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Reviews Asymmetric Cation Coordination in Oxide Materials: Influence of Lone-Pair Cations on the Intra-octahedral Distortion in d0 Transition Metals P. Shiv Halasyamani Department of Chemistry and the Center for Materials Chemistry, University of Houston, 136 Fleming Building, Houston, Texas 77204-5003 Received May 3, 2004. Revised Manuscript Received June 29, 2004
The oxides that contain both a d0 transition metal (Ti4+, Nb5+, W6+, etc.) and a lone-pair cation (Sn2+, Se4+, Te4+, etc.) are examined to investigate the influence of the lone-pair cation on the intra-octahedral distortion of the d0 transition metal. The direction and magnitude of the out-of-center distortion are also examined. When an intra-octahedral distortion is observed, at least one of the d0 transition metal-oxide bonds needs to either be terminal or should link to another d0 transition metal. With respect to the direction of the out-of-center distortion, Ti4+, V5+, and Nb5+ usually displace toward an edge (local C2 direction) or corner (local C4 direction), whereas Mo6+ and W6+ are observed distorting toward an edge (C2) or face (local C3 direction). Finally, the magnitude of the distortion scales as Mo6+ > V5+ > W6+ > Nb5+ > Ta5+ > Ti4+.
Background and Introduction Asymmetric oxide coordination environments are often observed in two families of cations, octahedrally coordinated d0 transition metals (Mn+ ) Ti4+, Nb5+, W6+, etc.), and lone-pair cations (Am+ ) Sn2+, Se4+, Te4+, etc.). These asymmetric environments are often required for a host of technologically important materials properties such as piezoelectricity, ferroelectricity, nonlinear optical phenomena, and dielectric behavior. With both the d0 transition metals and lone-pair cations, the primary distortive cause1 can be attributed to second-order Jahn-Teller (SOJT) effects (electronic effects).2-7 For the octahedrally coordinated d0 transition metals, SOJT effects occur when the empty d-orbitals of the metal mix with the filled p-orbitals of the ligands. In extended structures, this mixing results in a host of nearly degenerate electronic configurations that can be removed through the spontaneous distortion of the d0 transition metal (see Figure 1). The situation with the lone-pair cations is somewhat more complex. Historically, the original work of Sidgwick and Powell8 followed by the valence shell electron pair repulsion (VSEPR) theory of Gillespie and Nyholm9 attempted to rationalize the coordination geometry of the lone-pair cation. However, it was Orgel10 who explained the structural distortion and polarization through the mixing of the metal cation s- and p-orbitals. Recently, this traditional view of metal cation s-p orbital mixing has been shown to be incomplete. Watson, Parker, and co-workers,11,12 Lefebvre et al.,13,14 and Spaldin, Seshadri, and coworkers15,16 have shown that the oxide anion plays an important role in the lone-pair formation. Specifically, these researchers argue that the interaction of the s-
Figure 1. MO6 octahedron (M ) d0 transition metal) indicating the three possible directions for the out-of-center distortion.
and p-orbitals of the metal cation with the oxide anion p-states is critical for lone-pair formation. Regardless of how the lone pair is created, its structural consequences are profound (see Figure 2), as the lone-pair “pushes” the oxide ligands toward one side of the cation, resulting in a highly asymmetric coordination environment. The nature of the structural changes between the two families of cations is, however, different. With the d0 transition metal-centered octahedra, a distortion can occur along one of three directions, either toward an edge (local C2 direction), toward a face (local C3 direction), or toward a corner (local C4 direction) (see Figure 3).17 Each distortion results in bond asymmetries within the MO6 octahedron: C2, two “short”, two “long”, and two “normal” M-O bonds; C3, three “short” and three “long” M-O bonds; and C4, one “short”, one “long”, and four “normal” M-O bonds. As will be demonstrated,
10.1021/cm049297g CCC: $27.50 © 2004 American Chemical Society Published on Web 08/13/2004
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Figure 2. AO3E and AO4E polyhedra (A ) lone-pair cation) indicating the structural effect of the lone pair (shown schematically).
