Electronic Structures and Optical Properties of BiOX (X = F, Cl, Br, I) via DFT Calculations

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1 Electronic Structures and Optical Properties of BiOX (X = F, Cl, Br, I) via DFT Calculations WEN LAI HUANG State Key Laboratory of Multi-Phase Complex Systems, Institute of Process Engineering, Chinese Academy of Sciences, Beijing , People s Republic of China Received 14 April 2008; Accepted 12 November Published online 29 December 2008 in Wiley InterScience ( Abstract: Based on the density functional theory (DFT), the lattice constants and atomic positions of BiOX (X = F, Cl, Br, I) species have been optimized, and the electronic and optical properties of the relaxed species have been calculated, with Bi 5d states considered or not. Relaxation generally results in the shrinkage in a and the expansion of c. Relaxed BiOCl, BiOBr, and BiOI present indirect band gaps, whereas BiOF exhibits a direct or somewhat indirect band-gap feature corresponding to the relaxation and calculation with the Bi 5d states or not. The bottom of the conduction band is quite flat for relaxed BiOI, and apparently flat in BiOBr, and shows observable flatness in BiOCl as well when considering the Bi 5d states. The top of the valence band is rather even as well for some species. The obtained maximum gaps for relaxed BiOF, BiOCl, BiOBr, and BiOI are 3.34, 2.92, 2.65, and 1.75 ev, respectively. The density peak of X np states in the valence band shifts toward the valence band maximum with the increasing X atomic number. The bandwidths, atomic charges, bond orders, and orbital density have also been investigated along with some optical properties. q 2008 Wiley Periodicals, Inc. J Comput Chem 30: , 2009 Key words: density functional theory; bismuth oxyhalide; band structure; density of states; optical properties Introduction Besides excellent performance in the oxidative cracking or dehydrogenation reactions, 1 3 layered bismuth oxyhalides have demonstrated outstanding photocatalytic activities and, more recently, 4 7 attracting research interest in both the experimental and theoretical aspects. According to the absorption spectra, the band gap of BiOCl has been determined to be indirect 4 with the width of 3.44, 3.46, or 3.51 ev within the ultraviolet range, 4,5,8 whereas BiOBr and BiOI exhibit band gaps of 2.91 and 1.92 ev, respectively, within the visible-light range (unfortunately, the gap features have not been determined). 5,6 Nanoparticles of BiOCl, BiOBr, and BiOI have been synthesized in reverse microemulsions, and concerning BiOI, the band-gap expansion was observed from 1.94 ev for the bulk material up to 2.96 ev for the nanoparticles. 7 BiOCl nanoparticles with novel morphologies has been fabricated in confined nanoreactors formed by self-organized lyotropic liquid crystals. 9 Bismuth oxyhalide nanobelts and nanotubes have also been prepared via hydrothermal method, and the absorption patterns were observed to be dependent on the synthetic conditions. 10 Recently, rapid synthesis of metal oxyhalides has been reported via exothermic solid-state metathesis (SSM) reactions, 11 and Chen et al. 12 systematically examined the controlling parameters under solution-phase conditions, and created BiOCl nanocrystals as well. 13 As regards with the theoretical aspect, the electronic structure of BiOCl has been calculated via the tight-binding linear muffintin orbital (TB-LMTO) method using local density approximation (LDA), 4 where 6s and 6p states were considered for Bi. The indirect band-gap nature computed is in agreement with the experimentally observed linear relationship between the square root of the product (of absorption coefficient and photon energy) and energy, although the achieved gap width is relatively small. In this work, the density functional theory (DFT) calculations will be reported on the electronic structures and optical properties of BiOX (X = F, Cl, Br, and I) fully relaxed considering either the Bi 5d states as valence basis sets or not. The results will be described and compared. Computational Method DFT calculations were conducted using the plane-wave pseudopotential (PW-PP) DFT method as implemented in the CASTEP code. 14 The generalized gradient approximation (GGA) from Correspondence to: W. L. Huang; wlhuang@home.ipe.ac.cn Contract/grant sponsor: National Natural Science Foundation of China; contract/grant numbers: q 2008 Wiley Periodicals, Inc.

