- and 
 nanocrystalline diamond thin films . the averaged chemisorption energy eads , avg was used for studying the more global 
 effect of b doping , while the local effect was obtained by calculating 
 the adsorption energy eads , last for one 
 of the terminating species ( on an otherwise 100% terminated surface ) 
 that is being bonded to the surface on a position closest to the b 
 atom in the lattice . there are in fact three adsorbates that have 
 this neighboring position , which all link to the b atom via only one 
 c atom . these adsorbates are from here on called adjacent adsorbates . as can be seen in table 1 , the calculated 
 averaged chemisorption energies showed that there is no significant 
 global effect of b doping . the differences in averaged chemisorption 
 energy , eads , avg , for the b- and 
 nondoped diamond surfaces are very small , 0.02 < eads , avg < 0.06 ev . in fact , these numerical 
 differences are almost negligible and within the error of limits for 
 the theoretical method used . however , when comparing the averaged 
 adsorption energy , eads , avg , with the 
 adsorption energy for only one adsorbate , eads , last ( onto an otherwise 100% terminated surface ) , it is obvious that 
 the local effect of b doping is quite substantial . the values of eads , last are for all adsorbate types less than 
 the averaged eads , avg . in addition , the 
 lower values foreads , last realtive eads , avg for the nondoping scenario reflect the 
 existence of steric repulsions among the adsorbates for 100% surface 
 termination . even though there is 
 no evidence for a global effect by the dopants , 
 there is an apparent local effect that affects the adjacent adsorbates . the difference in adsorption energy for the b- and nondoped surfaces , 
 eads , last , is substantial and can not 
 be neglected ( 0.10 < eads , last < 0.94 ev ) . thus , it is thereby confirmed that the b dopant will 
 induce a weakening effect on the bonds between the three adjacent 
 adsorbates and their binding surface c atoms . the averaged adsorption 
 energies clearly show that it is the oon - top adsorbate 
 that will be most efficient ( of the 
 four adsorbate types ) in stabilizing the diamond ( 111 ) surfaces , with 
 almost identical values for the nondoped and b - doped scenarios ( 5.06 
 versus 5.04 ev ) . unfortunately , it was not possible to achieve 
 a stable 100% surface coverage with o in obridge formation . the underlying reason is most probably the low number of unpaired 
 electrons per surface c site . the diamond ( 111 ) surface has only one 
 unpaired electron per surface c atom , which forces the terminating 
 o atom to bind to two surface c atoms and with a maximum surface coverage 
 of 50% . an earlier theoretical investigation by d. petrini and k. 
 larsson also showed that an obridge surface coverage larger 
 than 25% will render highly unstable diamond ( 111 ) surfaces . hence , when initially positioning the o in obridge formations at 100% coverage , the o  o bridge bonds 
 were in the present study observed to break during the geometry optimization 
 and to instead form oon - top formations ( at 100% 
 coverage ) . it is thereby possible to conclude that a very high concentration 
 of o atoms at the surface may force the surface composition into oon - top positions . it must be emphasized that this observation 
 was made as a result of 0 k calculations , and hence , there is no energy 
 barrier involved in this structural reorganization ( from initial bridge 
 to on - top o positions ) . as presented above , the effect of the b dopant 
 is more obvious when calculating the adsorption energy for an adjacent 
 adsorbate ; eads , last = 4.28 ev 
 for a b - doped o - terminated surface , which is less exothermic compared 
 to eads , last = 4.90 ev for a nondoped 
 surface . a 100% termination with oh species resulted in an averaged 
 adsorption 
 energy ( 3.86 ev for nondoped versus 3.82 ev for b - doped ) 
 that is less favorable than that for o adsorption and is also the 
 least favorable termination type within the present study . the underlying 
 reasons to this result are most probably the degree of steric hindrances 
 induced by neighboring oh adsorbates . there is in fact two competing 
 interadsorbate interactions , ( i ) hydrogen bonding and ( ii ) induced 
 steric repulsions . the former one will stabilize the surface system , 
 and the latter will destabilize and thereby weaken the surface  adsorbate 
 bonds . the steric effect can be further visualized by studying the 
 values of adsorption energies for the nondoped situation , eads , avg = 3.86 ev and eads , last = 3.43 ev . the adsorption of the last 
