Journal of Structural Chemistry. Vol. 50, No. 5, pp. 861-866, 2009 Original Russian Text Copyright © 2009 by V. N. Serezhkin and V. S. Urusov
STEREOCHEMISTRY OF VANADIUM IN OXYGENCONTAINING COMPOUNDS V. N. Serezhkin1 and V. S. Urusov2
UDC 548.3
Using Voronoi–Dirichlet (VD) polyhedra and the method of overlapping spheres, we analyze the coordination of 714 crystallographically different vanadium atoms in the structure of compounds containing VOn polyhedra. Vanadium atoms are found to be bonded to 4, 5, 6, or 7 oxygen atoms. The effect of the valence state and coordination number of vanadium atoms on the main parameters of their VD polyhedra is considered. A unified linear dependence between the solid angles of VD polyhedron faces corresponding to V–O bonds and the respective interatomic distances varying in a range of 1.55 Å to 2.79 Å is stated to exist. It is shown that the parameters of VD polyhedra can be used to determine the valence state of vanadium atoms. Keywords: vanadium, oxygen-containing compounds, stereochemistry, crystal chemistry, Voronoi– Dirichlet polyhedra.
The crystal structure of almost 6000 oxygen-containing vanadium compounds has been found at present [1, 2]. From the standpoint of the bond valence model (BVM) [3] and based on a new formulation of the distortion theorem of ionic coordination polyhedra [4], the most important features of vanadium crystal chemistry has recently been considered by the example of inorganic compounds containing VɈ6 octahedra [5]. This work is carried out to analyze the features of stereochemistry of vanadium in crystalline compounds of various types (including organic oxygen-containing ligands), in whose structures ionic coordination polyhedra of Vz+On (z = 2, 3, 4, 5) are present.
EXPERIMENTAL A crystal chemical analysis was performed using the TOPOS program package [6] in which main principles of the stereoatomic model of the structure of crystalline substances were implemented [7]. Within the model, the geometrical image of any atom is the Voronoi–Dirichlet (VD) polyhedron consisting of a convex polytope bounded by planes drawn through the centers of segments connecting this atom with all its neighbors perpendicular to these segments. The number of faces, form and volume of the VD polyhedron (VVDP) of any atom in the structure of crystals is unambiguously determined by the way of the mutual arrangement of all atoms in the space. Further we use the sphere radius (RSD), whose volume equals VVDP of this atom as a one-dimensional parameter characterizing the atom size in the crystal. In the general case, the VD polyhedron of some atom A has a composition of AXnZm, where X are atoms that form chemical bonds with the central atom Ⱥ, Z are atoms whose VD polyhedra have also a common face with the VD polyhedron of the atom A, but the corresponding contacts are not chemical bonds, and the total number of VD polyhedron faces is the sum n+m. Thus, the stereoatomic model simultaneously takes into account not only the first (i.e. valence), but also second (non-valence) coordination sphere of all atoms.
1
Samara State University;
[email protected]. 2Moscow State University. Translated from Zhurnal Strukturnoi Khimii, Vol. 50, No. 5, pp. 898-904, September-October, 2009. Original article submitted November 7, 2008. 0022-4766/09/5005-0861 © 2009 Springer Science+Business Media, Inc.
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The method of overlapping spheres [8], which uses the characteristics of VD polyhedra of all atoms contained in the crystal structure, allows the objective division of all interatomic interactions of any atom Ⱥ into valence Ⱥ–ɏ and non-valence Ⱥ/Z (the slash denotes the presence of a common face for the VD polyhedra of chemically unbound atoms given left and right from the slash) interactions. Note also that in the stereoatomic model the role of the interatomic interaction parameter is played not only by the corresponding internuclear distance, but also by the solid angle (:) at which the common face of VD polyhedra of atoms is “seen” from the nucleus of Ⱥ or X (Z) atoms. Using the TOPOS program package, all compounds containing coordination VOn polyhedra in the structure were selected from the databases [1, 2]. Crystallographic data were allowed for only under conditions that 1) the compound structure is determined with the R-factor d0.05; 2) coordinates of every last atom contained in the compound are found; 3) statistical placement of any atoms is absent; 4) the integer oxidation number corresponds to each vanadium atom. Overall 412 compounds satisfied the above requirements and became the objects of crystal chemical analysis. The structure of these compounds, whose list can be obtained from the authors on request (
[email protected]), contained 714 crystallographically different types of vanadium atoms, including 8 V2+, 146 V3+, 265 V4+, and 295 V5+. Based on the information about unit cell parameters, symmetry space groups, and atomic coordinates, we calculated the characteristics of VD polyhedra of basis atoms of these compounds using the TOPOS program package.
