Ab Initio Calculations of Hydroxyl Impurities in CaF2

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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
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Ab Initio Calculations of Hydroxyl Impurities in CaF2

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