Ab Initio Calculations of Hydroxyl Impurities in CaF2

Articlepubs.acs.org/JPCCAb Initio Calculations of Hydroxyl Impurities in CaF 2H. Shi* and L. ChangKey Laboratory of Cluster Science of Ministry of Education, School of Science, Beijing Institute of Technology, Beijing 100081,People's Republic of ChinaR. JiaDepartment of Mathematics and Natural Sciences, Bergische Universitaẗ Wuppertal, D-42097 Wuppertal, GermanyR. I. EglitisInstitute of Solid State Physics, University of Latvia, 8 Kengaraga Strasse, Riga LV1067, LatviaABSTRACT: OH − in CaF 2 crystal and the (111) surface have been studied by usingdensity functional theory (DFT) with hybrid exchange potentials, namely, DFT-B3PW. Three bulk and 20 surface OH − configurations were investigated, and we foundthat Configs OH (111) for the bulk case and HO (\) 11 and HO (\) full for the surface case are theenergetically most favorable configurations. For the (111) CaF 2 surface atomic layers,the surface hydroxyls lead to a remarkable XY-translation and a dilating effect inthe Z-direction, overcoming the surface shrinking effect in the perfect slab. Bond populationanalysis shows that there is a considerable covalency between the oxygen and hydrogenatoms, and the surface effect strengthens the covalency of surface OH − impurities. Thestudies on band structures and density of states of the surface OH − -impurity systemsdemonstrate that there are two defect levels induced by OH − impurities. The O porbitals form two superposed occupied O bands, located above the valence bands(VBs), and the H s orbitals do the major contribution to an empty H band, locatedbelow the conduction bands. Because of the surface effect, the O bands move downward, toward the VBs with respect to therelevant bands in the bulk case, and this leads to narrowing of the VB → O gap and widening of the O → H gap whichcorresponds to the first optical absorption. Additionally, the study on the formation of OH − impurities shows that isolatedhydroxyls are favorite to substitute fluorine ions and adsorb on the surface energetically in CaF 2 . On the other hand, theformation of OH − impurities may also be due to the aggregation of separated oxygen and hydrogen impurities in CaF 2 . Theformation of OH − impurities could be avoided in CaF 2 crystal if we can control the concentration of the oxygen atoms near thesurface, because oxygen does the primary contribution to the formation of OH − impurities in CaF 2 .I. INTRODUCTIONAlkaline-earth fluorides such as CaF 2 and BaF 2 , whose bandgaps are larger than 10 eV, are very important for many opticalapplications. As an example, a recent demand for lens materialsavailable in short-wavelength lithography is a typical application.The currently targeted wavelength is 157 nm (about 8 eV) from anF 2 -excimer laser. This wavelength is far shorter than the transparentregion of quartz that is the most popular optical material in theultraviolet (UV) region. Additionally, CaF 2 can be chosen as anoptical material also due to its cubic crystal structure with perfectoptical isotropy, due to its chemical durability and its mechanicalproperties which make it applicable for lens fabrication. 1−3 Also,CaF 2 can be used as a material for radiation detection. 4 Consideringthe high technological importance of alkaline fluorides, itis not surprising that during the last years, they have been thesubject of many experimental and theoretical studies. 5−28It is well-known that optical and mechanical properties ofcrystals are strongly affected by defects and impurities unavoidablypresent in any real material. Contemporary knowledge of defectsin solids has helped to create a field of technology, namely defectengineering, which is aimed at manipulating the nature andconcentration of defects in a material so as to tune its properties ina desired manner or to generate different behaviors. CaF 2 couldbecome an important optical material if one could avoid or, atleast, control the photoinduced defect formation, which so far inapplications degrades its optical quality. Therefore, it is significantto understand the nature of defects in CaF 2 .Coloration effects in alkaline-earth fluorides are stronglyinfluenced by some impurities. Investigations by Adler et al. 29and Adler and Bontinck 30 show that alkaline-earth fluoridesreacts readily with water vapor at high temperatures andsuggest that the resulting hydrolysis gives rise to a variety ofdefects which includes O 2− ions in fluorine sites and chargecompensatingfluorine vacancies, hydrogen impurities dissolvedReceived: November 17, 2011Revised: February 3, 2012Published: February 16, 2012© 2012 American Chemical Society 6392 dx.doi.org/10.1021/jp211075g | J. Phys. Chem. C 2012, 116, 6392−6400