 oh species , on an otherwise completely oh - terminated diamond surface , 
 showed the largest difference in energy ( compared to an average value 
 for a 100% termination ) , 0.43 ev . the combined effect by the adsorbates 
 can be further observed by studying the values of adsorption energies 
 for the adjacent adsorbates ( eads , last ) , 3.33 ( b doping ) versus 3.43 ( nondoping ) ev . these 
 two values represent the smallest difference in adsorption energy 
 in the present study ( 0.1 ev ) when comparing b- and nondoped surfaces 
 for all different termination types . the most plausible explanation 
 to this observation is that the effect of the b dopant will be somewhat 
  concealed  by the influence of the steric repulsions 
 among the oh adsorbates . the f adsorbate showed the second most 
 efficient tendency to form 
 stable diamond ( 111 ) surfaces , with averaged adsorption energies of 
 4.58 ( nondoped surface ) and 4.52 ev ( b - doped surface ) . these numerical values were very similar to the results obtained for 
 the h - terminated surfaces , 4.34 ( nondoped surface ) and 4.28 
 ev ( b - doped surface ) . in addition , the numerical values for h and 
 oh termination are also rather similar and are both on the low - energy 
 edge of the adsorption energy trend for these adsorbate types , 3.86 
 ( nondoped oh - terminated surface ) and 3.82 ev ( b - doped oh - terminated 
 surface ) . these results are strongly supported by the calculations 
 of adsorption energies for the adjacent terminating species : h - terminated 
 surface ( 4.38 ( nondoped surface ) and 3.44 ev ( b - doped 
 surface ) ) , f - terminated surface ( 4.27 ( nondoped surface ) and 
 3.34 ev ( b - doped surface ) ) , and oh - terminated surface ( 3.43 
 ev ( nondoped surface ) and 3.33 ev ( b - doped surface ) ) . these 
 results show that the diamond ( 111 ) reactivity toward h versus f is 
 very similar and only somewhat more pronounced compared to that for 
 oh . the underlying cause for the much higher reactivity toward o will 
 be analyzed and discussed in section 3.c . furthermore , the present study has revealed a larger destabilizing 
 effect by the b dopant on the adjacent h and f adsorbates , compared 
 to that on the o and oh adsorbates . the reason for this induced bond - weakening 
 effect by b will be further discussed in the text below . in 
 nondoped diamond , all c c bonds are electron pair single 
 bonds because the c atom has four valence electrons and is bonded 
 to four other c atoms ( i.e. , sp hybridized ) . when one 
 boron atom will substitutionally replace one carbon atom within the 
 second c layer , an element has been introduced into the diamond lattice 
 with one less valence electron . hence , the four bonds between the 
 b atom and its four neighboring c atoms must be deficient by a total 
 of one electron . a b dopant in this position will result in a zero 
 energy barrier for the h abstraction reaction from the surface and 
 has therefore been chosen as the preferable position in the present 
 study . the underlying cause for this effect is the electron redistribution 
 within the surface region due to introduction of the three - valence 
 b element into the structure . as the result of the geometry 
 optimization in the present study , all b c bonds were elongated 
 to different extents for the b - doped and surface - terminated diamond 
 ( 111 ) surfaces ( as compared with the c , who showed that local bond elongation will 
 take place in boron - doped diamond . this 
 is an indication of bond weakening and does fit very well with the 
 deficiency of one electron in the vicinity of b. however , the situation 
 was completely different for the nonterminated b - doped diamond surface . the bond length between the b atom and the three binding surface c 
 atoms in the first c layer decreased , while the bond length between 
 the b atom and third - layer c atom increased . as a result of these 
 bond length changes , the b atom moved up toward the layer of surface 
 c atoms ( see figure 2 ) . c 
 distance is 1.946  , which is quite longer than the other three 
 b  c bonding lengths ( 1.5101.512  ) . these results 
 give evidence of the preferred valence electron configuration by b 
 ( i.e. , by forming only three covalent bonds to neighboring c atoms ) . moreover , the three binding surface c atoms showed very small negative 
 atomic charges ( 0.09 to 0.12 ) , which is an indication 
 of almost perfectly covalent bonds with minor ionic contributions . in addition , the bonds between the three surface c atoms and the b 