RESULTS AND DISCUSSION According to the data obtained (Table 1), V atoms can manifest all CNs in a range from 4 to 7 with respect to oxygen atoms. The octahedral coordination, usually distorted, corresponding to CN of 6 is most characteristic of vanadium. CNs of 5, 4, and 7 are less frequently observed for V atoms (|13%, 10%, and 1% sampling size respectively). The VO5 coordination polyhedra have the form of a trigonal bipyramid or a square pyramid, and at CN 4 they are in the form of tetrahedra. Maximum CN of 7 with coordination polyhedra in the form of pentagonal bipyramid is observed only for V5+ atoms in peroxocomplexes. In the structure of compounds from the above sampling, the VD polyhedra of 714 crystallographically different vanadium atoms have in total 6302 faces, 4066 of which correspond to V–O bonds. Hydrogen, oxygen, and carbon atoms most often play the role of Z atoms participating in non-valence V/Z interactions, hence, 1251, 560, and 103 faces respectively are accounted for them. The length of V–O bonds in the VOn coordination polyhedra varies in a range from 1.55 Å to 2.79 Å (Table 1), while the equivalent solid angles are of 27% to 5% of the total 4S steradian solid angle. Despite the variety of the number of faces and the form of VD polyhedra, according to regression analysis data, both valence and nonvalence interactions, regardless CN of vanadium atoms, are described by the unified linear dependence :(V–O) 39.9(1) – 11.56(5)r(V–O)
(1)
with the correlation coefficient r = –0.953 for all 4626 faces of the V–O or V/O type (Fig. 1a). This fact well agrees with the data [9], according to which, it is the linear dependence of type (1) with |r| t 0.9 that in the general case is the existence criterion of the short-range order caused by chemical interactions in the crystal structure. Moreover, it is known [10] that the characteristics of valence interactions such as bond valence values in the BVM method and solid angles of VD polyhedra are two alternative, very similar, however, not identical crystal chemical approaches. Let us note for comparison that _r_ = 0.188 corresponds to the similar distribution (:, r) for 1251 V/H faces, i.e. these non-valence interactions do not result in correlation of the mutual arrangement of vanadium and hydrogen atoms. At the same time, the dependence :(V/V) 9.5(7) – 3.3(3)r(V/V)
(2)
with _r_ = 0.889 | 0.9 corresponds to the distribution (:, r) for 45 V/V faces with r(V–V) < 3 Å (Fig. 1b). This gives grounds to assume that even relatively weak (because :(V/V) < 2% of 4S av.) V–V interactions affect the mutual arrangement of vanadium atoms in the structure of oxygen-containing crystals and they should be taken into account in the crystal chemical analysis, especially as the interatomic distances (2.7-3.0 Å), comparable in length with V–V bonds in the body-centered cubic 862
TABLE 1. Characteristics of VD Polyhedra of Vanadium Atoms Surrounded by Oxygen Atoms* Atom CN V2+ V3+
4+
V
5+
V
4 6 4 5 6 4 5 6 4 5 6 7
Coordination Number of polyhedron V atoms Tetrahedron Octahedron Tetrahedron Trigonal bipyramid Octahedron Tetrahedron Square pyramid Octahedron Tetrahedron Trigonal bipyramid Octahedron Pentagonal bipyramid
r(V–O), Å
Nf
Nnb
VVDP, Å3
1 7 1 2
16 15(4) 14 17(4)
3 1.5 2.5 2.4
13.0 1.458 0.07 0.0918 2.01-2.03 2.02(1) 9.7(2) 1.321(8) 0.01(2) 0.0832(5) 2.07-2.27 2.13(4) 10.5 1.359 0.10 0.0928 1.85-1.99 1.89(7) 9.3(2) 1.306(10) 0.01(1) 0.090(1) 1.83-2.19 1.97(16)
143 4 58
9(3) 11(1) 10(2)
0.5 1.8 1
8.1(2) 1.247(11) 0.02(2) 0.0838(6) 1.61-2.46 2.01(5) 858 9.1(1) 1.294(6) 0.04(2) 0.092(5) 1.67-1.96 1.83(7) 16 8.6(2) 1.270(10) 0.14(5) 0.094(3) 1.56-2.25 1.89(15) 290
203 62 31
8(2) 11(2) 9(1)
0.3 1.8 0.8
7.6(2) 1.219(11) 0.06(3) 0.0849(7) 1.57-2.49 1.97(18) 1218 8.5(2) 1.266(11) 0.08(4) 0.099(2) 1.58-1.88 1.72(9) 248 7.7(2) 1.226(12) 0.12(3) 0.093(3) 1.58-2.07 1.84(16) 155
193 9
8(1) 8(1)
0.3 0.1
7.0(1) 7.0(1)
RSD, Å
1.187(7) 1.187(6)
DA, Å
G3
range
average
P
4 42 4 10
0.05(2) 0.0857(7) 1.55-2.79 1.93(22) 1158 0.08(2) 0.086(2) 1.58-2.71 1.97(26) 63
*For each type of V atom we give: CN is the coordination number; Nf is the average number of VD polyhedron faces; Nnb is the average number of non-valence contacts per one V–O bond; VVDP is the VD polyhedron volume; SVDP is the total area of VD polyhedron faces; RSD is the radius of the sphere whose volume equals VVDP; DA is the shift of the V atom nucleus from the geometrical center of gravity of its VD polyhedron; G3 is the dimensionless value of the second inertia moment of the VD polyhedron; r(V–O) is the length of bonds in VOn coordination polyhedra; P is the total number of bonds. Root-mean-square deviations are given in parentheses.