The Journal of Physical Chemistry CArticleThe calculated atomic displacements of the OH − andsurrounding atoms for Config OH (111) are listed in Table 1.Table 1. Atomic Relaxations (D (% a 0 ), as a Percentage ofthe Lattice Constant, 5.50 Å) and Effective Charges (Q(e))of the OH − and Surrounding Atoms in the CaF 2 96-AtomSupercell for Config OH (111)aatoms (shell) no. D (% a 0 ) Q (e) ΔQ (e)O 1 1.93 −0.997 −H 1 − +0.275 −Ca1 3 1.10 +1.772 −0.031Ca2 1 0.73 +1.799 −0.004F1 3 0.34 −0.913 −0.011F2 3 0.32 −0.915 −0.013F3 6 0.33 −0.901 +0.001F4 3 0.28 −0.903 −0.001F6 3 0.18 −0.900 +0.002a ΔQ(e) is the charge difference between the defective and perfectcrystals (Q Ca = +1.803 e, Q F = −0.902 e in perfect CaF 2 ). The shelllabels have been defined in Figure 1.The three Ca1 atoms are repulsed from the OH − by around1.10% of a 0 , and the one Ca2 moves toward the OH − byaround 0.73% of a 0 . The OH − −Ca1 and OH − −Ca2 distancesboth increase by around 0.25% and 1.20% of a 0 , respectively,implicating a repulsion of the OH − impurity to the neighborcalcium atoms. Finally, the relaxations of neighbor fluorineatoms are slight and less than 0.4% of a 0 .Table 1 also presents the effective charges of the OH − andsurrounding atoms for Config OH (111) . The total charge of theOH − , i.e., the sum of the O and H charges, is −0.722 e, beingmuch smaller than the charge of the substituted fluorine atom(−0.902 e) by 0.180 e. Around 0.097 and 0.072 e localized onthe four nearest Ca and six second-nearest F, respectively,transfer inward to the OH − . For Configs HO (111) and OH (100) ,the effective charges of OH − are −0.713 and −0.737 e, beingclose to the corresponding value of Config OH (111) . We alsocalculated the OH − charges in Ca(OH) 2 and Ba(OH) 2 crystals.The results show that the total effective charges of OH − inCa(OH) 2 and Ba(OH) 2 are equal to −0.781 and −0.825 e,respectively. The OH − charge in Ca(OH) 2 is larger than OH −as impurities in CaF 2 crystal by around 0.4−0.7 e , and thisphenomenon can be explained by the fact that fluorine has astronger oxidative property than that of OH − . It is well-knownthat the hydroxyl has a considerable covalency between theoxygen and hydrogen, which is also demonstrated by our bondpopulation calculations for the OH − −CaF 2 systems. Thepresence of the covalency of OH − in CaF 2 is also clearlyshown in the charge density map (see Figure 2). The covalentbonds between the oxygen and hydrogen atoms are 486, 508,and 536 me for Configs OH (111) , HO (111) , and OH (100) ,respectively. Compared with the covalent bonds in Ca(OH) 2(458 me) and Ba(OH) 2 (434 me) crystals, the covalency of theOH − impurities in CaF 2 is stronger than that in the hydroxidecrystals. Here, we can conclude that OH − as an atomic grouphas a steady geometrical structure instead of electronicproperties in different materials.Alkaline-earth fluorides with defects degrade their opticalquality and exhibit optical absorption. Our calculations on thedefect levels induced between the valence bands (VBs) andconduction bands (CBs) suggest a possible mechanism for theoptical absorption. In the one-electron approximation scheme,Figure 2. Electron density contours in CaF 2 with OH − from the (110)side view, being from 0 to 0.4 e/bohr 3 with a linear increment of 0.01e/bohr 3 .the experimentally observed optical absorption could be due toan electron transition from the ground state to the empty bandinduced by the OH − impurities. Our calculated band structureregarding the OH − -impurity system of Config OH (111) is shownin Figure 3, and the optical band gaps for Configs OH (111) ,Figure 3. Calculated B3PW band structure for the 96-atom supercellmodeling the OH − impurity in CaF 2 for Config OH (111) .HO (111) and OH (100) are collected in Table 2. The optical bandgaps between the VBs and CBs for the CaF 2 96-atom supercellTable 2. Direct Optical Band Gaps (eV) (Γ → Γ) of theOH − -Impurity Systems for Configs OH (111) ,HO (111) , andOH (100)gaps OH (111) HO (111) OH (100)O → H 9.04 8.99 9.04O → CB 9.74 9.78 10.24VB → H 10.47 10.52 10.65VB → CB 11.17 11.32 11.85containing a OH − at the Γ point are 11.17, 11.32, and 11.85 eVfor Configs OH (111) ,HO (111) , and OH (100) , respectively, beingmuch larger than the relevant gap of the perfect CaF 2 crystal(10.96 eV). It is implied that the OH − impurities widen theVB−CB gap, especially for Config OH (100) . For Config OH (111) ,the empty defect level induced by OH − impurities is located0.70 eV below the bottom of the CB at the Γ point (see Figure 3).The occupied defect levels, containing two superposed bands6394dx.doi.org/10.1021/jp211075g | J. Phys. Chem. C 2012, 116, 6392−6400