2 Electronic and Optical Properties of BiOX 1883 Table 1. Experimental 18 and Optimized Lattice Parameters of BiOX. Species a (Å) d a (%) c (Å) d c (%) d V (%) u X u Bi BiOF / / / BiOF a BiOF b BiOCl / / / BiOCl a BiOCl b BiOBr / / / BiOBr a BiOBr b BiOI / / / BiOI a BiOI b a Relaxed without Bi 5d states. b Relaxed with Bi 5d states. d a : Relative deviation from the experimental a. d c : Relative deviation from the experimental c. d V : Relative deviation from the experimental V (cell volume). Perdew-Burke-Ernzerhof (PBE) 15 was employed for the exchange-correlation functional. Ultrasoft pseudopotentials were used for O, F, Cl, Br, and I, while both ultrasoft and norm-conserving pseudopotentials were utilized for Bi. The 2s and 2p states were considered for O with six electrons, and the ns and np (n = 2, 3, 4, and 5 for X = F, Cl, Br, and I, respectively) states were involved for X with seven electrons. As to Bi, the ultrasoft pseudopotential includes only 6s and 6p states with five electrons, whereas the norm-conserving one involves additionally the semicore 5d states with total 15 electrons. A plane-wave cutoff of 550 or 380 ev was adopted correspondingly when the Bi 5d states were considered or not to achieve a total-energy difference below 0.01 ev/atom, and 12 empty orbitals were applied except during the computation of optical properties where 36 empty orbitals were taken into account to extend the energy range. The Brillouin zone was sampled using a Monkhorst-Pack k-point grid to keep the k-point separation along each of the three reciprocal lattice directions around 0.04 Å 21. Lattice constants and atomic positions were optimized until the energy change between two ionic steps was smaller than ev/atom, all the force components were smaller than 0.01 ev/å, and all the stress components were smaller than 0.02 GPa, through the Broyden, Fletcher, Goldfarb, Shanno (BFGS)-based method. 16 The band structures were calculated along the special lines connecting the following high-symmetry points: G (0,0,0), X (0,0.5,0), Z (0,0,0.5), M (0.5,0.5,0), R (0,0.5,0.5), and A (0.5,0.5,0.5) in the k-space. Atomic and bond populations were evaluated via the Mulliken population analysis, 17 and the spatial distribution of orbital density was investigated by describing the corresponding isosurfaces. The BiOX species belong to the P4/nmm (number 129) tetragonal structure, and the atoms occupy the following special positions: O in 2a, X in 2c with a fractional parameter u X, and Bi also in 2c but with a different parameter u Bi. The experimental lattice parameters 18 are listed in Table 1, and the unit cell of BiOF is illustrated in Figure 1 as a representative. The site notations in this figure will be adopted hereinafter. In this work, the experimental values of lattice parameters were exploited as the starting points, and both the atomic positions and lattice constants were optimized (to accelerate the procedure, the atoms were relaxed first with the cell constants fixed, and then together with the cell relaxation). Electronic structures and optical properties were calculated subsequently using the optimized parameters, and the same Bi pseudopotential as in the relaxation step (two types of Bi pseudopotentials were utilized as mentioned earlier). Results and Discussion Optimized Lattice Structures The optimized lattice parameters are listed in Table 1. Compared with the experimental values, relaxation shrinks the constant a, and inclusion of Bi 5d states impairs the shrinkage. Meanwhile, relaxation elongates the constant c except BiOF with Bi 5d states, dramatically for BiOCl and BiOBr when adopting Bi 5d states. In terms of cell volume, relaxation with Bi 5d states leads to apparent expansion of BiOCl, BiOBr, and BiOI. Because the optimized structures correspond to the ground state (0 K and 0 Pa), and the experimental lattice parameters were determined under ambient conditions, such discrepancies might imply the negative coefficient of thermal volumetric expansion, and anisotropy of thermal linear expansion (positive in the xy plane, whereas negative in the z direction) of these species below room temperature. Figure 1. The unrelaxed BiOF unit cell.