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are intrinsic to the [M5+OF5]2- and [M6+O2F4]2- octahedra and, unlike the materials examined herein, are not dependent on the crystal structure framework. The secondary distortion involves hydrogen bonding between the anion and the occluded cation species (pyridinium or 5-hydrozy-2-methylpyridinium). In addition, the secondary distortion is weaker and serves to reinforce the primary distortion. The question that this review proposes to address is the following: How do the lone-pair groups, that is, the AOnE polyhedra, influence the intra-octahedral distortion of the d0 transition metal? In other words, how does the secondary distortion (interactions between the AOnE polyhedra and the MO6 octahedra) affect the primary distortion (intra-octahedral displacement) of the d0 transition metal? To answer this question, oxides, both centrosymmetric and noncentrosymmetric, that contain a d0 transition metal and a lone-pair cation were examined. Oxide materials with cationic disorder and/ or oxygen vacancies were excluded. Primary Distortive Effects (Electronic Effects)
Figure 3. Out-of-center distortions of the d0 transition metal along the local C2 [110], C3 [111], and C4 [001] directions.
individual d0 transition metals exhibit a definite preference with respect to the direction of their distortion. Also, the average magnitude of the distortion varies greatly between d0 transition metal cations. The lonepair cations are almost always observed in asymmetric coordination environments, attributable to the lone pair “pushing” the oxide ligands toward one side of the cation (see Figure 2). Thus, these cations may be considered as “pre-distorted”, as any additional distortion will result in unfavorable oxide-oxide or oxide-lone pair interactions. As will also be demonstrated, the “predistorted” nature of the AOnE polyhedra profoundly influences the direction of the intra-octahedral distortion of the d0 transition metal. It has been recently reported that with halide ligands the lone-pair cation’s tendency to distort decreases with increasing coordination number.18 With oxide ligands this does not seem to be the case. For example, three-, four-, and fivecoordinate Te4+ are all in asymmetric coordination environments attributable to the lone pair on the cation. In addition to the primary distortion (SOJT or electronic), secondary distortive effects also occur. The secondary effects are attributable to bond networks and lattice stresses that, for our purposes, are between the MO6 and the AOnE polyhedra. Primary and secondary distortion concepts were first introduced by Kunz and Brown.1 More recently, Poeppelmeier et al.19 demonstrated for the first time that primary and secondary distortion concepts could be used to explain the direction and magnitude of out-of-center distortions in metal oxyfluoride octahedra. Specifically, [M5+OF5]2- (M ) V5+ or Nb5+) and [M6+O2F4]2- (M6+ ) Mo6+ or W6+) octahedra were examined. In both cases the metal distorts toward the oxygen atom(s). These primary distortions
Both d0 transition metals and lone-pair cations undergo structural changes attributable to electronic, SOJT, effects. With both families of cations, the structural changes result in asymmetric (locally acentric) coordination environments. In addition to discussing the main topic of this article, namely, the influence of AOnE polyhedra on the intra-octahedral distortions of d0 transition metals, it is relevant to examine the out-ofcenter displacement in more detail. Specifically, the direction and magnitude of the intra-octahedral distortion in materials containing both d0 transition metals and lone-pair cations will be examined. Table 1 presents a distribution of the C2 (edge), C3 (face), or C4 (corner) out-of-center distortion, for each d0 transition metal in combination with a lone-pair cation. The most prominent aspect of Table 1 is the number of gaps, or instances, where no compound has been synthesized. This indicates that there are a great deal of opportunities and