The Journal of Physical Chemistry C(the gap is less than 0.01 eV), induced by OH − impurities, arelocated 1.43 eV above the VB top at the Γ point. Since hydroxylhas weaker oxidative property than that of fluorine, the hydroxybinding force to the outer-shell electrons is smaller, leading tothe occupied OH − bands shifting upward with respect to theVB top, mainly consisting of F outer p orbitals. From Figure 3and Table 2, we conclude that the first optical absorption,corresponding to an electron transition from the occupied OH −bands to the empty OH − band, should be centered around9.04 eV, being much larger than the relevant value of 4.24 eVfor CaF 2 containing F centers (an electron trapped in thefluorine vacancy). 22 It is because the trapped electron in the Fcenter is more delocalized than the valence electron ofhydroxyl. Unlike the (111)-oriented configurations, for ConfigOH (100) , the two occupied OH − bands separate slightly and thegap is around 0.05 eV.To further study the electronic structure and electrontransitions in a OH − -impurity system, we calculated the densityof states (DOS) of the OH (111) system, as we can see in Figure 4.Articlecorresponding to the substitutional OH − impurity located atthe No. 1, 3, 4, and 6 fluorine sublayers, respectively, as we cansee in Figure 5. As discussed before, hydroxyls orient the (111)Figure 5. Schematic sketch of the (111) slab containing OH −impurities. The big and small circles denote oxygen and hydrogenatoms, respectively.Figure 4. Total and partial density of states (DOS) for the OH −impurities (Config OH (111) ) in the CaF 2 crystal.According to our calculation, the O p orbitals form the twosuperposed occupied OH − bands, named O bands, and the Hs orbitals do the major contribution to the empty defect band(so-called H band) below the CB bottom. Unlike the occupiedO bands with a very sharp peak in the DOS figure, the DOS ofthe unoccupied H band is diffused and very close to the CB.Additionally, the O p orbitals also make some contribution to theVB top, as we can see Figure 4, which mainly consists of F porbitals in perfect CaF 2 crystal.B. OH − Impurities in the CaF 2 Surface. As an extensionof previous studies on hydroxyl impurities in CaF 2 bulks, weperformed calculations for surface OH − impurities. For a (111)slab of CaF 2 , there are three sublayers in each F−Ca−F layerfrom the side view, and OH − impurities could be only locatedat the upper and lower fluorine sublayers. So, a OH − at onefluorine sublayer has two configurations corresponding to thecases of O above H and H above O, labeled OH and HO,respectively, in this paper. We calculated eight differentconfigurations of the surface OH − impurities, named ConfigOH 11 , HO 11 , OH 12 , HO 12 , OH 21 , HO 21 , OH 22 , and HO 22 ,6395direction in CaF 2 bulks. However, we could not confirmwhether the OH − orients also along the (111) direction forsurface OH − -impurity systems. Therefore, we additionallysimulated the eight configurations mentioned above, butwhose initial guessed orientations are not along the (111)axis accurately, in which some configurations do not convergeto the (111) direction after geometrical relaxations via a searchof the minimum total energy, indicating that the (111)-orientedOH − is not the most stable configuration for surface OH − -impurity systems. We add the superscript (|) or (\) to expressthe (111)-oriented and (111)-unoriented OH − impurities,(|)respectively, such as Configs OH 11 and OH (\) 11 , etc. Ourcalculated results show that the energetically most favorableconfiguration for the surface OH − impurity is Config HO (\) 11 ,inwhich the angle between the OH − axis and the (111) directionis around 3.2°. Table 3 lists the relative energies of ConfigTable 3. Total Energies (eV) of All the Surface OH − -(\)aImpurity Configurations with Respect to Config HO 11(\) (|)sublayer HO OH HO OH11 0.00 +0.62 +0.09 +0.7012 +0.62 +0.73 +0.70 +1.0621 +0.62 +0.64 +0.95 +0.8222 +0.63 +0.76 +0.70 +1.14a (|) and (\) express the (111)-oriented and (111)-unoriented OH − ,respectively.HO (\) 11 for other configurations. It implicates a trend of OH −impurities locating near the surface. From Table 3, we foundthat most of Configs HO have lower energies with respect tothe corresponding Configs OH, indicating a preference of thehydrogen atom locating above the oxygen atom for the surfaceOH − -impurity systems, and the (111)-unoriented Configs aredx.doi.org/10.1021/jp211075g | J. Phys. Chem. C 2012, 116, 6392−6400