3 1884 Huang Vol. 30, No. 12 Figure 2. The band structures of (a) BiOF, (b) BiOCl, (c) BiOBr, and (d) BiOI relaxed with Bi 5d states. Band Structures The electronic band structures shown in Figure 2 correspond to the relaxed species with the consideration of Bi 5d states. The energy range is kept the same for each species, covering all the occupied bands and the conduction band (the first six empty orbitals). The energy zero is set at the valence-band maximum. According to the analyses of projected atomic wavefunctions in the next section, the Bi 5d orbitals form the lowest highly localized (atomic-like) band, and the localization strengthens with the growing X atomic number (see W Bi5d in Table 2). The X ns orbitals are also rather localized in comparison with those of O 2s and Bi 6s (refer to the bandwidths in Table 2). With the growth in X atomic number, the dispersion of X ns orbitals improves generally, and that of O 2s or Bi 6s ones declines. For all the orbitals (particularly the s-type), general flatness can be observed along the reciprocal [001] direction (MA, GZ, and XR lines), and large dispersion emerges in the reciprocal [100] or [010] (GX and ZR) and [110] (GM and ZA) directions, implicating the marked localization along the z-axis and significant extension along the x-ory-axis. The valence-band orbitals along the reciprocal [001] direction are much flatter within relaxed BiOCl and BiOBr, and relatively dispersive in relaxed BiOF (especially along AM). From BiOF to BiOI, the conduction-band orbitals display improving dispersion along the AM line, and strengthening localization (shrinking bandwidth) along the RX line. Involvement of Bi 5d states increases the W O2s, reducing the W Bi6s (except BiOF) and W Xns (except BiOF) values. Concerning the widths of valence and conduction bands, it is obvious that with the rising X atomic number, the W vb of relaxed BiOX (except BiOF) increases while the W cb decreases. Introduction of Bi 5d states reduces the W vb apparently and narrows the W cb (except BiOF) slightly. It is known that more dispersed valence and conduction bands are more beneficial to the mobility of photo-generated holes and electrons, respectively, bettering the photocatalytic performance. 4,19 21 The widths of valence and conduction bands might be correlated with the structural parameters in Table 3. As disclosed in the next section, the valence band in each species is constructed mainly by the bonding hybridization of Bi 6p, O 2p, and X np orbitals. The Bi atom is coordinated with 4 O and 4 X atoms, Table 2. Band Parameters (in ev) of Relaxed BiOX. Species E g W Bi5d W Xns W O2s W Bi6s W vb W cb E X-peak BiOF a 3.34 / BiOCl a 2.64 / BiOBr a 2.35 / BiOI a 1.57 / BiOF b BiOCl b BiOBr b BiOI b a Relaxed without Bi 5d states. b Relaxed with Bi 5d states. E g : Band-gap width. W Bi5d : Bandwidth of Bi 5d orbitals. W Xns : Bandwidth of X ns orbitals (n 5 2, 3, 4 and 5 for X 5 F, Cl, Br and I respectively). W O2s : Bandwidth of O 2s orbitals. W Bi6s : Bandwidth of Bi 6s orbitals. W vb : Valence-band width. W cb : Conduction-band width. E X-peak : The peak position of X np DOS in the valence band from the valence band maximum.