challenges for synthetic chemists. Table 1 may be divided between two groups of four cations each, Ti4+, Zr4+, Hf4+, and V5+ and Nb5+, Ta5+, Mo6+, and W6+. This division is based on the number of examples within each group. These numbers should not be confused with distinct materials, as in some instances the compound in question can contain more than one intra-octahedrally distorted d0 transition metal. With two of the first four cations, Ti4+ and V5+, only C2 (edge) and C4 (corner) distortions are observedsno C3 (face) distortions are found. With the second four d0 transition metals listed in Table 1, Nb5+, Ta5+, Mo6+, and W6+, a total of 108 examples of an intra-octahedrally distorted d0 transition metal with a lone-pair cation have been reported. A C3 (face) distortion is observed for Nb5+ in only 3 of 18 instances, specifically in Ba2Nb6Te2O21,20 Sr2Bi2Nb2O9,21 and Sr2Bi2Ta2O9.21 In the remaining 15 examples, either a C2 (edge) or a C4 (corner) distortion is observed, indicating some similarity between Nb5+, Ti4+, and V5+. Fewer examples involving Ta5+ are available (16), and with this cation all three types of distortions (edge, face, and corner) are observed in roughly equal frequency. For the last two cations, Mo6+ and W6+, a marked change in the number of examples
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Table 1. Oxides Containing Octahedrally Coordinated d0 Transition Metals and Lone-Pair Cations: Direction of the Intra-Octahedral Distortion Se4+ C2 Ti4+ Zr4+ Hf4+ V5+ Nb5+ Ta5+ Mo6+ W6+
C3
Sn2+ C4
C2
C3
Sb3+ C4
C2
C3
Te4+ C4
C3
C4
C2
C3
Bi3+ C4
C2
4
2
1
1 3 2 5
C3
I5+ C4
C2
C3
3
3
C4
1
1 1 3
2 1
4 2 6 2
1 1 2 1
1
2 1
Table 2. Percent Distribution of the Direction of the Intra-octahedral Distortion for the d0 Transition Metal Cations
Ti4+ V5+ Nb5+ Ta5+ Mo6+ W6+
C2
Pb2+
% C4 (corner)
% C2 (edge)
% C3 (face)
total # of environments
71 56 50 31 0 3
2 44 33 31 64 42
0 0 17 38 36 55
7 9 18 16 44 31
as well as in the direction of the distortion is observed. Forty-four and 30 examples with Mo6+ and W6+, respectively, are observed. A C4 (corner) distortion is observed in only one W6+ example; specifically, there is one C4distorted W6+-centered octahedron in Sb2WO6.22 With the remaining 73 instances, only C2 (edge) or C3 (face) distortions are observed. The directional preferences of the intra-octahedral distortions in the d0 transition metal cations become immediately obvious from examining Table 2. In addition to examining directional preferences, the magnitudes of out-of-center distortions were also investigated. As shown previously, the magnitude of the distortion depends inversely on the energy gap between the HOMO and LUMO states.1 For this study, the magnitude of the distortion was quantified by taking into account the six M-O bond lengths as well as deviations from 180° of the three trans O-M-O bond angles. Using the numbering scheme given in Figure 1, these trans bond angles are as follows: θ1 ) ∠O1M-O4, θ2 ) ∠O2-M-O5, and θ3 ) ∠O3-M-O6. Taking the difference in the associated bond lengths and dividing by the cosine of each angle results in the magnitude of the out-of-center distortion: ∆d ) (|(MO1) - (M-O4)| ÷ |cos θ1|) + (|(M-O2) - (M-O5) | ÷ |cos θ2|) + (|(M-O3) - (M-O6)| ÷ |cos θ3|). A nonzero value will only be obtained if the cation is displaced from the center of its octahedron. If the oxide ligands move in equal and opposite directions, the magnitude of the out-of-center distortion will be zero. The ∆d range from 0.00 to 1.54, thus the magnitudes may be quantified as follows:
no distortion: ∆d ) 0.00-0.05 weak distortion: ∆d ) 0.05-0.40 moderate distortion ∆d ) 0.40-0.80 strong distortion ∆d > 0.80
4 1 17 5
1 3 5 11
1 6 1
1
2 1
1
2 3
4
3