The Journal of Physical Chemistry CArticlethe more energetically favorable configurations with respect tothe corresponding (111)-oriented Configs. Additionally, wealso calculated the (111) CaF 2 slabs full covered by OH − . Forthe full-covered slabs, hydroxyls can only replace the surfacefluorine sublayer, so we may classify the full-covered slabs intofour configurations, i.e., HO (|) full ,HO (\) full ,OH (|) full , and OH (\) full . Ourcalculated results demonstrate that the most stable full-coveredconfiguration is Config HO (\) full , in which the deviation angleequals around 2.2°, and the total energies of Configs HO (|) full ,OH (|) full , and OH (\) full are larger than that of Config HO (\) full by 0.06,0.63, and 0.58 eV, respectively. So, we can conclude that for thefull-covered slabs, hydrogen atoms prefer to locate aboveoxygen atoms obliquely. Configs HO (\) 11 and HO (\) full are morestable than other surface OH − systems; therefore, we mainlyfocus our current discussion on these two Configs.The geometrical structures of the surface OH − are calculatedand depicted in Table 4. According to our studies on bulkTable 4. Geometrical Properties of the Surface OH −Impurities a for all Configs(\) (|)sublayer HO OH HO OH11 0.96(3.2°) 0.97(28°) 0.97 0.9812 0.97(5.3°) 0.97(58.1°) 0.97 0.9621 0.97(65.0°) 0.96(4.8°) 0.96 0.9722 0.97(5.0°) 0.96(57.9°) 0.97 0.95full 0.96(2.2°) 0.97(2.5°) 0.97 0.98a OH − length (Å) and deviation angle shown in brackets.OH − -impurity systems, the lengths of OH − in CaF 2 and BaF 2 ,as well as in H 2 O, Ca(OH) 2 , and Ba(OH) 2 , are all around0.96−0.97 Å, indicating that the OH − as a diatomic group has asteady geometrical structure. Our calculated CaF 2 surface OH − -impurity lengths for all the configurations are around 0.96−0.98 Å,as we can see in Table 4. It is implied that the surface effect onthe length of surface hydroxyls is not remarkable. From Table4, we found that some Configs, such as OH (\) 12 ,HO (\) 21 , andOH (\) 22 , have very big deviation angles (around 60°), and theorientations of other Configs approach the (111) direction. Inan ideal cubic CaF 2 bulk, the angle between the (111) and(100) axes is 54.7°, being close to those big obliquities ofaround 60°. Therefore, we can consider these Configs with bigdeviation angles as Config OH (100) , namely, the (100)-orientedconfiguration in the bulk case, locating near the (111) surface.It is implied that despite the (111)-oriented OH − beingenergetically more favorable in CaF 2 bulk, hydroxyls located atsome specific fluorine sublayers near the surface prefer the(100) orientation. Here, we can classify the eight (111)-unorientedconfigurations into three OH − types, i.e., OH (111) ,HO (111) ,andOH (100) in the bulk case. Configs OH (\) 11 ,HO (\) 12 ,OH (\) (\)21 ,andHO 22belong to the OH (111) type, Config HO (\) 11 belongs to the HO (111)type, and Configs OH (\) 12 , HO (\) (\)21 , and OH 22 belongs to theOH (100) type. From Tables 3 and 4 and this classification, we canconclude that OH − impurities with HO (111) ,OH (111) ,OH (100) ,andOH (111) configurations prefer to locate at the No.1, 3, 4, and 6fluorine sublayers, respectively.The relaxations of atoms surrounding the surface OH −impurity are shown in Figure 6 and Table 5. For ConfigHO (\) 11 , all the atoms near the surface shift toward the positiveY-axis from the top view, as we can see Figure 6. The oxygenand the six nearest fluorine atoms, i.e., F1, F2, and F3, on theupper sublayer of the first layer have considerable XY-shifts6396Figure 6. Top view of the surface OH − -impurity nearest-neighborgeometry with an indication of relaxation shifts for Config HO (\) 11 . Thedirections of atomic displacements in the XY-plane are shown witharrows. The fluorine and calcium atoms in different shells are labeled.The upper and lower panels denote the first and second layers of the(111) CaF 2 slab, respectively.over 2% of a 0 , the XY-displacements of fluorine atoms locatedat the lower sublayer of the first layer and the upper sublayer ofthe second layer are around 1−2% of a 0 , and the XYtranslationsof the fluorine atoms on the lower sublayer of thesecond layer equal 0.7% of a 0 approximately. Here, we canconclude that the atomic layers containing surface OH −impurities have a remarkable XY-translation. Because of thesurface shrinking effect, the atomic coordinates of most of thesurface atoms reduce, whereas the oxygen atom shifts outwardfrom the surface by around 2.22% of a 0 . Table 5 also lists thedisplacements of atoms at the top two layers for Config HO (\) full ,i.e., the full-covered case. Similar to Config HO (\) 11 , the toplayers have an obvious XY-translation with respect to thedeeper layers and the surface OH − layer moves upward byaround 3.32% of a 0 , implicating a dilating effect induced by fullcoveringhydroxyls.Table 6 presents the effective charges of the surface OH − forall the (111)-unoriented configurations. The OH − charges formost Configs are larger than the OH − charge in the CaF 2 bulk(−0.722 e). Especially for Config HO (\) 11 , the effective charge ofthe surface OH − equals −0.746 e and is larger by around 0.024 e.Because of the surface effect, −0.005 e localized on thehydrogen atom transfers inward toward the surface and the oxygenatom attracts −0.028 e from the surrounding atoms. We alsocalculated the effective charges of atoms surrounding the OH −impurity,aswecanseeinTable5.Thechargedifferencesofthedeeper fluorine and calcium atoms are negligible, whereas thedx.doi.org/10.1021/jp211075g | J. Phys. Chem. C 2012, 116, 6392−6400