 dopant were found to display larger electron bond populations ( 0.920.94 ) 
 compared to the bond between the third - layer c atom and the b dopant 
 ( 0.39 for bond population ) , which again supports the observation of 
 a weakened covalent bond formation to the lower c carbon . the model of 
 a geometry - optimized b - doped diamond ( 111 ) surface 
 without any surface termination . atomic structure of the ( a ) nondoped and ( b ) b - doped diamond ( 111 ) 
 surface , visualizing the upper layer carbon , boron , and adsorbate 
 atom positions . for the nondoped diamond model , the abbreviations 
 are as follows : a : adsorbate ; c1 : carbon atoms in the first layer ; 
 c2 : carbon atom in the second layer ; c3 : carbon atom in the third 
 layer . for the b - doped diamond model , the abbrevations are as follows : 
 aa , ab , ac : adjacent adsorbates ; c1a , c1b , c1c : carbon atoms in the 
 first layer ( binding to the doping boron atom ) ; b : boron atom substitutionally 
 positioned in the second c layer ; c3a : carbon atom in the third layer 
 ( binding to the doping boron atom ) . as can be seen in table 2 , the bond 
 lengths 
 between the adjacent adsorbates and the surface carbon atoms that 
 are binding to the b dopant ( ra  c ) there is an observed 
 bond lengthening for the adsorbates h , f , and oh , while the o adsorbate 
 gives a shortened length . however , the effect of b doping on the bond 
 lengthening is not so pronounced ; it is at most 0.02  . the largest 
 change in bond length is observed for the oh - terminated surface ( 0.02 
  ) . the underlying reason for this observation is most probably 
 the induced steric hindrances between the oh adsorbates , which also 
 may explain the rather low adsorption energy for this type of adsorbate 
 ( as discussed in section 3.a ) . abbreviations ( see figure 3 ) : 
 a : adsorbate ; b : boron atom within the second 
 diamond c layer ; c1a , c1b , c1c : carbon atoms in the first diamond 
 c layer , directly binding to the b atom ; c2 : carbon atom in the second 
 diamond c layer ; c3a : carbon atom in the third diamond c layer , directly 
 binding to the b atom . for 
 adsorbate csurface bonds farther away from 
 the b doping element , there was , for all terminating species investigated , 
 no observable influence by b on the bond lengths . this was also the 
 situation for all c  c bonds at a distance larger than 3  
 from b. hence , it is thereby possible to conclude that the combined 
 effect by the boron doping and type of adsorbate will only affect 
 the upper surface region most adjacent to the b dopant . the 
 boron element does only have three valence electrons , while the carbon 
 element has four . as stated above , the b dopant will thereby introduce 
 a deficiency of electrons within the system . furthermore , the electronegativities 
 of the c and b atoms are 2.55 and 2.04 , respectively . thus , a polarization of electron density within the b  c 
 bond , with the preference for electrons in the vicinity of the c atom , 
 is highly expected . in the present systems , however , not all of the 
 c atoms within the b  c bonds showed negative charges . the reason 
 for this observation is most probably the effect of the adjacent adsorbates 
 binding to these c atoms . despite this circumstance , the b atoms were 
 still observed to donate electrons to the binding c atoms and thereby 
 to show a more positive charge compared to the c atom . the total electron density maps have 
 been calculated for the various systems in the present investigation , 
 diamond ( 111 ) surfaces that are terminated with either h , oh , oon - top , or f species ( see figure 4 ) . the purpose with these plots is to provide an overview of electron 
 redistribution when substituting a b atom into the diamond lattice . in addition , table 3 shows the mulliken bond 
 population analysis for the b the molecule h6c2bc3h9 ( see figure 5 ) has been used as a reference 
 compound for b c 
 in h6c2bc3h9 is 0.87 , 
 with a corresponding bond length of 1.596  . it must be stressed 
 that this bond length is somewhat prolonged due to the steric repulsions 
 between the three - dimensional ch3 groups that are residing 
 on the b and c atoms . thus , it is highly expected that a more realistic 
 bond population of a b  c bond ( i.e. , without the influence 
 of steric hindrances ) should be even larger than the value of 0.87 . 
 as visualized in figure 4 for the oon - top termination , the electronic 
 bond population between the b atom and each of the three surface c 
 atoms is within the interval 0.650.70 , which is on the lower 
 range when compared to the other termination types ( 0.790.85 ) . 