Table 3 lists the oxides examined in this review along with the direction and magnitude of the distortion. Based on this list, the average magnitude of the intraoctahedral distortion scales as Mo6+ (1.21) > V5+ (1.10) > W6+ (0.90) > Nb5+ (0.62) > Ta5+ (0.38) > Ti4+ (0.34). The numbers in parentheses are the average magnitude of distortion for each cation. Thus Mo6+, V5+, and W6+ may be considered as strong distorters, whereas Nb5+ is a moderate distorter, and Ta5+ and Ti4+ are weak distorters. This trend scales with the electronegativity of these cations as recently reported by Woodward and his colleagues.23 In other words, these data indicate that, on average, a more electronegative cation will undergo a larger distortion. Secondary Distortive Effects (Bond Networks and Lattice Stresses) The main purpose of this article is to investigate the influence of the AOnE polyhedra on the intra-octahedral distortion of the d0 transition metal, i.e., secondary distortive effects. It is suggested that the Am+ cations be considered as “pre-distorted” since any additional distortion of the Am+ cation would result in unfavorable oxide-oxide or oxide-lone-pair interactions. For the materials reviewed herein a lone pair is always formed, which places the Am+ cations in asymmetric coordination environments. This pre-distorted nature distinguishes the lone-pair cations from the d0 transition metals since there are examples of d0 transition metal complexes where the secondary distortive effect overrides the primary distortive effect, leaving the d0 metal in the center of an undistorted octahedron. Examining materials containing these undistorted d0 transition metals more closely is important to better understand the secondary distortive effects. Undistorted d0 transition metal-centered octahedra are observed in a few materials, namely, MTe3O8 (M4+ ) Ti4+, Zr4+, or Hf4+),24 TiSe2O6,25 and one Ti4+-centered octahedron in Bi4Ti3O1226 and Sm2Bi2Ti3O12.27 It is perhaps not surprising that an undistorted environment is observed with the weakest distorting d0 cation, Ti4+. The MTe3O8 phases will be examined first. All three materials in this series are isostructural, crystallizing in the cubic space group Ia3 h . If the MO6 octahedra are examined, it is observed that all six oxide ligands are further bonded to a Te4+ cation. In other words, there are no M4+-O-M4+ bonds (see Figure 4a). The lack of M4+-O-M4+ bonds coupled with the cubic symmetry may suggest an imposition of six equal M-O bond lengths. The cubic symmetry alone, however, cannot be the sole reason for the undistorted M4+ environment. It is noted that Na2SeMoO628 is also cubic (space group
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Table 3. Direction and Magnitude of the Primary Distortion in Materials Containing Octahedrally Coordinated d0 Transition Metals and Lone-Pair Cations compound
distortion direction
M4+ (Ti4+, Zr4+, and Hf4+) TiSe2O625 undistorted TiTe3O824 undistorted Bi2Ti4O1129 C2 C2 Bi4Ti3O1226 undistorted C4 Sm2Bi2Ti3O1227 undistorted C4 PbTiO333(tet) C4 PbTi3O734 C4 C4 C4 PbZrO335,36(orth) C3 24 ZrTe3O8 undistorted PbHfO337(orth) C3 HfTe3O824 undistorted
∆d 0.00 0.00 0.65 0.19 0.08 0.79 0.00 0.51 0.57 0.30 0.67 0.32 0.22 0.00 0.32 0.00
compound
distortion direction
M5+ (V5+, Nb5+, and Ta5+) V2Se2O938 C4 C4 K(VO2)3(SeO3)230 C2 NH4(VO2)3(SeO3)239 C2 (VO2)2(SeO3)340 C4 C4 Cs(VO2)3(TeO3)241 C2 Te2V2O942 C4 43 Pb(VPO6)(H2O) C2 Nb2Se4O1344 C4 C4 SbNbO431 C2 LaTeNbO644 C2 C2 La4Te3Nb2O2344 C2 BiNbTe2O845 C4 C4 Te4Nb2O1346 C4 C4 C4 C4 Te3Nb2O1147 Ba2Nb6Te2O2120 C2 C3 C4 C4 PbBi2Nb2O948 BiNbO449 C2 SrBi2Nb2O921 C3 21 BaBi2Nb2O9 C3 C2 SbTaO432 Ta2Te2O950 C3 C3 20 BaTa6Te2O21 C2 C3 C4 CaBi2Ta2O951 C3 SrBi2Ta2O951 C3 BaBi2Ta2O951 C3 C4 Bi4Ta2O1152 C4 Bi7Ta3O1853 C2 C2 ∼C2 ∼C2 C4 C4
P213), but in this material the Mo6+ cation is distorted toward a face, along the local C3 direction. A similar situation to MTe3O8 is observed in TiSe2O6,25 which is monoclinic (space group P21/c). All of the six oxide ligands around Ti4+ are further connected to a Se4+ cation (see Figure 4b). Again there are no Ti4+-O-Ti4+ bonds. Thus, it is suggested that because there are no M-O-M bonds, or for that matter any terminal M-O bonds, rather than the cubic symmetry, for MTe3O8, that
∆d 1.28 0.99 1.16 1.12 1.11 0.83 1.20 1.07 1.20 0.50 0.40 0.61 0.94 0.94 0.62 0.81 0.48 0.51 0.42 0.41 0.66 0.68 0.28 0.51 0.45 0.66 0.96 0.96 0.61 0.29 0.39 0.68 0.28 0.51 0.47 0.47 0.47 0.24 0.29 0.40 0.38 0.19 0.09 0.35 0.32