The Journal of Physical Chemistry CArticleTable 5. Atomic Relaxations (as a Percentage of the Lattice Constant, 5.50 Å) and Effective Charges (Q(e)) of the (111) CaF 2Surfaces Containing OH − for Configs HO (\) (\)a11 and HO 11HO 11(\)layer sublayer atoms (no.) XY (% a 0 ) Z (% a 0 ) Q (e) ΔQ (e) atoms XY (% a 0 ) Z (% a 0 ) Q (e) ΔQ (e)no. l 1 0 (1) 1.96 +2.22 −1.025 − O 0.96 +3.32 −1.010 −Fl (2) 2.37 −0.18 −0.895 +0.007F2 (2) 2.19 −0.15 −0.895 +0.007F3 (2) 2.67 −0.32 −0.895 +0.0072 Cal (1) 2.46 −0.52 +1.769 −0.034 Ca 1.01 −0.31 +1.718 −0.085Ca2 (2) 1.69 −0.31 +1.771 −0.032 F 0.67 −0.63 −0.945 −0.0433 F4 (1) 1.32 −0.71 −0.918 −0.016F5 (2) 1.66 −1.00 −0.918 −0.016F6 (1) 1.35 −0.54 −0.906 −0.004F7 (2) 1.52 −0.50 −0.907 −0.005no. 2 1 Fl (1) 1.74 −0.24 −0.900 +0.002 F 0.78 −0.09 −0.902 0F2 (2) 1.67 −0.18 −0.900 +0.002F3 (1) 1.60 −0.01 −0.901 +0.001F4 (2) 1.66 −0.17 −0.900 +0.0022 Cal (1) 1.20 −0.35 +1.801 −0.002 Ca 0.58 −0.27 +1.802 −0.001Ca2 (2) 1.22 −0.45 +1.801 −0.0023 F5 (l) 0.76 −0.47 −0.902 0 F 0.37 −0.33 −0.902 0F6 (2) 0.79 −0.35 −0.901 +0.001F7 (2) 0.78 −0.40 −0.901 +0.001F8 (2) 0.69 −0.33 −0.901 +0.001a Positive signs in Z-columns correspond to outward atomic displacements (toward the vacuum). The directions of atomic displacements in the XYplaneare indicated in Figure 6. ΔQ(e) labels the change in the effective charge compared to perfect CaF 2 crystal (Q Ca = +1.803 e, Q F = −0.902 e).The symbols in atom columns are defined in Figure 6.(\)HO fullTable 6. Effective Charges (e) and Bond Populations (me)ofSurface OH − Impurities for All the (111)-UnorientedConfigurationselectron transfer regarding the first-layer atoms is considerable.Around −0.160 e localized on the fluorine sublayer of the firstlayer (including the six fluorine atoms and one OH − impurity) isattracted by the three Ca atoms and six F atoms at the second andthird sublayers. Tables 6 and 5 also list the results of effectivecharge calculations for the OH − full-covered configurations. TheOH − charge for Config HO (\) full is −0.771 e, being much larger thanthat of the bulk case by 0.049 e, and effective charges of −1.010and +0.239 e are localized on the O and H, respectively. Around−0.085 and −0.043 e localized on the surface OH − transfersdownward to the nearest Ca and F, respectively. Additionally, wecompared Config HO (\) full with Ca(OH) 2 for the atomic effectivecharges and geometrical structures. The OH − charge of −0.781 ein Ca(OH) 2 is close to that of Config HO (\) full (−0.771 e). The H−(\)O−Ca angles in Ca(OH) 2 (around 118°) and Config HO full(around 113°) are also closed. Therefore, we can consider the fullcoveringOH − as a piece of (CaOH) + membrane filmed on theCaF 2 surface.Table 6 also lists the bond populations for the surface OH − -impurity and full-covered systems. We found that the OH −covalencies for Configs HO (\) 11 (546 me), OH (\) 12 (544 me), and(\) (540 me) are much stronger than that of the bulk case byOH 22HO (\) OH (\)sublayer O H O−H O H O−H11 −1.025 +0.280 +546 −1.003 +0.272 +49012 −1.007 +0.278 +494 −1.032 +0.290 +54421 −1.004 +0.283 +496 −1.004 +0.280 +49822 −1.003 +0.280 +494 −1.023 +0.285 +540full −1.010 +0.239 +512 −1.017 +0.278 +492639760, 58, and 54 me, respectively. The bond populations betweenoxygen and hydrogen for other Configs are all larger than thatof the bulk OH − impurity. We can conclude here that thesurface effect strengthens the covalency of OH − impuritieslocated near the surface. Compared with the covalent bonds ofhydroxyls in Ca(OH) 2 (458 me) and Ba(OH) 2 (434 me)crystals, the covalency of surface OH − impurities is also muchstronger. For the OH − full-covered configuration, i.e., Config HO (\) full ,the surface effect on the strengthening OH − -covalencyis not quite pronounced, whereas the bond populationequals 512 me, still being much larger than that in Ca(OH) 2(458 me). Combining the previous discussion about thegeometrical structures of OH − impurities,weindicatethatthe OH − as an atomic group has a steady geometricalstructure instead of electronic properties in differentmaterials. Also the main surface effect on the OH − impuritiesis on the electronic structures instead of the geometricalstructures.To investigate the surface effect on the optical band gaps, westudied the band structures of the surface OH − -impuritysystems. The theoretical optical band gaps for all the (111)-unoriented configurations are collected in Table 7, and theband structure of Config HO (\) 11 is shown in Figure 7. FromTable 7, we can conclude that the surface effect reduces theVB → CB gaps, which are around 11.1−11.5 eV and smallerthan that in the bulk cases (11.17, 11.32, and 11.85 eV forConfigs OH (111) ,HO (111) , and OH (100) respectively). The O →H gaps, i.e., the first possible optical absorption, for most of theconfigurations except Config OH (\) 11 , are larger than thecorresponding gaps in the bulk cases (9.04, 8.99, and 9.04 eVfor Configs OH (111) , HO (111) , and OH (100) , respectively).Especially for Configs HO (\) 12 and OH (\) 22 , the O → H gapsare larger by around 0.3 eV. Further analysis of the band gapsshows that for most of the surface OH − -impurity configurations,dx.doi.org/10.1021/jp211075g | J. Phys. Chem. C 2012, 116, 6392−6400

The Journal of Physical Chemistry CArticleTable 7. Direct Optical Band Gaps (eV) (Γ → Γ) of the Surface OH − for the 10 (111)-Unoriented Configurations(\) (\) (\) (\) (\) (\) (\) (\) (\) (\)gaps HO 11 HO 11 HO 12 HO 12 HO 21 HO 21 HO 22 HO 22 HO full HO fullO 1 → H 9.23 8.97 9.37 9.21 9.19 9.23 9.26 9.32 7.89 8.75O 2 → H 9.24 8.98 9.38 9.21 9.22 9.24 9.26 9.34 7.89 8.76O 1 → CB 9.79 9.46 9.77 9.86 9.76 9.96 9.88 10.06 9.36 9.83O 2 → CB 9.80 9.47 9.78 9.86 9.79 9.97 9.88 10.08 9.36 9.84VB → CB 11.31 11.09 11.0 11.36 11.08 11.16 11.08 11.46 11.10 11.32Figure 7. Calculated B3PW band structures for Configs HO (\) 11 (left)and HO (\) full (right).the occupied defect levels induced by O atoms move downwardaround 0.1−0.3 eV (toward VB) with respect to the bulk cases,leading to widening of the O → H gaps. From Figure 7, we alsofound that the empty defect band induced by H atoms is veryclose to the CB bottom and there is nearly no separated Hband, which almost superposes with the CB. Unlike the surfaceOH − -impurity systems, the O → H gaps for the OH − fullcoveredsystems are narrower than that of the bulk case byaround 1.1 and 0.3 eV for Configs HO (\) full and OH (\) full , respectively.Especially for Config HO (\) full ,theO→ H gap reduces to 7.89 eV,being much smaller than the relevant gap of 9.04 eV in the bulkcase. It is mainly due to the downward shift of the unoccupiedH band, which moves toward the O bands by around 1 eV, as wecanseeFigure7.To further study the electronic structure and electron transitionsin a surface OH − -impurity system, we calculated the DOSof Config HO (\) 11 , as we can see in Figure 8. Our previous bulkOH − -impurity study demonstrated that the O p orbitals formthe two superposed occupied O bands, i.e., so-called O bands,and the H s orbitals do the major contribution to the emptydefect band, named H band in the bulk case, below the CBbottom. In the 2D cases, the symmetry of p x ,p y , and p z states isbroken by the (111)-terminated surface; therefore, the p-stateelectrons are not equivalent in the three directions. Our DOScalculations show that the two superposed occupied O bandsmainly consist of O p x and p y orbitals.Because of the surface effect, the O p x and p y orbitals movedownward, toward the VB top, with respect to the O p orbitalsin the bulk cases, and this leads to narrowing of the VB → Ogaps and widening of the O → H gaps. As discussion above,there is no remarkably separated defect band induced by Hatoms located below the CB bottom, being in agreement withour DOS calculation on H atoms (see Figure 8).Figure 8. Total and projected DOS for Config HO 11 (\) .C. Formation of OH − Impurities. Finally, we studied theformation of OH − impurities in CaF 2 . We computed theformation energy of the OH − impurity in CaF 2 crystal. In thesupercell calculation for an isolated OH − , the formation energyof a neutral (the charge of total supercell is neutral) OH −impurity in CaF 2 could be expressed as follows(OH−) (iso)= +− (iso)EformationEF− E(OH ) − EOH− − E(perfect)(1)where E (iso) F− and E (iso) OH− are the energies for isolated fluorine andhydroxyl ions and E(OH − ) and E(perfect) are the totalenergies of the defective crystal containing a OH − impurity andthe perfect crystal, respectively. Our calculated OH − -impurityformation energy equals −1.00 eV, indicating that the totalenergy of a OH − -impurity system and an isolated F − is lowerthan the total energy of a perfect CaF 2 crystal and an isolatedOH − . It implicates that isolated hydroxyls are favorite to substitutefluorine ions in CaF 2 crystal. According to our