 the surfaces with h , oh , or f terminations resulted in bond populations 
 of 0.770.83 ( h ) , 0.730.82 ( f ) , and 0.800.84 
 ( oh ) , the latter being the largest values for all four terminations 
 scenarios . it must be stressed that all of these values are smaller 
 than that for an ordinary covalent single b  c bond ( 0.87 as 
 in h6c2bc3h9 ) . this reflects 
 the fact that there are fewer electrons involved in the formation 
 of bonds between the b dopant and the surrounding c atoms within b - doped 
 diamond , which leads to bond weakening because the binding orbitals 
 will not be fully occupied . this bond weakening has been identified 
 with bond lengthening , as discussed in section 3.b . 2d slices showing the total electron density (  , 
 in units 
 of e ) distribution maps for the b atom and 
 its two binding surface c atoms for ( a ) h - terminated , ( b ) oon - top - terminated , ( c ) f - terminated , and ( d ) oh - terminated diamond ( 111 ) 
 surfaces . the gray spheres are c atoms , and the pink ones are b atoms . c 
 bond is 0.87 , 
 and the corresponding bond length is 1.596  . in addition , this assumed bond weakening effect 
 is further supported 
 by the total electron density maps , which all demonstrate a lower 
 electron density ( i.e. , brighter color ) along the b  c bond 
 ( see figure 4 ) . as can be seen from the electron 
 density maps in figure 4a  d , the b c 
 bonds for the oon - top - terminated surfaces show the 
 absolute least electronic density compared to the other three surface 
 termination types ( h , oh , and f ) . furthermore , the adsorption oon - top was found to bind hardest to the surface in comparison 
 with the other three termination types ( shown in section 3.a ) . f- and h - terminated surfaces showed slightly 
 less electron density along the b  c bond , as compared with 
 neighboring c furthermore , the situation is much more 
 different for the oh - terminated surface . the electron density along 
 the b c bond is here found to be very similar to that for the 
 surrounding c  c ones ( see figure4b ) . this agrees well with the adsorption energy analyses in section 3.a where the oh - terminated surface showed the 
 least effects of the adsorbates and surface c bond weakening in four 
 terminated surfaces in the present study due to the steric repulsion . 
 also , h- and f - terminated surfaces showed a larger adsorption energy 
 difference between eads , avg and eads , last , which meant larger bond weakening 
 induced by the b dopant . all calculated electron bond populations , 
 between the adjacent 
 adsorbates ( a ) and the binding surface carbon atoms ( c ) , are also 
 shown in table 3 . o bonds within 
 the b - doped oon - top - terminated surface showed comparably 
 large values of electron bond population ( 0.810.85 ) as compared 
 with the nondoped scenario ( 0.77 ) . compared to the nondoped 
 situation , the o - terminated surface showed a shortened c  a 
 bond length . on the other hand , the oh - terminated surface showed 
 a somewhat 
 smaller c  o bond population value for b doping ( 0.55 ) , compared 
 to nondoping ( 0.58 ) . moreover , the bonds between the adjacent adsorbate 
 and their binding surface c atom , for h- and f - terminated surfaces , 
 showed almost identical bond population values when comparing b - doped 
 with nondoped surfaces : h : 0.88 ( b - doped ) versus 0.89 ( nondoped ) ; 
 and f : 0.440.45 ( b - doped ) versus 0.45 ( nondoped ) . csurface bond population values 
 showed a good correlation with bond lengths ( see section 3.b ) . this means that the bond population is inversely 
 proportional to the bond length , that is , the longer the bond length , 
 the smaller the bond population . the results 
 obtained from the bond population analysis in section 3.c.1 were found to agree well with the conclusion 
 that can be drawn from the mulliken charges ( as presented in table 3 ) . it can there be seen that the resulting atomic 
 charge of b for the oon - top termination is + 0.41 
 e , while the atomic b charges for the other three termination types 
 are smaller , + 0.39 ( h ) , + 0.36 ( f ) , and + 0.33(oh ) e. as can furthermore 
 be seen from figure 4 , for all b - doped diamond 
 surfaces investigated , the surface carbon atoms gained electron density 
 from the b atom , and thus , these atoms showed a more negative charge 
 compared with c atoms farther away from the doped area . it also seems 
 that the degree of electron transfer from the electropositive b dopant 
 to the binding and more electronegative c atoms is most profound for 
 the oon - top - terminated diamond surfaces . to 
 be more specific , for the h - terminated surfaces , the c h bonds 
 will be polarized with a negative charge on the c atom and a positive 
 charge on the h atom . the origin of this dipole formation is the difference 
 in electronegativity with a value of 2.20 for h and 2.55 for c. the atomic charge of the surface c atom , being 
 bonded to the b dopant ( c1a ) , is 0.40 , which is to be compared 
 with the corresponding c atom ( c1 ) in nondoped diamond ( 111 ) , 0.24 . this is expected because the electronegativity for b is smaller than 
 that for c. for the terminating species that are more electronegative 
 than the element c , the atomic charges of c1a versus c1 will be positive . 
