- Email: [email protected]
Bond-valence sums for Tc–O systems from EXAFS data
Inorganica Chimica Acta 358 (2005) 865–874 www.elsevier.com/locate/ica
Bond-valence sums for Tc–O systems from EXAFS data Dennis W. Wester *, Nancy J. Hess Pacific Northwest National Laboratory, RSEG, P.O. Box 999, Richland, WA 99354, USA Received 21 April 2004; accepted 4 October 2004 Available online 22 October 2004
Abstract Literature data for structures containing exclusively Tc–O bonds were used to calculate unit-valence parameters R0 for Tc(VII), ˚ , respecTc(VI), Tc(V) (five-coordinate), Tc(V) (six-coordinate), Tc(IV) and Tc(III) as 1.909, 1.955, 1.870, 1.859, 1.841 and 1.768 A tively. A second method of estimating R0 was developed to validate the calculated values for these oxidation states because crystallographic data are limited. The method was first tested and shown to be valid using literature data for Cr, Mn, Fe and Co complexes. The validated R0 values for Tc were used to calculate bond-valence sums (BVS) for Tc solids and aqueous solutions using EXAFS data for the bond distances and coordination numbers. The calculated BVS showed good agreement with the expected values for the assumed Tc oxidation states. Ó 2004 Elsevier B.V. All rights reserved. Keywords: Bond-valence sums; R0 values; Tc–O systems; EXAFS
1. Introduction There has been increased interest in Tc environmental chemistry due to the presence of Tc in radioactive waste produced by nuclear weapons production facilities and the presence of Tc in commercial nuclear fuel. The fate of Tc in the environment is a major concern for licensing applications for nuclear waste repositories and for the closure of decommissioned US. Department of Energy (DOE) facilities because of the long half-life of 99Tc and the mobility of Tc under most environmental conditions. The fate of Tc in the environment is largely dependent on the local redox conditions. Although Tc can be present in oxidation states from (I) to (VII), most environmental conditions are sufficiently oxidizing that Tc is present in the Tc(VII) state and as the highly soluble anion, TcO4 . However, under anoxic condi*
Corresponding author. Tel.: +1 509 376 7195; fax: +1 509 375 1517. E-mail address: [email protected] (D.W. Wester). 0020-1693/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.ica.2004.10.002
tions the dominant oxidation state is Tc(IV) which forms poorly soluble amorphous solids. X-ray absorption spectroscopy (XAS) analysis has been an increasingly popular tool for the investigation of environmental samples [1–3]. It requires minimal sample preparation, preserves the essential chemistry, and can be used to examine the speciation of Tc in complicated liquid matrices and amorphous or crystalline solids. XAS provides element-specific oxidation-state determination from analysis of the X-ray absorption near-edge structure (XANES) and the identity of coordinating atoms and their atomic distances from analysis of the extended X-ray absorption fine structure (EXAFS). Even for ideal samples, analysis of the EXAFS can be highly model-dependent. Some EXAFS parameters, such as coordination number and disorder, are highly correlated. Since environmental samples are often dilute and/or inhomogeneous and are less than ideal XAS samples, we desired a tool to verify the coordination environment determined by modeling the EXAFS data.