previousdiscussion, the surface OH − impurities with Config HO (\) 11 havethe lowest energy, which means that the hydroxyl adsorptionon the CaF 2 surface is favorable energetically.On the other hand, the formation of OH − impurities in CaF 2crystal may also be due to the aggregation of separated oxygenand hydrogen impurities. To verify this aggregation, we calculatedthe association energy, defined as the energy differencebetween the remote oxygen and hydrogen impurities, and theOH − impurity. The corresponding value is +6.12 eV. With thisdefinition, the positive sign indicates stable aggregation. In thisformation mode, there should be isolated oxygen and hydrogenimpurities in CaF 2 crystal. Similar to the calculation on theformation energy of the OH − impurity in CaF 2 crystal, we alsocalculated the formation energies of the oxygen and hydrogen6398dx.doi.org/10.1021/jp211075g | J. Phys. Chem. C 2012, 116, 6392−6400

The Journal of Physical Chemistry CArticleimpurities in CaF 2 . For the oxygen impurity, the formationenergy equals −0.71 eV. The negative sign indicates the stabilityof oxygen replacing fluorine in CaF 2 . We also investigated theoxygen impurity located near the (111) CaF 2 surface. Accordingto our calculation, the energy of the oxygen located at the surfacehas the smallest value, indicating a trend of the oxygen impuritylocated near the surface. The total energies of the oxygenimpurity at the second, third, and fourth fluorine sublayers arelarger than that for the first fluorine sublayer by 1.14, 1.24, and1.16 eV, respectively. Additionally, for the hydrogen impurity, theformation energy is +0.33 eV. Unlike the oxygen case, theformation of a hydrogen impurity in CaF 2 needs extra energy.Further, according to our calculation regarding a hydrogen atomadded on the CaF 2 surface, the hydrogen atom has a trend ofseparating from the surface.Here, we can summarize that oxygen does the primarycontribution to the formation of OH − impurities in CaF 2 .Isolatedoxygen atoms surrounding CaF 2 adsorb on the surface easily, andthen, the oxygen impurities trap the hydrogen atoms near thesurface, forming the OH − impurities. So, if we can control theconcentration of the oxygen atoms near the surface, the formationof OH − impurities could be avoided in CaF 2 crystal.IV. CONCLUSIONSWe applied the first-principles approach within the hybridDFT-B3PW scheme to calculations on OH − in CaF 2 . Threebulk configurations including Configs OH (111) ,HO (111) , andOH (100) , and 16 surface configurations including 8 (111)-oriented and 8 (111)-unoriented OH − impurities were studied.For the bulk case, Config OH (111) , in which the hydroxylorients along the (111) axis and the oxygen occupies a regularfluorine site, is the energetically most favorable configuration.For the surface case, we found that Config HO (\) 11 , in which theOH − is located at the upper fluorine sublayer of the first surfacelayer, H lies above O obliquely, and the obliquity is around3.2°, is the most stable configuration for the surface OH − -impurity systems. We also performed calculations on the (111)CaF 2 surfaces full covered by OH − . Config HO (\) full has thelowest total energy among the four OH − full-covered configurations,and the deviation angle equals around 2.2°. Thelengths of surface OH − impurities for all the configurations arearound 0.96−0.98 Å, being close to that in the bulk cases(0.95−0.97 Å), as well as in water molecule and Ca(OH) 2 andBa(OH) 2 crystals, indicating that the surface effect on thelength of surface hydroxyls is not remarkable and the OH − as adiatomic group has a steady geometrical structure. Thecalculations on the relaxations of atoms surrounding the surfaceOH − impurity demonstrated that the atomic layers containingsurface OH − impurities have a remarkable XY-translation.Effective charge analysis shows that the OH − charge equalsaround −0.722 e, being much smaller than the fluorine (substitutedby the OH − ) charge (−0.902 e) in perfect CaF 2 crystal,and some charges localized on the neighbor atoms (especiallyfor the nearest calcium atoms) transfer inward to the OH − .Because of the surface effect, the charges of the surface OH −impurities are larger than those of the bulk cases for most of thesurface OH − configurations. Bond population calculationsindicate that the surface effect strengthens the covalency ofOH − impurities located near the surface. The main surfaceeffect on the OH − impurities is on the electronic structuresinstead of the geometrical structures.The studies on band structures and DOS of the OH − -impurity systems demonstrate that there are two defect levels6399induced by OH − impurities. One is two superposed occupied Obands mainly consisting