Fig. 1. Dependence of solid angles : (given in % of 4S steradian) of VD polyhedron faces on the interatomic distances corresponding to these faces: (ɚ) 4626 V–O or V/O faces for VD polyhedra of 714 vanadium atoms, (b) 45 V/V faces for VD polyhedra of 41 vanadium atoms, the line corresponds to regression equation (2).
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structure of metallic vanadium (2.62 Åu8 and 3.02 Åu6), correspond to the V/V faces of VD polyhedra. Note also that V/V contacts depicted in Fig. 1b belong mainly to the compounds of three and four valent vanadium, including V2O3 {64796} and VO2 {34416}, for which the metal–insulator transition is well known. Hereinafter in curly brackets the compound code in databases is given [1, 2]. The presence of V/V faces seems to be one of the necessary conditions for the direct electron exchange between metal atoms, and it can result in changing or balancing their oxidation numbers in the structures of crystals containing aliovalent vanadium atoms, in particular, in numerous oxides of the homological series VnO2n–1. According to the results obtained, depending on CN and the oxidation number of vanadium atoms, the volume of their VD polyhedra varies in a rather wide range from 7.0 Å3 to 13 Å3, whereas the radii of spherical domains lie within 1.181.46 Å (Table 1). At constant CN the corresponding RSD (or VVDP) decreases with increasing metal oxidation number, while at the fixed valence state of vanadium atoms the RSD values decrease with increasing CN of the metal. As previously [11], this can be explained by that an increase in CN or oxidation number of vanadium leads to a decrease in the contribution of nonvalence V/Z interactions. For instance, as seen from Table 1, the number of valence contacts per one V–O chemical bond (Nnb) in VD polyhedra with a composition of VOnZm (Nnb = m/n = (Nf – CN)/CN)) regularly decreases from 1.8 to 0.1 with increasing V5+ CN from 4 to 7. Here the total solid angle (:bnd) corresponding to all V–O bonds in coordination V5+On polyhedra naturally increases amounting to 89.5%, 93.2%, 99.7%, and 99.8% of the total solid angle at n = 4, 5, 6, and 7 respectively. A similar situation is observed in a series of V2+O6–V3+O6–V4+O6–V5+O6 octahedra, in which :bnd = 91.9%, 99.0%, 99.5%, and 99.7% respectively. Note that when Nnb | 0, and hence, :bnd | 100%, the volume of vanadium VD polyhedron in the VOn complex is determined by the valence state of the metal atom and does not depend on its CN. In the sampling discussed, the only example of this type is V5+ atoms with CN 6 and 7, for which VVDP (7.0(1) Å3) or RSD (1.187(7) Å) coincide regardless that the length of V–O bonds both in V5+O6 octahedra and V5+O7 pentagonal bipyramids changes no more than by 1 Å (Table 1). The form of coordination polyhedra, and hence, the VD polyhedra also differs. This, in our opinion, is one more argument in favor of the standpoint [8, 9, 11], according to which complexing atoms Ⱥ in the crystal structure can be considred as non-rigid (capable of deformation) spheres with the radius RSD. The dimensionless parameter G3 [7] that characterizes the degree of sphericity of VD polyhedra of V atoms in the structure of compounds under study (G3 = 0.077 for the sphere) varies in a range from 0.083 to 0.104. Since at all CNs G3 > 0.082, in accordance with [7], it is possible to assume that the directed, i.e. substantially covalent, interatomic V–O interactions strengthening with decreasing vanadium CN mainly contribute to the formation of the coordination sphere of V atoms in the structure of crystals. As for the other AXn complexes, with increasing vanadium CN the G3 value, in general, regularly decreases (Table 1). In other words, the uniformity of the vanadium atom surrounding by all neighboring atoms enhances in the crystal structure. For