4 Electronic and Optical Properties of BiOX 1885 Table 3. Bond Angles and Interatomic Distances (Within One Unit Cell if Not Specified) in Relaxed BiOX. Angle (8) Distance (Å) Species Bi O Bi Bi X Bi Bi O Bi1 X1 or Bi2 X2 Bi1 X2 or Bi2 X1 BiOF a BiOCl a c BiOBr a c BiOI a c BiOF b BiOCl b c BiOBr b c BiOI b c a Relaxed without Bi 5d states. b Relaxed with Bi 5d states. c Within two adjacent unit cells. and in BiOF (except after relaxation without Bi 5d states), an additional F atom is located closer to the Bi atom than the normally coordinating 4 F atoms (consult the Bi X distances in Table 3). With the increase in the X atomic number, both the bond angle of Bi O Bi and the atomic radius of X augment, which might help to raise the overlapping and thus W vb. However, in the same X sequence, the Bi X Bi angle falls, and both the Bi X and Bi O distances grow, lessening the overlapping and hence the W vb. These two competitive factors might explain the first dropping and then rising of W vb with the growing X atomic number. According to the next section, the conduction band of BiOX consists principally of the antibonding hybridization of Bi 6p and O 2p orbitals (the component of X np is negligible), so the W cb is determined basically by the Bi O interaction. Although the Bi O Bi angle increases from BiOF to BiOI, the expansion of the Bi O distance in the same species order leads to an overall slight reduction in the W cb value. Incorporation of Bi 5d states enhances the Bi O Bi angle but simultaneously the Bi O distance, and these opposite aspects cause the W cb to rise for BiOF, and drop for the other species, in comparison with the counterparts in the absence of Bi 5d states. Meanwhile, the inclusion of Bi 5d states reduces the Bi X Bi angle and generally improves the Bi X distance (except for Bi1 F1 or Bi2 F2), hence narrowing the W vb. The band-gap structures of these relaxed species are presented in Figures 3 and 4 within the same energy range to facilitate mutual comparison, and the gap values have also been provided in Table 2. For BiOF, the conduction band minimum appears at the Z point, but the valence band maximum locates either at the Z point when relaxed with the Bi 5d states, showing a direct-transition band-gap nature, or somewhere on the ZR line if relaxed ignoring the Bi 5d states, reflecting the indirect character. Actually, the highest occupied orbital is rather flat near the Z point along both the ZR and ZA lines. Inclusion of Bi 5d states narrows the gap by 0.14 ev. The conduction-band minimum of relaxed BiOCl is also situated at the Z point, but the valence band maximum is positioned near the R point on the ZR line, showing an indirect nature, in accord with the experimental result. 4 After applying the Bi 5d states, the bottom of the conduction band seems pretty flat. The highest valence-band orbital also shows energy close to the valence-band maximum along the whole RX and part XG (near the X point, especially in Fig. 4) lines. The conduction-band minimum obtained here agrees with that reported by Zhang et al. 4 using the TB-LMTO program within the LDA. For this species, consideration of Bi 5d states brings a wider gap (2.92 ev). In comparison, the experimental value is 3.44, 3.46, or 3.51 ev. 4,5,8 The indirect gap of relaxed BiOBr is obvious as well, and the orbitals around the gap display more sensitivity to the incorporation of Bi 5d states. The bottom of the conduction band can be determined to be at the Z point after relaxation in the absence of Bi 5d states, but it is quite flat along the whole GZ line once relaxed in the presence of the Bi 5d states (the calculated minimum is located near the Z point on the GZ line). Essentially, the bottom flatness is observable even in Figure 3c. The highest occupied orbital on the part MG line is close in energy to the valence-band maximum, especially when considering the Bi 5d states. The involvement of Bi 5d states also favors the gap expansion, yielding a gap around 2.65 ev, in contrast to the experimental 2.91 ev. 6 The bottom of the conduction band in relaxed BiOI is flat obviously, though the actual position of the calculated minimum is situated somewhere near the G point on the GZ line. The valence-band maximum locates near the R point on the ZR line, but the energy of the highest occupied orbital along the whole RX and part ZR (near R) and XG (near X) lines is very close to the maximum, imparting a quite flat top. The band gap widens when the Bi 5d states are taken into account, with a value of 1.75 ev, comparable with the experimental 1.92 or 1.94 ev. 5,7 Concerning the photocatalytic activity, the gap width determines the utilization of light energy, indirect gaps are more advantageous than direct ones for hindering the recombination of the excited electrons with holes, and the flat transition positions might also promote the transition process. Density of States Figure 5 plots the total and partial electronic density of states (PDOS) of relaxed BiOX with the inclusion of Bi 5d states, within the energy range covering the whole occupied bands and

5 1886 Huang Vol. 30, No. 12 Figure 3. The band gaps of (a) BiOF, (b) BiOCl, (c) BiOBr, and (d) BiOI relaxed without Bi 5d states. the conduction bands, and the energy zero corresponds to the valence band maximum in each species. The lowest band in each species can be assigned to the Bi 5d orbitals, and the next three low-energy bands are constructed by the s-type orbitals, among which the highest is originated from the Bi 6s states, and the lowest can be attributed to either F 2s for BiOF or O 2s in other Figure 4. The band gaps of (a) BiOF, (b) BiOCl, (c) BiOBr, and (d) BiOI relaxed with Bi 5d states.