 for the terminating species oon - top , f , and oh , 
 the atomic charges are + 0.15 ( + 0.27 ) , + 0.19 ( + 0.34 ) , and + 0.06 ( + 0.22 ) , 
 respectively . for each couple of values , the first value represents 
 the doping situation ( c1a ) , and the value within parentheses represents 
 the nondoping situation ( c1 ) . it is hence completely clear that there 
 is a withdrawal of electrons from the b element to these types of 
 electronegative adsorbates . these results are further emphasized 
 when calculating the charges 
 of the adjacent adsorbates , which were furthermore observed to undergo 
 slight changes when substituting c with b in the lattice . for both the b - doped and nondoped situation , the partial electron transfer 
 between the terminating species and the binding surface c atoms followed 
 the differences in electronegativity . the calculated atomic charges 
 for oon - top ( 0.24 for doping versus 0.28 
 for nondoping ) , oh ( atomic charge for the oxygen : 0.55 for 
 doping versus 0.58 for nondoping ) , f ( 0.32 for doping 
 versus 0.31 for doping ) all indicated partial electron transfer 
 from the surface c to the respective adsorbate . for the situation 
 with h - termination ( i.e. , with a less electronegative value compared 
 to c ) , the opposite situation was observed ( + 0.20 for doping versus 
 + 0.23 for nondoping ) . this result is understandable because the electron 
 density at c1a is higher than that at c1 due to the presence of b 
 with its tendency to withdraw electrons toward its surrounding c atoms 
 ( thereby lowering the withdrawal capability of c1a with respect to 
 the terminating h ) . it is interesting to note that a smaller electron 
 density is moved from the adsorbate h to the binding surface c atoms , 
 while it should have been the opposite if the results were completely 
 based on the differences in electronegativity . in addition , the degree of electron transfer toward 
 the oon - top adsorbates , for the b doping situation , 
 was smaller than the corresponding transfer for a nondoped situation 
 ( oon - top charge of 0.24 versus 0.28 ) . the situation is identical for the oh adsorbates ( o ( in oh ) charge 
 of 0.67 versus 0.68 ) . however , the situation was different 
 for f termination , where the effect of b doping on the electron distribution 
 is not completely clear due to larger variation in f atomic charges . 
 however , by looking at the averaged atomic charges for the three adjacent 
 f adsorbates ( 0.32 versus 0.31 ) , the b dopant effect 
 will be similar to the h termination situation in the way that the 
 degree of electron transfer will increase by introducing b dopants 
 into the diamond lattice , either toward f ( making f more negative ) 
 or from h ( making h more positive ) . the spin density maps 
 for all systems under investigations are plotted in figure 6 . these maps show the difference between - 
 and -electron densities ( i.e. , spin up versus spin down ) . if 
 the -spin density is dominating over the corresponding -spin 
 values , a positive value will be the result in these plots . in a similar 
 manner these spin density maps make it possible to visualize the resulting 
 spin distribution for the various systems and especially to get some 
 information about the combined effect of b doping and surface termination . 
 for all types of surface termination that was used in the present 
 study , the electron spin density was observed to surround the bonds 
 between the b dopant and the surface c atoms ( see figure 6 ) . the h- , oh- , and f - terminated surfaces looked 
 very similar in that the -spin is dominating . it is thereby 
 possible to draw the conclusion that the deficiency of electrons in 
 the b dopant showed a rather local impact on the b c bonds 
 and in this case for only two of total of three bonds . in addition , 
 the f - terminated surface showed a numerically larger value of the 
 spin density ( 0.16/ ) compared with the h- and oh - terminated 
 surfaces ( 0.08 versus and ( 00.10/ ) ( see 
 figure 6a , c , d ) . it is worth noticing that the 
 two spin - polarized b  c bonds in the h- , oh- , and f- terminated 
 surfaces will also display longer bond lengths ( table 2 ) and smaller bond population values ( table 3 ) compared to the other two b the observation is , thereby , that the weaker 
 the b  c bond ( with longer bond length and less electron density ) , 
 the larger the spin density along the bond . it is thereby possible 
 to draw the conclusion that the bonding state of the b in addition to the localized 
 b  c bond spin densities , a minor spin density was also found 
 to distribute at the three adjacent f adsorbates ( aa , ab , ac ) for 
 the f - terminated surface and at some oh adsorbates for the oh - terminated 
 surface . this observation is most probably caused by the large values 
 of electronegativity of the f and oh adsorbates . this result is clearly 
 supported by the observation made in section 3.c.2 , which clearly shows that electrons from the b dopant 
 will be attracted to adjacent f and oh adsorbates . spin density maps for 