the octahedral Vz+O6 complexes, a difference in the average G3 value (0.0832, 0.0838, 0.0849, and 0.0857 at z = 2, 3, 4, and 5 respectively) from the theoretical value of 0.0833 for the regular octahedron is caused by a distortion of coordination polyhedra because the overwhelming majority of V atoms with CN of 6 have low (triclinic or monoclinic) ɋ1, Ci. or ɋs site-symmetry in the structure, while the cubic Oh site-symmetry of the regular octahedron is observed only in one of 554 cases (the SrVO3 structure {96291}). The highest G3 values correspond to atoms with tetrahedral coordination, for which the average G3 value rather regularly increases from 0.092 to 0.099 with increasing vanadium oxidation number. Here in Vz+O4 tetrahedra, :bnd also grows (55%, 78%, 79%, and 89% at z = 2, 3, 4, and 5 respectively). Therefore, the fact that the real G3 value for all V atoms with CN of 4 is smaller than the theoretical value of 0.104 for the ideal tetrahedron can be considered to be a consequence of the effect of non-valence V/Z interactions (Table 1). Note also that in the structures of compounds in question regular Vz+O4 tetrahedra with Td site-symmetry are absent because all vanadium atoms with CN of 4 have ɋ1, ɋs, or ɋ3v site-symmetry. In the sampling discussed, a shift of V atoms from the center of gravity of their VD polyhedra (DA, Table 1) is on average 0.06(4) Å and is usually zero within 2V(DA). However, here the overwhelming majority of coordination polyhedra of vanadium atoms are more or less distorted. This is indicated by both characteristics of V–O bonds in Vz+On polyhedra (Table 1) and the distribution of these bonds depending on their length (Fig. 2). In particular, in 460 of 714 Vz+On polyhedra, 864
Fig. 2. Distribution of 4626 V–O or V/O contacts (with a step of 0.01 Å) in VD polyhedra of 714 vanadium atoms depending on the V–O interatomic distance. one (at z = 3 and n = 6; z = 4 and n = 5 or 6; z = 5 and n = 4, 5, 6, or 7), two (only at z = 5 and n = 4, 5, or 6) and even three (the only example is the V5+ atom with CN of 4 in the KV2SeO7 structure{80178}) V–O bonds are much shorter (they are in the 1.55-1.65 Å range) than the other bonds whose length can reach 2.79 Å. As noted [5], within BVM the shortened bonds (the first maximum with r = 1.60 Å correspond to them in Fig. 2) can be considered as double (vanadyl) with the valence s | 2.00. These short bonds (one, two, or three) appear as a result of the vanadium atom shift to one of the vertices, the edge or face centers of the Vz+On coordination polyhedron respectively. In particular, increased (on average to 0.12-0.14 Å) DA for V(IV) and V(V) with CN of 5 is due to the shift of vanadium atoms to the apical oxygen atom in V4+O5 square pyramids one short and four long bonds (r(V–O) = 1.61(3) Å and 1.97(4) Å respectively) appear in the polyhedra, while in the second case, two short and three long bonds (1.62(2) Å and 1.96(6) Å respectively) form. Here the O = V = O angle is 108(2)q in VO 2 dioxocations. Unlike V5+O5 bipyramids, in V3+O5 trigonal bipyramides, for which DA | 0, V(III) atoms are almost in the
center of gravity of the polyhedra and form three short (in the equatorial plane, r = 1.85(2) Å) and two long (2.14(5) Å) V–O bonds. As seen from Table 1, regardless the character of the distortion of Vz+On polyhedra that strongly affects the difference in V–O bond lengths in the structures of crystals, at fixed CN of vanadium atoms the parameters of their VD polyhedra (VVDP or RSD) depend only on the vanadium oxidation number. This allows us to use the RSD values to determine the valence state of metal atoms in the compounds that contain vanadium atoms with different crystal chemical roles. As an example, let us consider V3Ɉ5 {16445} and V4Ɉ7 {19012} oxides that were not included into the set of 412 compounds because the ICSD