6 Electronic and Optical Properties of BiOX 1887 Figure 5. The total and partial DOS of (a) BiOF, (b) BiOCl, (c) BiOBr, and (d) BiOI relaxed with Bi 5d states. species. The X np, O 2p, and Bi 6p orbitals constitute together both the valence and conduction bands, and the Bi 6s states appear at the top of the valence band as well. In each species, the Bi 6p states dominate the conduction band but contribute the least to the valence band. The contribution of X np orbitals is negligible in the conduction band, but prominent in the valence band, indicative of a somewhat localized feature with an apparent peak that approaches the valence band maximum with the increasing X atomic number (Table 2). Besides the p-orbital hybridization in the valence and conduction bands, the overlap between Bi 6s and O 2p for BiOF, BiOCl, and BiOBr (as to BiOI, I 5s states also partake) or between Bi 5d and O 2s in BiOCl, BiOBr, and BiOI (for BiOF, F 2s states participate as well) can also be discerned. Similar trends appear in the results obtained without considering the Bi 5d states (that are accordingly absent). The positions of d-band centers relative to the Fermi energy have been found to be related with the reactivity of metal surfaces, and the density peak of metal states shifting toward the Fermi level in some heavy-metal azides has also been associated with the explosive sensitivity. 25 Analogously, maybe the observation that the density peak of the localized X np states approaches the valence-band maximum with the X atomic number in this work also accounts somewhat for the discrepancy of the reported photocatalytic activity among the BiOX species. 4 6 Application of Bi 5d states generally pushes the peaks closer to the tops of the valence bands (Table 2). As described earlier, the valence bands of BiOX species consist primarily of O 2p and X np states, whereas the conduction bands are composed basically of Bi 6p orbitals. Therefore, these species might be assigned to the p-to-p (O 2p and X np tobi 6p) charge-transfer type. Similar to the descriptions for p-to-d charge-transfer-type transition-metal compounds, 26 the band gap might also be evaluated by ~D 2 W cb. The charge-transfer energy D here might decrease with the reduction in either the electronegativity of the nonmetal X atom or the Madelung potential within the species. The Pauling electronegativity values of F, Cl, Br, and I are 3.98, 3.16, 2.96, and 2.66, respectively, 27 and their Mulliken electronegativity values are 10.41, 8.29, 7.59, and 6.76 ev correspondingly, calculated as the arithmetic average of the electron affinity and the ionization energy, 28 using the public data 27 ; both of them showing an apparently falling trend with the X atomic number. The Madelung potential might be

7 1888 Huang Vol. 30, No. 12 Table 4. Atomic Populations and Charges (in e) Within Relaxed BiOX (n 5 2, 3, 4, and 5 for X 5 F, Cl, Br, and I, respectively). Atomic populations Charges Species Bi 5d Bi 6s Bi 6p O2s O2p X ns X np Bi O X BiOF a / BiOCl a / BiOBr a / BiOI a / BiOF b BiOCl b BiOBr b BiOI b a Relaxed without Bi 5d states. b Relaxed with Bi 5d states. compared among the species using the Bi O and Bi X distances. According to Table 3, these distances increase monotonically with the rising X atomic number, indicating the declining potential. Therefore, the reducing D value could be expected with the growth in the X atomic number. In the same X