866
D.W. Wester, N.J. Hess / Inorganica Chimica Acta 358 (2005) 865–874
With traditional use of the bond-valence sum (BVS), the oxidation state of a central atom can be determined if the R0 value and the lengths of the bonds from donor atoms to the central atom are known. The BVS method has been applied to a variety of metals mainly coordinated to a single type of donor atom, oxygen being the most common [4–13]. The bond lengths are typically determined from X-ray crystal structures, but EXAFS data could also be used. For example, the BVS method in combination with EXAFS has been used previously in studies of metal atoms in proteins [14–19]. For our application, the oxidation state can be determined from analysis of the XANES data so we sought to use the BVS method to verify, and perhaps aid in the construction of, coordination spheres based on EXAFS modeling. A review of the literature revealed that the R0 parameters for calculating BVS for Tc were not available, so our first task was to derive the R0 parameters from the existing X-ray crystal structures for Tc compounds where the Tc environment is composed only of oxygen atoms. The data were limited so we then developed a method of estimating R0 values by comparing the parameters for two oxidation states and tested this method against Cr, Mn, Fe and Co compounds for which there is abundant BVS data. We then used published EXAFS analyses of Tc compounds to compare the known or assumed oxidation state to that determined from BVS calculations. We first review the basics of the BVS approach below. 1.1. BVS method Several detailed discussions of the BVS method have appeared [20–28]; however, the BVS method can be traced back to Pauling [29]. Pauling first postulated the electrostatic valence principle for predominantly ionic crystals, according to which ‘‘the electric charge of each anion in a stable coordination structure tends to compensate the strength of the electrostatic valence bonds reaching to it from the cations at the centers of the polyhedra of which it forms a corner’’. From this, the mathematical expression X zj ¼ sij ; ð1Þ i
can be derived, where zj is the valence of cation j and sij is the valence of the individual bonds between the cation and surrounding anions, i. Later, Pauling [30] proposed for carbon compounds an empirical relation between the bond length Rij and the bond order nij Rij ¼ R b lnðnij Þ;
ð2Þ
where R is the length of a single bond (i.e., nij = 1) and ˚ . For inorganic compounds, the bond valence b = 0.31 A sij is a more accurate description than the strict bond or-
der. In addition, for inorganic compounds, including those of transition metals, the parameter b is commonly ˚ [31,32]. accepted [20–22,31–33] to have a value of 0.37 A Subsequent studies have shown this value to be generally accurate [20–22,32,33]. Eq. (2) is commonly rearranged and expressed as sij ¼ exp½ðR0 Rij Þ=b;
ð3Þ
where R0 depends upon the identity of the ij pair. By combining Eqs. (1) and (3), it can be seen that the valence of atom j can be calculated if the value of R0 and the lengths Rij of all bonds to an atom are known X zj ¼ exp½ðR0 Rij Þ=b: ð4Þ i
In fact, the R0 values for many common atom pairs are known [31–34]. Not surprisingly, R0 has been found to be dependent on both oxidation state and coordination number [8].
2. Experimental An examination of published parameters for performing BVS calculations revealed that the parameters for Tc have not appeared [31–34]. Thus, we surveyed the ICSD and Cambridge Structural databases for X-ray crystal structures of Tc compounds in which the Tc lies in an environment composed entirely of oxygen atoms. These compounds were sorted based on the reported oxidation state. Using the reported Tc–O bond distances, we calculated an R0 value for each compound by solving Eq. (4) for R0 after setting zTc equal to the re˚ . For some Tc oxiported integral valence and b = 0.37 A dation states, multiple compounds were identified and the calculated R0 values were averaged. The average R0 values were then used to back-calculate the oxidation state of the individual compounds. Compounds for which the calculated oxidation state differed significantly from the reported oxidation state were excluded from the data set and the average R0 was recalculated. For the Tc(VII) compounds, this process had to be carried out twice in order to produce an average R0 value for which all calculated oxidation states were acceptable. In addition, the Tc(V) compounds were also sorted by coordination number prior to determining R0 values. These calculations yielded the R0 values for Tc(VII)– Tc(III). The calculated R0 values were also estimated by a second method by comparing the R0 and Rij values for a pair of oxidation states, OX1 and OX2, and using Eq. (3). Specifically, Eq. (3) can be solved for b for each oxidation state. Since b is independent of oxidation state, the two equations are equal and the R0 value of one oxidation state can be estimated given the R0 value of the other oxidation state, the Rij values of both oxidation
D.W. Wester, N.J. Hess / Inorganica Chimica Acta 358 (2005) 865–874
states, and the average bond valence sij for both oxidation states, as shown in Eq. (5) below R0;OX2 ¼
lnðsij;OX2 Þ ðR0;OX1 Rij;OX1 Þ þ Rij;OX2 : lnðsij;OX1 Þ
ð5Þ
This method was also tested on transition metal–oxygen systems for which BVS data are currently available. We then tested whether the BVS approach could be used to verify the coordination environment determined by EXAFS analysis. To do this, we first surveyed the literature to extract EXAFS determinations of Tc compounds, where the coordination environment was composed solely of oxygen atoms. These compounds included both solid and solution samples. We used the calculated R0 values from XRD determinations and Eq. (4) to calculate the oxidation state using the EXAFS determinations for the bond lengths, Rij, and coordination numbers. We used the published coordination numbers in the BVS calculations although those determined by EXAFS analysis often have a non-integer value and, in some cases, are not in agreement with the accepted coordination number for the assumed oxidation state. The calculated oxidation state was then compared to the known or assumed oxidation state.