compound
distortion direction
M6+ (Mo6+ and W6+) Na2SeMoO628 C3 K2SeMoO628 C3 Rb2SeMoO628 C3 54 K2Se2MoO8 C2 Cs2(MoO3)3(SeO3)55 C3 (NH4)2(MoO3)3(SeO3)55 C3 BaSeMoO656 C3 BaMo3Se2O1156 C2 57 Sb2MoO6 C2 C2 CuSbMo2O858 C3 LiSbMo2O859 C3 MoTe2O760 C2 61 A4Mo6Te2O24 ‚H2O C2 (A ) K, Rb) C2 C2 (NH4)6Mo6Te8O43 ‚ H2O62 C2 63 A2TeMo2O6(PO4)2 ∼C2 (A ) K, Rb, Cs, Tl) Na2Te4MoO1264 C2 A2Mo3TeO1261 C2 (A ) NH4, Cs) 65 A4TeMo6O22 C2 (A ) NH4, Rb) C3 ∼C3 BaTeMo2O966 C3 C3 67 AMoO2(IO3)4OH C3 (A ) Nd, Sm Eu) AMoO3(IO3)68 C2 (A ) K, Rb, Cs) 69 (NH4)2(WO3)3(SeO3) C3 Cs2(WO3)3(SeO3)69 C3 SnWO432 C3 Sb2WO622 ∼C2 ∼C4 70 Na2TeW3O9 C2 C2 ∼C2 C3 C3 C3 ∼C3 C3 K2TeW3O1271 C3 C3 C3 A2TeW3O1271 C3 (A ) Rb, Cs) C2 Na2TeW4O1264 BaTeW2O966 C2 C3 BiTeW2O1072 C2 Bi2Te2W3O1273 C2 C2 74 PbWO4 C2 C3 CuBiW2O875 C2 C3 Bi2W3O976 C3 C3 Bi2WO677 C2
∆d 1.47 1.54 1.53 1.01 1.04 1.11 1.40 1.05 1.11 0.99 1.18 1.28 1.31 1.24 1.23 1.26 1.27 0.83 0.74 1.13 1.13 1.44 1.32 1.23 1.21 1.30 1.19 0.67 0.88 0.69 0.26 0.69 0.76 0.80 0.95 0.66 0.93 0.94 1.18 1.19 0.72 1.11 1.21 1.48 0.74 1.00 0.88 0.85 0.94 0.94 0.89 0.91 0.95 0.91 0.89 0.79 1.27
results in an undistorted d0 transition metal environment for MTe3O8 and TiSe2O6. This leads directly to the question: Why does it seem necessary for there to be M-O-M or terminal M-O linkages for an intra-octahedral distortion to occur? In MTe3O8 and TiSe2O6, with respect to the d0 transition metal, there are only M-O-A bonds. Thus how, or why, would the Am+ cation further distort from its predistorted environment and still retain structural stabil-
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Figure 4. Undistorted TiO6 octahedra in (a) TiTe3O8 and (b) TiSe2O6. Note that all of the oxide ligands surrounding Ti4+ are connected to either a Te4+ or a Se4+ cation.
ity? Upon examination of Figure 2, the Am+ cation could move toward or away from its lone pair, that is, either “up” or “down”. The former would increase oxide-oxide ligand repulsions, whereas the latter would increase lone-pair-oxide repulsions. Either displacement would be structurally unfavorable. Additionally, the AOnE polyhedra could be further distorted by an increase or a decrease in one of the A-O bond lengths. This arbitrary change in bond length also seems unlikely without some other structural compensation. It is suggested that the structural rigidity of the “pre-distorted” AOnE polyhedra, that is, TeO4 and SeO3 polyhedra in MTe3O8 and TiSe2O6, that inhibits the M4+ cation from undergoing an intra-octahedral distortion. In other words, if the M4+ cations were to undergo an intraoctahedral displacement, the Am+ cation (Te4+ or Se4+) would be forced into an extremely distorted, structurally unfavorable environment. Thus, in MTe3O8 and TiSe2O6, the TeO4 and SeO3 polyhedra respectively serve as blocking groups; i.e., the d0 transition metal will not distort toward an oxide ligand bridging to these lonepair cations, but rather away from the oxide ligand. Since in MTe3O8 and TiSe2O6 the MO6 octahedra are completely surrounded by TeO4 or SeO3 groups respectively, the Mn+ cation is trapped, undistorted, within its octahedron (see Figure 4a,b). Thus, since the d0 transition metal distorts away from the oxide ligand(s) that bridge to a lone-pair cation, the lone-pair cation serves to reinforce the direction of the intra-octahedral distortion. Figures 5 and 6, with Ti4+, V5+, Nb5+, and Mo6+, illustrate this concept. With these cations, and with respect to the materials listed in Table 3, the d0 transition metal distorts away from the oxide ligand bridging to a lone-pair cation. For example, in Bi2Ti4O1129 (Figure 5a), K(VO2)2(SeO3)230 (Figure 5b), and SbNbO431 (Figure 6a), the d0 transition metal undergoes
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Figure 5. Out-of-center distortion for (a) Ti4+ in Bi2Ti4O11 and (b) V5+ in K(VO2)2(SeO3)2. In both materials, the distortion is away from the oxide ligands that link to a lone-pair cation.