sequence, the W cb also decreases, but the extent might be minor, compared with that of the D declining, and hence the overall result is the gap narrowing (Table 2). Atomic Charges, Bond Orders, and Orbital Density Distribution The atomic populations and charges within the relaxed BiOX calculated via the Mulliken population analysis are listed in Table 4. In the X sequence from F to I, the atomic populations of O remain almost constant, while those of Bi and X increase and decrease correspondingly, reflecting the reducing oxidation capability of X. The evolution of atomic populations largely occurs on the p-type orbitals. The presence of Bi 5d states increase slightly the Bi 6s, O 2p, and X np populations. It is proposed that internal fields due to dipole moments can promote the charge separation, enhancing photocatalytic activities. 4,21 Using the charges in Table 4 and lattice parameters in Table 1, the dipole moments of BiO 4 X 4 polyhedra (one Bi atom coordinated with 4 O and 4 X atoms) within relaxed BiOX have been evaluated and listed in Table 5. Generally, inclusion of Bi 5d states elevates the dipole moments. BiOF gives the highest value, and in the case with Bi 5d states, the following sequence is BiOI [ BiOBr [ BiOCl. Based on the calculated bond orders in Table 5, the covalency of Bi O bonds within relaxed BiOX can be identified, and higher levels appear in relaxed BiOBr and BiOI, which might partially be ascribed to their larger Bi populations (Table 4). Concerning the Bi X interactions, the results seem somewhat complicated. With the increasing X atomic number, Bi1 X1 or Bi2 X2 evolves from antibonding to bonding states, and Bi1 X2 or Bi2 X1 gives a reverse trend. The covalency strengthens generally in the same X sequence, and Bi1 X2 or Bi2 X1 shows a higher degree than Bi1 X1 or Bi2 X2 for each species. The growing covalency can also be observed by other measures such as the effective ionic valences or electronegativity differences. The former is defined to be the difference between the formal ionic charge and the Mulliken charge on the anion species. 28 As listed in Table 4, the Mulliken charge on X changes from (20.67) to (20.29) in the absence (presence) of Bi 5d states, so the effective ionic valence in the relaxed BiOX is from 0.34 (0.33) to 0.67 (0.71) with the increase in the X atomic number, considering the formal ionic charge of X as It is known that a greater value represents a higher level of covalency (a value of zero corresponds to an ideal ionic bond). 28 In respect of the electronegativity, both Pauling and Mulliken values can be adopted. The Pauling electronegativity values of Bi and O are 2.02 and 3.44, respectively (those of X have been provided in the previous section), and the Pauling electronegativity differences between X and Bi are 1.96, 1.14, 0.94, and 0.64 for X = F to I correspondingly. Smaller values imply stronger covalency, and as a comparison, the difference between O and Bi is The Mulliken electronegativity values of X have been offered in the preceding section, and similarly, those of Bi and O are deduced as 4.12 and 7.54 ev, respectively. Consequently, the Mulliken electrone- Table 5. Bond Populations (in e) and Dipole Moments (in D) Within Relaxed BiOX. Species Bi O Populations Bi1 X2 or Bi2 X1 Bi1 X2 or Bi2 X1 Dipole moment BiOF a BiOCl a BiOBr a BiOI a BiOF b BiOCl b BiOBr b BiOI b a Relaxed without Bi 5d states. b Relaxed with Bi 5d states.