database [1] gives only the average oxidation number (3.333) for four different vanadium atoms in the V3Ɉ5 structure, whereas for V4Ɉ7 the vanadium valence state is not given at all. The experimental RSD values of vanadium atoms in the structures of these oxides (Table 2) provide the opportunity to assign a certain integer oxidation number to each of them and to characterize the oxides by formulas of V 4+ V23 O 5 and V24 V23 O 7 for V3Ɉ5 and V4Ɉ7 respectively. For the first of them, the authors have drawn the same conclusion based on the BVM method [5]. Another example is the C2H20N6O13S2V {WAJKOI} structure that, judging by the name of the compound in the database [2], should contain two valent vanadium atoms. However, the calculated RSD values (Table 2) indicate that both vanadium atoms are in the four rather than two valent state. Reference to the original source gives grounds to consider that the contradiction revealed is due to the inattentiveness of database compilers [2], who did not take into account that in the {WAJKOI} structure described in the work [12] under the title of “Structural characterisation of MIIguanidinium sulphate hydrates (ɆII = Mn, Fe, Co, Ni, Cd, VO),” VIV=Ɉ vanadyl groups rather than VII serve as ɆII, unlike the other metals. Thus, the combination of different crystal chemical approaches to the analysis of current structural databases allows the most complete characterization of the
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TABLE 2. Characteristics of Vanadium Atoms in Some Compounds Compound
Atom
Site multiplicity
CN
Range r(V–O), Å
RSD , Å*
exp
z
|'RSD|, Å*
V3Ɉ5 {16445}
V+ V2+ V3+ V4+ V+ V2+ V3+ V4+ V+ V2+
4 4 2 2 4 4 4 4 4 4
6 6 6 6 6 6 6 6 6 6
1.72-2.17 1.89-2.13 1.96-2.04 1.98-2.04 1.82-2.07 1.91-2.05 1.73-2.15 1.90-2.12 1.59-2.24 1.59-2.24
1.223 1.262 1.252 1.247 1.210 1.237 1.223 1.255 1.222 1.221
4 3 3 3 4 3 4 3 4 4
0.004 0.015 0.005 0 0.009 0.010 0.004 0.008 0.003 0.002
V4Ɉ7 {19013}
C2H20N6O13S2V {WAJKOI}
exp exp *|'RSD| is the absolute difference ( RSD – RSD), where RSD is the value calculated for the given vanadium atom based on crystal structural data, and RSD is the overall average value from Table 1, the closest in magnitude at given CN, which determines the z value (or oxidation number) of the metal atom in the Vz+On polyhedron. Since for all vanadium atoms CN is 6, at z = 3 and 4 the values of 1.247 Å and 1.219 Å respectively were used as RSD.
stereochemistry of transition metal atoms, whose complicated electronic structure provides no opportunity to carry out any quantitative quantum chemical calculations. The authors are grateful to RFBR (grant No. 85-05-74082) and the Program for Leading Scientific Schools (grant No. NSh-8091.2006.5) for support.
REFERENCES Inorganic Crystal Structure Database, Gmelin-institut fur Anorganische Chemie & FIC Karlsruhe (2007). Cambridge Structural Database System, Version 5.29, Univ. Cambridge, UK. V. S. Urusov, Acta Crystallogr., B51, No. 5, 641 (1995). V. S. Urusov, Dokl. Akad. Nauk, 408, No. 3, 355 (2006). V. S. Urusov and V. N. Serezhkin, Kristallografiya, 54, No. 2, 218 (2009). V. A. Blatov, A. P. Shevchenko, and V. N. Serezhkin, Koordinats. Khim., 25, No. 7, 483 (1999). D. V. Korol’kov and G. A. Skorobogatov, Theoretical Chemistry [in Russian], Izd. SPGU, St. Petersburg (2004). V. N. Serezhkin, Yu. N. Mikhailov, and Yu. A, Buslaev, Zh. Neorg. Khim., 42, No. 12, 2036 (1997). V. N. Serezhkin and Yu. A. Buslaev, ibid., No. 7, 1178. V. S. Urusov, Dokl. Akad. Nauk, 380, No. 3, 359 (2001). V. N. Serezhkin, L. B. Serezhkina, D. V. Pushkin, and A. V. Vologzhanina, Koordinats. Khimi., 31, No. 10, 775 (2005). 12. M. Fleck, L. Bohaty, and E. Tillmanns, Solid State Sciences, 6, No. 5, 469 (2004). 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.
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