Figure 6. Out-of-center distortion for (a) Nb5+ in SbNbO4 and (b) Mo6+ in Cs2Mo3TeO12. In both materials, the distortion is away from the oxide ligands that link to a lone-pair cation.
an out-of-center distortion toward an edge (C2). In Bi2Ti4O11, the Ti4+ cation displaces away from O(6), the oxide ligand that bonds to the Bi3+ cation, whereas in K(VO2)2(SeO3)2 and SbNbO4 a slightly different situation is observed. In both of these materials, the axial oxide ligands bond to a lone-pair cation, Se4+ or Sb3+, respectively. The V5+ and Nb5+ cations are blocked from distorting toward a corner, owing to the SeO3 and SbO4 asymmetric polyhedra. Instead both d0 transition metal cations displace toward an edge (C2). In Cs2Mo3TeO12
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(Figure 6b), the lone-pair cation, Te4+, bridges to the Mo6+ cation through the “bottom” axial ligand, O(4), whereas the “top” axial ligand, O(2), is terminal. One could have expected Mo6+ to displace directly toward the terminal oxide ligand, O(2), that is, a corner (C4) distortion. As has been noted, however, C4-Mo6+ distortions are simply not observed. Thus, the Mo6+ distorts toward a face (C3), but still away from the Te4+ cation. Conclusions and Outlook This review has examined oxide materials that contain a d0 transition metal (Mn+) and a lone-pair cation (Am+). An intra-octahedral distortion may occur in a Mn+ cation if there is at least one M-O-M bond, or at least one M-O terminal bond. In the examples described herein, if the MO6 octahedron is fully bonded to AOnE polyhedra, the Mn+ cation is effectively trapped and will not distort. This undistorted environment is also attributable to the structural rigidity of the AOnE polyhedra. Since the AOnE polyhedra are pre-distorted, any additional structural distortion would only increase repulsive interactions within the polyhedra. Thus, the d0 transition metal tends to distort away from the oxide ligand, bridging to a lone-pair cation. With respect to the direction and magnitude of the out-of-center distortion, Ti4+, V5+, and Nb5+ are usually observed displaced toward either an edge (local C2) or a corner (local C4), whereas Mo6+ and W6+ distort toward an edge (C2) or a face (local C3). With the magnitude, the out-of-center distortion scales as Mo6+ > V5+ > W6+ > Nb5+ > Ta5+ > Ti4+. Based on this review, several opportunities and challenges are apparent. The most obvious is synthetic. From a quick glance at Table 1, it is clear that there are numerous opportunities for synthetic exploration. For example, except for Sn2WO4,32 there are no reported compounds with Sn2+ and a d0 transition metal. Second, whereas the magnitude of the out-of-center distortion seems to scale with the electronegativity, at present there is no clear understanding for the directional preference (see Table 2). In other words, why are edge (C2) and face (C3) distortions so common (and corner (C4) so rare) for Mo6+ and W6+? Why do Ti4+, V5+, and Nb5+ prefer edge (C2) and corner (C4) displacements? Likely, the greatest challenge is controlling the distortions in any new material. At present it seems clear that the d0 transition metal will usually undergo an intra-octahedral distortion in a direction away from the oxide ligand bonded to a lone-pair cation. Controlling the distortion to align in any solid-state material is, at a minimum, difficult. Not only will new materials be necessary, but also interactions between synthetic and theoretical chemists are crucial to fully address these challenges. Acknowledgment. I wish to thank Prof. Kenneth R. Poeppelmeier, Dr. Janet Kirsch, Prof. Nicola Spaldin, and Prof. Ram Seshadri for productive and stimulating discussions. I also thank the Robert A. Welch Foundation for support. This work was also supported by the NSF-Career Program through DMR-0092054 and an acknowledgment is made to the donors of the Petroleum Research Fund, administered by the American Chemical Society, for partial support of this research. P.S.H. is a Beckman Young Investigator.
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