8 Electronic and Optical Properties of BiOX 1889 Figure 6. The density isosurfaces of the highest valence-band orbital (top) and the lowest conductionband orbital (bottom) of relaxed BiOX (X = F, Cl, Br, I from left to right sequentially) with the consideration of Bi 5d states. The perspective direction is similar to that in Figure 1, and the line intersections represent the atomic sites (O in red, Bi in purple, and X in the rest). gativity differences between X and Bi are 6.30, 4.18, 3.47, and 2.64 ev for X = F to I subsequently. The declining trend appears again, consistent with the increasing covalency. By the way, the value between O and Bi is 3.42 ev. The change in the overlap population sign might be connected with the different structures surrounding the bond. The Bi1 X2 (or Bi2 X1) interaction is direct, whereas the Bi1 X1 (or Bi2 X2) interaction penetrates either an X layer or an O layer. When the shortest Bi1 X1 (or Bi2 X2) distance is within one unit cell, the interaction is realized through the intermediate X2 (or X1) layer. If the nearest-neighboring Bi1 X1 (or Bi2 X2) is within two adjacent unit cells, the interaction occurs through an O layer. Relaxed BiOF belongs to the former case, while the other species can be assigned to the latter one (see Table 3). In the former case, the bonding interaction tends to form on the Bi1 X2 (or Bi2 X1), and the Bi1 X1 (or Bi2 X2) is antibonding. In the latter case, perhaps owing to the promotion of surrounding O atoms on the O layer, the Bi1 X1 (or Bi2 X2) prefers to be bonding, and the Bi1 X2 (or Bi2 X1) becomes antibonding. Relaxed BiOCl seems to be an exception, but can also be taken as an intermediate example, possibly due to the smaller radius of Cl, in comparison with those of Br and I. Consideration of Bi 5d states weakens all these covalent bonds to a certain extent, maybe because they disturb the spatial distribution of the overlapping orbitals. It is interesting that the bonding and antibonding states appear on the two types of Bi X interactions [Bi1 X1 (or Bi2 X2) and Bi1 X2 (or Bi2 X1), respectively]. The hybridization of the total 18 Bi 6p, O 2p, and X np states in the unit cell should form nine bonding states and nine antibonding ones. According to Figure 2, the valence and conduction bands involve 12 and 6 orbitals, respectively, which means that the valence band contains nine bonding and three antibonding states. From Figure 5 it is obvious that the X np states reside almost completely in the valence band, and therefore, the three antibonding orbitals in the valence band might mainly correspond to the Bi X interactions. If these occupied bonding and antibonding states were distributed equally to the two types of Bi X interactions, the Bi X would be nonbonding. This seems unrealistic and conflicts with the predictions based on the effective ionic valences and electronegativity differences between Bi and X. Moreover, the two types of Bi X interactions are situated within different circumstances and reasonably not equivalent. Hence, they display bonding and antibonding features, respectively, and the bonding preference might be relevant to the structural characteristics, as described in the preceding paragraph. To further understand the band structures, the spatial distribution of orbital density has also been investigated, and Figure 6 presents the density isosurfaces (at a fixed isovalue) of the high-

9 1890 Huang Vol. 30, No. 12 est valence-band and the lowest conduction-band orbitals for the relaxed species with the consideration of Bi 5d states. It is visible that X np states contribute increasingly to the highest valence-band orbital from X = F to I, and dominate for X = Cl, Br, and I. The isosurfaces around Bi sites are originated from Bi 6s states (Fig. 5). For the other valence-band orbitals with decreasing energy, density isosurfaces (not shown here) reveal that the X np states prevail first, and then the O 2p states govern until the lowest level. The lowest conduction-band orbital (Fig. 6 bottom) is composed mostly of Bi 6p states. With the increasing X atomic number, the Bi 6p states tend to create a second high-density region and increase its weight, possibly due to the growing Bi1 X2 (or Bi2 X1) distance. The Bi 6p isosurfaces also show an increasing tendency to extend into the neighboring unit cell in the same X sequence. Optical Properties The optical properties of relaxed BiOX attained with Bi 5d states are presented in Figure 7, including absorption coefficients and dielectric functions. To probe the anisotropy, the electric field vector was selected parallel to the a or c-axis of each species. For each species, the absorption edge is sharper and the first absorption peak is higher in the [100] direction than in the [001] direction, which is in line with the more localized feature along the reciprocal [001] direction (for the present species, the basis vectors in the reciprocal space are parallel to