 the supercell models of b - doped diamond ( 111 ) 
 surfaces with ( a ) h termination ( isosurface = 0.025/ ) , ( b ) oon - top termination ( isosurface = 0.04/ ) , ( c ) f termination ( isosurface = 0.05/ ) , and ( d ) oh termination ( isosurface = 0.06/ ) 
 ( left column ) . the 2d slices of spin density c  b  c planes 
 ( middle column ) and spin density c  b  a planes ( right 
 column ) are shown on the right - hand side of this figure . the dark - colored 
 spheres show the c atoms and the bright - colored ones the b atoms . the 3d spin density is shown on the left - hand side of the figure . it is only the oon - top - terminated surface ( d ) that 
 shows an isosurface with both positive ( dark color ) and negative values 
 ( bright color ) . it is also here obvious 
 that o in the on - top position will induce 
 a special effect on the diamond surface and its properties . the oon - top adsorbate shows a large spin density , and the 
 isosurface visualizes a mixture of both - and -spins 
 that are distributed over the diamond surface and located at the various 
 oon - top adsorbates . the 
 underlying reason for these high spin density values ( 0.06/ ) is the radical nature of the o adsorbate . the bond population 
 analysis shows that the numerical value of the bond order for this 
 type of c  o bond is around 0.8 . o 
 single bond instead of the c = o double bond . because the o element 
 has six valence electrons , a monoradical o adsorbate must be formed 
 when attached to the diamond surface with only one covalent bond ( figure 6b ) . the fact that both spin - up and spin - down types 
 of spin densities are present among the oon - top adsorbates 
 is most probably due to spatial repulsions . this distribution of spins 
 for the oon - top termination is clearly visible in 
 figure 6d . a ff is the differential 
 change in electron density when an infinitesimal number of electrons 
 is either added to or removed from the system under investigation . it has here been used as a quite helpful tool 
 to predict the distribution of chemical reactivity on the surface 
 from intrinsic electronic properties . as presented in section 3.c.2 , the ffs will give qualitative information 
 with respect to electrophilic , nucleophilic , and radical attack of 
 the various surface sites . as presented in figure 7 , the maps of 2d ffs are colored from white ( which visualizes 
 the smallest value and is hence least susceptible to the specific 
 attack ) to black ( which represents the largest value and shows the 
 most susceptible surface sites with respect to the specific attack ) . 
 as can be seen in figure 7 , the ffs are largest 
 for the three adjacent adsorbates to the b dopant and are hence the 
 most reactive ones . however , the degree of reactivity differs a lot 
 between the different adsorbate types , which in practice means that 
 the susceptibility to a specific attack depends completely on the 
 combined effect of b doping and surface termination . in the present 
 section , only the most susceptible and reactive surface sites will 
 be the target for discussions and comparisons . ffs mapped onto the 2d 
 isosurface charge density of the adsorbates 
 [ ( a ) h , ( b ) oon - top , ( c ) f , or ( d ) oh ] attached 
 to diamond ( 111 ) , showing the susceptibility of electrophilic ( left 
 column ) , nucleophilic ( middle column ) , and radical ( right column ) 
 attack . the bigger spheres in the slices represent the three adjacent 
 adsorbates ( linked to the surface c atoms that bind to the b dopant ) . the 100% h - terminated surfaces 
 showed overall much smaller values 
 of the ffs , even though the adjacent h atoms to the b dopant showed 
 a somewhat larger tendency for reactivity ( 0.02 for electrophilic , 
 0.015 for nucleophilic , and 0.006 for radical ) . for the oh - terminated 
 surface , the o atoms in two of these adsorbates were found to display 
 a larger susceptibility ( 1.5 ) for a nucleophilic attack and a very 
 minor susceptible ( 0.08 ) for a radical attack . on the other hand , 
 the h atoms in these oh adsorbates showed susceptibility toward electrophilic 
 attack ( 0.02 ) . the f - terminated adsorbates closest to the b dopant 
 ( especially one of them ) showed large values ( 1 ) of susceptibility 
 for a nucleophilic attack and a very minor susceptible ( 0.05 ) for 
 a radical attack . in summary , for h- , oh- , and f - terminated surfaces , 
 the ffs indicate that the b dopant will increase the reactivity for 
 the adjacent c adsorbates to the b dopant . more specifically , the 
 b dopant will largely induce susceptibility for a nucleophilic attack 
 to ( i ) adjacent f adsorbates and to ( ii ) the o atoms in adjacent oh 
 adsorbates . the oon - top - terminated surface 
 is also in this 
 sense completely different from the other terminated surfaces . first 
 of all , we have here the largest susceptibility toward an attack from , 
 for example , gaseous species . half of the oon - top adsorbates show a strong susceptibility toward an electrophilic 
 attack , and the remaining half of the oon - top adsorbates 
 show a strong susceptibility to a nucleophilic attack ( with a value 