of the O p orbitals, located above theVBs, and the other is an empty H band to which the H sorbitals do the major contribution, almost superposing with theCBs. Because of the surface effect, the O bands move downward,toward the VBs with respect to these bands in the bulk case, andthis leads to narrowing of the VB → O gap and widening of theO → H gap which corresponds to the first optical absorption.Finally, we investigated the formation of OH − impurities inCaF 2 . The calculation on the formation energy of the OH −impurity shows that isolated hydroxyls are favorite to substitutefluorine ions and adsorb on the surface energetically. On theother hand, the formation of OH − impurities in CaF 2 may alsobe due to the aggregation of separated oxygen and hydrogenimpurities. The formation of oxygen impurities is favorable,whereas that of hydrogen impurities is unfavorable energetically.So, we concluded that oxygen does the primary contribution tothe formation of OH − impurities in CaF 2 , and if we can controlthe concentration of the oxygen atoms near the surface, theformation■of OH − impurities could be avoided in CaF 2 crystal.AUTHOR INFORMATIONCorresponding Author*E-mail address: shihongting@gmail.com.NotesThe authors declare no competing financial interest.■ ACKNOWLEDGMENTSH.S. was supported by NSFC Grant No. 11004008.R.I.E. was supported by ESF Grant No. 2009/0202/1DP/1.1.1.2.0/APIA/VIAA/141.■ REFERENCES(1) Letz, M.; Parthier, L. Phys. Rev. B 2006, 74, 064116.(2) Burnett, J. H.; Levine, Z. H.; Shirley, E. L. Phys. Rev. B 2001, 64,241102(R).(3) Letz, M.; Parthier, L.; Gottwald, A.; Richter, M. Phys. Rev. B 2003,67, 233101.(4) Shimizu, Y.; Minowa, M.; Suganuma, W.; Inoue, Y. Phys. Lett. B2006, 633, 195.(5) Barth, J.; Johnson, R. L.; Cardona, M.; Fuchs, D.; Bradshaw, A. M.Phys. Rev. B 1990, 41, 3291.(6) Bennewitz, R.; Smith, D.; Reichling, M. Phys. Rev. B 1999, 59,8237.(7) Catti, M.; Dovesi, R.; Pavese, A.; Saunders, V. R. J. Phys.: Condens.Matter 1991, 3, 4151.(8) Ching, W. Y.; Gan, F. Q.; Huang, M. Z. Phys. Rev. B 1995, 52,1596.(9) de Leeuw, N. H.; Cooper, T. G. J. Mater. Chem. 2003, 13, 93.(10) de Leeuw, N. H.; Purton, J. A.; Parker, S. C.; Watson, G. W.;Kresse, G. Surf. Sci. 2000, 452, 9.(11) Foster, A. S.; Barth, C.; Shluger, A. L.; Nieminen, R. M.;Reichling, M. Phys. Rev. B 2002, 66, 235417.(12) Gan, F. Q.; Xu, Y. N.; Huang, M. Z.; Ching, W. Y.; Harrison, J. G.Phys. Rev. B 1992, 45, 8248.(13) Jockisch, A.; Schroder, U.; Dewette, F. W.; Kress, W. J. Phys.:Condens. Matter 1993, 5, 5401.(14) Ma, Y. C.; Rohlfing, M. Phys. Rev. B 2008, 77, 115118.(15) Merawa, M.; Llunell, M.; Orlando, R.; Gelize-Duvignau, M.;Dovesi, R. Chem. Phys. Lett. 2003, 368, 7.(16) Puchin, V. E.; Puchina, A. V.; Huisinga, M.; Reichling, M.J. Phys.: Condens. Matter 2001, 13, 2081.(17) Puchina, A. V.; Puchin, V. E.; Kotomin, E. A.; Reichling, M.Solid State Commun. 1998, 106, 285.(18) Rubloff, G. W. Phys. Rev. B 1972, 5, 662.dx.doi.org/10.1021/jp211075g | J. Phys. Chem. C 2012, 116, 6392−6400

The Journal of Physical Chemistry CArticle(19) Schmalzl, K.; Strauch, D.; Schober, H. Phys. Rev. B 2003, 68,144301.(20) Verstraete, M.; Gonze, X. Phys. Rev. B 2003, 68, 195123.(21) Wu, X.; Qin, S.; Wu, Z. Y. Phys. Rev. B 2006, 73, 134103.(22) Shi, H.; Eglitis, R. I.; Borstel, G. Phys. Rev. B 2005, 72, 045109.(23) Shi, H.; Eglitis, R. I.; Borstel, G. J. Phys.: Condens. Matter 2006,18, 8367.(24) Shi, H.; Eglitis, R. I.; Borstel, G. J. Phys.: Condens. Matter 2007,19, 056007.(25) Shi, H.; Eglitis, R. I.; Borstel, G. Comput. Mater. Sci. 2007,39, 430.(26) Jia, R.; Shi, H.; Borstel, G. Phys. Rev. B 2008, 78, 224101.(27) Shi, H.; Luo, L.; Johansson, B.; Ahujia, R. J. Phys.: Condens.Matter 2009, 21, 415501.(28) Shi, H.; Jia, R.; Eglitis, R. I. Phys. Rev. B 2010, 81, 195101.(29) Adler, H.; Kveta, I. S.B. Osterreich Akad. Wiss. Math.-Nat. Klasse.Abt. II 1957, 166, 199.(30) Bontinck, W. Physica 1958, 24, 650.(31) Becke, A. D. J. Chem. Phys. 1993, 98, 5648.(32) Perdew, J. P.; Wang, Y. Phys. Rev. B 1986, 33, 8800.(33) Perdew, J. P.; Wang, Y. Phys. Rev. B 1989, 40, 3399.(34) Perdew, J. P.; Wang, Y. Phys. Rev. B 1992, 45, 13244.(35) Saunders, V. R.; Dovesi, R.; Roetti, C.; Causa, M.; Harrison,N. M.; Orlando, R.; Zicovich-Wilson, C. M. CRYSTAL-2006 UserManual; University of Torino: Torino, Italy, 2006.(36) Dovesi, R.; Ermondi, C.; Ferrero, E.; Pisani, C.; Roetti, C. Phys.Rev. B 1984, 29, 3591.(37) Monkhorst, H. J.; Pack, J. D. Phys. Rev. B 1976, 13, 5188.(38) Pisani, C. Quantum-Mechanical Ab-initio Calculations of theProperties of Crystalline Materials ; Lecture Notes in Chemistry 67;Springer-Verlag: Berlin, Heidelberg, Germany, 1996.6400dx.doi.org/10.1021/jp211075g | J. Phys. Chem. C 2012, 116, 6392−6400