those in the real space) of the valence-band orbitals (Fig. 2), more apparently for relaxed BiOCl and BiOBr whose orbitals exhibit more flatness along the [001] direction. In relaxed BiOCl, BiOBr, or BiOI, the linearity of (ae) 1/2 E (photon energy) is found along the absorption edges, suggesting the indirect gap consistent with the preceding band structures. For relaxed BiOF, a shoulder exists on the absorption edge, but the linear (ae) 2 E relationship holds on each side of the turning point, explicating the persistent direct feature (but with different gap widths). The absorption peaks can be assigned referring to the e 2 (x) in Figure 7c. The e 2 (x) peaks distribute in a sequence similar to that in DOS (Fig. 5). With increasing photon energy, the first peak corresponds to the transitions from the valence band to the conduction band. The second peak in relaxed BiOF also accounts for such transitions, but likely at a different transition position. The next three peaks can be assigned to the transitions from the s-orbitals, and the last peak might be owing to the transitions from the Bi 5d orbitals. The valence-band transitions in the [100] direction are stronger than those in the [001] direction. The main absorption peaks in Figure 7a can be specified similarly, and the transitions from different valence-band orbitals to different conduction-band or higher empty orbitals (36 empty orbitals were adopted during the calculations of optical properties) produce several weak peaks neighboring them. The separate high absorption peak around 28 ev and the weak peaks in the subsequent higher energy range are ascribed to the transitions from the Bi 5d orbitals and vanish when the Bi 5d states are abandoned during the calculations. From Figure 7b, it is observed that both the first maximum and minimum shift toward the lower energy with the increasing X atomic number, reflecting the reducing binding strength within Figure 7. The absorption coefficients a(x), real e 1 (x), and imaginary parts e 2 (x) of the dielectric functions of relaxed BiOX with the consideration of Bi 5d states. The electric field vector is in the [100] (black curves) or [001] (gray curves) direction.

10 Electronic and Optical Properties of BiOX 1891 the species. The e 1 (0) value [e 1 (x) atx p= 0, which is correlated with the refractive index n, i.e., n ¼ ffiffiffiffiffiffiffiffiffiffi e 1 ð0þ] increases from relaxed BiOF to BiOI, and is higher in the [100] direction (5.10, 5.89, 6.34, 7.76 sequentially) than in the [001] direction (4.64, 4.79, 5.15, 6.51 correspondingly). The relaxed BiOX species exhibit apparent optical anisotropy. Steeper absorption edges, higher first peaks of a(x), e 1 (x), and e 2 (x), and larger e 1 (0) values are found in the [100] direction than in the [001] one. Among the species, e 1 (0) increases from relaxed BiOF to BiOI. Conclusions The structural, electronic, and optical properties of BiOX have been studied theoretically by means of the PW-PP DFT method within GGA scheme, and the effect of Bi 5d states has also been scrutinized. Cell relaxation was carried out with the optimization of atomic positions, and smaller a and larger c lattice constants are generally obtained in comparison with the experimental values. The band-gap nature of relaxed BiOF calculated with Bi 5d states is direct, whereas all the other three species exhibit indirect gaps. This agrees with the existent experimental report of BiOCl, 4 though the gap characters of the other species have not been ascertained experimentally yet. After relaxation with Bi 5d states, the bottoms of the conduction bands for BiOCl, BiOBr, and BiOI are rather flat, so are the valence band maximums in BiOF and BiOI. The maximum gap widths acquired in this work are 3.34, 2.92, 2.65, and 1.75 ev for relaxed BiOF, BiOCl, BiOBr, and BiOI, respectively, signaling the well-known DFT underestimation, in accordance with the experimental values of BiOCl, BiOBr, and BiOI (that of BiOF has not appeared in the literature to the author s knowledge). Both the valence and conduction bands in relaxed BiOX are the hybridization of Bi 6p, O 2p, and X np (n =2,3,4,and5 for X = F, Cl, Br, and I, respectively) orbitals. The Bi 6p states dominate the conduction bands but contribute the least to the valence bands, and the X np states offer a reverse appearance. The density peak of X np states in the valence band shifts toward the valence band maximum from relaxed BiOF to BiOI. Orbital density analysis reveals that the X np states govern the highest valence-band orbital except X = F, and Bi 6p states control the lowest conduction-band orbital. The valence-band width increases from relaxed BiOCl to BiOI, whereas the conductionband width decreases from relaxed BiOF to BiOI. From relaxed BiOF to BiOI, the Mulliken atomic populations of Bi increases while those of X decreases, showing the reducing oxidative capability. 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