 of 9 for each ) . this is reasonable because the radical o adsorbates , 
 with their one unpaired electron , must be very reactive and thus will 
 react strongly with both electrophilic and nucleophilic species . what 
 is also interesting for this type of termination type is that the 
 adjacent o adsorbates even showed less susceptibility for attacks 
 compared to o adsorbates farther away from the b doping site . this 
 agrees very well with the mulliken population analysis described in 
 section 3.c.2 because the adjacent oon - top species showed less negative atomic charges ( due 
 to the effect of the b dopant ) and therefore would be less reactive 
 than other oon - top adsorbates . figure 8 shows the partial density of states 
 ( pdos ) for the b - doped diamond ( 111 ) surfaces with four different 
 types of terminating species . for comparison , the complete dos of 
 nondoped bulk diamond it is a well - known fact that the band gap will be underestimated when 
 using dft calculations , and the present method shows that the calculated 
 band gap for bulk diamond is 4.8 ev ( see figure 8) , which is compared to the experimental value of 5.5 ev . in order to study the detailed information regarding 
 the effect of b dopant and adsorbates , the pdoss for the different 
 atomic layers ( from adsorbates down to the third - layer c atoms ) are 
 shown in figure 8 . the pdos for the diamond 
 ( 111 ) surface with ( a ) h termination , 
 ( b ) oon - top termination , ( c ) f termination , and 
 ( d ) oh termination . for each terminating species , the various pdos spectra show ( from top to down ) pdos for the specific adsorbate , the 
 top three c layers ( 1c , 2c , 3c ) , the b dopant , and bulk ( nondoped ) 
 diamond . blue line : pdos ( s orbitals ) ; green line : pdos ( p orbitals ) ; 
 red line : dos ( total ) . for the h - terminated surface , there are no observable differences 
 between the pdoss of the different c atomic layers in the system ( excluding 
 the b dopant ) . earlier studies have shown that h - terminated diamond 
 surfaces under atmoshperic conditions will induce p - type surface doping . as can be seen in figure 8a , the estimated 
 band gaps for the upper three carbon layers are 2.5 ev , which is quite 
 smaller than the value for bulk diamond . the smaller band gap for 
 the surface carbons is most probably affected predominantly by the 
 terminating h atoms . for detailed observation of the b dopant effect , the pdos of three surface c atoms that bonded to the b dopant ( 1c  b ) 
 is plotted in figure 9a , compared to the pdos 
 of the surface c atom far away from doping area ( 1c - far ) . a small 
 electron hole above the fermi level appears in the pdos of 1c  b , 
 which is clearly characteristic of a p - type doping material . the peak within the range of 0.5 to 
 1.5 ev shown in 1c  b is a characteric peak of the b 
 dopant that can not be found in 1c - far . it indicated that the effects 
 of the b dopant can be quite local and not extend to a large area . pdos for 
 the diamond ( 111 ) surface with ( a ) h termination , ( b ) 
 oon - top termination , ( c ) f termination , and ( d ) 
 oh termination . the pdos of three surface carbon atoms bonded to the 
 b dopant ( named 1c  b ) and one surface carbon atom far away 
 from b dopant ( named 1c - far ) from the top down each graph . blue line : 
 pdos ( s orbitals ) ; green line : pdos ( p orbitals ) ; red line : dos ( total ) . the pdoss for the oon - top - terminated diamond 
 surface are presented in figure 8b . the pdoss 
 of the o atoms extend above the fermi level ( within an energy range 
 of 2 ev ) . these states are most probably induced by the unpaired 2p 
 electrons on the radical o atoms . more generally , the 2p electrons 
 at these o adsobates show a concentration of dos in the vicinity of 
 the fermi level . thus , the oon - top - terminated diamond 
 ( 111 ) surface is quite reactive and also electronically conductive , 
 which agress with earlier observations made by derry et al . these authors have also predicted that o - terminated 
 diamond ( 111 ) surfaces are metallic ( or conducting ) due to the fact 
 that the fermi level is positioned within the occupied upper - level 
 dos . the oon - top - terminated surface is also 
 quite 
 exceptional compared to the other termination scenarios , in that both 
 the b dopant and the surrounding c atoms in the second layer significanly 
 contribute to the surface electronic conductivity . there are some 
 occupied 2p electron states above the fermi level that originate from 
 terminated o atoms . the characteristic pdos peaks of adsorbed o in 
 on - top positions are located within the ranges of 19 to 22 
 and 4 to 5 ev . similar positions of peaks for first - layer 
 and second - layer c atoms exist but with decreasing intensity . this 
 is a fingerprint of the fact that there is a strong interaction between 
 the o adsorbates and the bindning surface c atoms . as can be seen 
 in figure 8 , the interactions beteen the o 
 adsorbates and the third atomic layer c atoms have diminished to 0 . 
 however , what is most interesting here are the pdos peaks in the interval 
 of 02.2 e ( resulting from especially the radical o adsorbate , 
 b dopant , and c in layer 2 and with a minor contribution from c atoms 
 in layer 1 ) , indicating a very strong interaction between these atoms . figure 8c shows the pdoss of b - doped diamond 
 ( 111 ) surfaces that are f - terminated . as was the situation with oon - top termination , there is a clear overlap between 
 o 2p electron peaks within the interval of 26 to 24 
 ev and especially the binding c atom in the first atomic c layer ( being 
 a strong indication of surface c  f binding ) . unlike h termination , 
 the band gap did not seem to change for the upper diamond ( 111 ) surface 
 ( as compared with nondoped bulk diamond ) . the pdos spectra for 
 an oh - terminated b - doped diamond surface showed 
 an almost identical feature as the f - terminated ones . overlapping 
 peaks ( 23.5 to 20 ev ) , involving oh and the first - layer 
 c atoms , indicated strong adsorbate  surface interactions , which 
 declined rapidly down into the c lattice . in addition , the band gap , 
 as compared to that for nondoped bulk diamond , did not seem to change 
 much for the upper diamond ( 111 ) surface . as was the situation with 
 h termination , one small hole appeared above the fermi level in the 
 pdoss of the f- and oh - terminated surfaces , as presented in figures 9c , d , respectively . the characteristic peak of the 
 b dopant appears below the fermi level also in the pdos of 1c  b , 
 which can not be found in the pdos of 1c - far . from these results , it is possible to conclude 
 that for both nondoped 
 and b - doped diamond ( 111 ) surface scenarios , the trend in the averaged 
 adsorption energy ( as a function of surface terminating species ) is 
 oh < h < f < oon - top . the adsorption energies were also found to be numerically quite similar 
 for the adsorbates h , oh , and f. the b dopant , substitutionally positioned 
 within the diamond ( 111 ) surface , was found to have a very minor influence 
 on the averaged adsorption energy for the various terminating species 
 investigated . however , the b dopant can have an obvious influence 
 on the adjacent adsorbates . adsorbate bonds , with the following trend for the various 
 surface termination species , oh < oon - top < 
 h < f. the electronic structure results agreed with the geometrical 
 structure 
 analysis . the considerable change of atomic charges takes place in 
 the four carbon atoms bonded to the b dopant . in addition , the b dopant 
 was found to increase the reactivity of adjacent h , oh , and f adsorbates 
 and decrease the reactivity of adjacent o adsorbates . finally , 
 comparing the four doss of the b atoms in the diamond 
 surfaces with four different species , the shapes of the valence and 
 conduction bands in the dos are quite different , which is largely 
 affected by the adsorbed terminated species . the b dopant may have 
 a local influence on the pdos of b - bonded surface carbon atoms and 
 not extend to a large area . the influence induced by the terminated 
 species can only affect the dos of the first two surface carbon layers , 
 but the third layer displays very little influence by the adsorbates 
 and is already close to the bulk diamond dos .
the effect of b doping on the surface 
 ( 111 ) reactivity has , in 
 the present study , been investigated for various surface terminations , 
 h , oh , oon - top , and f. this type of surface modification 
 has experimentally been proven to be extremely important for , for 
 example , applications based on surface electrochemistry . density functional 
 theory ( dft ) has here been used to study both the local and more global 
 effects of substitutionally positioned b atoms in the upper part of 
 the diamond ( 111 ) surface . for this purpose , 
 adsorption energies for 
 the various terminating species have been calculated , and the observed 
 results have been carefully analyzed in order to gain a deeper knowledge 
 about the atomic - level cause of the observed effects . as a result , 
 the b dopant shows a clear , but local , effect for all terminating 
 species investigated . 
 in addition , it is only the radical o - terminating 
 species that show a special and high reactivity on the diamond surface . 
 the other terminating species show a much lower reactivity , which 
 in addition are very similar .