3. Results and discussion 3.1. Calculation of R0 values for Tc(VII)–Tc(III) Table 1 lists the bond distances, bond valences, and BVS for Tc(VII) compounds, which all contained pertechnetate anions with the exception of Tc2O7. The iniTable 1 Tc(VII) compounds used in the analysis Compound
BVSa
References
[NpO2]2[TcO4]4 Æ 3H2O [Tc(1)] [NpO2]2[TcO4]4 Æ 3H2O [Tc(2)] [NpO2]2[TcO4]4 Æ 3H2O [Tc(3)] [NpO2]2[TcO4]4 Æ 3H2O [Tc(4)] ½Ph3 P ¼ NHþ 2 ½TcO4 [(C5H5)2Fe]TcO4 (l-CH3CO2)4Tc2(TcO4)2 CsTcO4 CsTcO4 {(CH3)3SnOTcO3}n [(NH3)4Pt][TcO4]2 (3,6-Dimethyl-3,6-diazaoctan-1,8-dithiolateS1,N3,N6,S8)Tc(V)O(TcO4) [Bu4N][TcO4]b [Me4N][TcO4]b [NH4][TcO4] KTcO4 Tc2O7
7.026 7.011 7.009 6.929 7.105 7.272 7.171 7.062 6.787 7.179 6.878 7.159
[35] [35] [35] [35] [36] [37] [38] [39] [40] [41] [42] [43]
9.030 7.572 6.999 6.831 6.744
[44] [45] [46] [47] [48]
a b
Calculated using R0 = 1.909. Omitted from calculation of R0.
867
tial average R0 value calculated using all compounds in ˚ . The compounds [Bu4N]Table 1 was 1.901 ± 0.026 A [TcO4] and [Me4N][TcO4] were eventually omitted from subsequent rounds of calculations because the back-calculated oxidation states differed significantly from 7. ˚. The final R0 value was 1.909 ± 0.008 A The values in Table 1 show that the BVS calculation gives good agreement with the expected oxidation state for pertechnetate compounds containing both free and coordinated anions. The BVS values calculated for the two compounds that contain coordinated pertechnetate, (l-CH3CO2)4Tc2(TcO4)2 [38] and {(CH3)3SnOTcO3}n [41], are well within the acceptable range. An examination of (l-CH3CO2)4Tc2(TcO4)2 and {(CH3)3SnOTcO3}n found that these complexes contain loosely coordinated TcO4 for which the Tc–O distances are within the range typical of Tc–O double bonds (1.64– ˚ ). However, the bonds to the bridging oxygen 1.73 A atoms are on the longer end of this range whereas the bonds to the terminal oxygen atoms are on the shorter end of it. The BVS value calculated for Tc2O7, which contains TcO3 units linked by an oxygen bridge, was very near the lower end of the acceptable range. In this structure the bridging Tc–O bond is significantly longer ˚ ) than the others. Therefore, it would appear (1.840 A that the BVS for Tc2O7 falls near the lower end of the acceptable limits because the three terminal oxygen atoms are unable to approach Tc close enough to compensate for the lengthening of the bond to the bridging oxygen atom, as proposed by Brown [49], resulting in a distorted tetrahedral environment. Table 2 lists the R0 values for compounds with Tc in lower oxidation states. For Tc(VI), only one compound with all oxygen donors, tris(3,5-di-tert-butylatecholato)technetium(VI), was found in the literature [50]. The ˚ with a back-calculated calculated R0 value was 1.955 A oxidation state of 6.005 for this six-coordinate compound. For Tc(V), structures for a total of four complexes with all oxygen donors were found [51–54]. Although all have the oxotechnetium(V) core, three are five-coordinate and one is six-coordinate. Using all four compounds, the initial calculation of R0 gave a value ˚ . However, the back-calculated of 1.867 ± 0.006 A oxidation state of the six-coordinate [AsPh4]2[TcO(ox)2-(Hox)] Æ 3H2O compound was 4.533, whereas the average back-calculated oxidation state of the five-coordinate compounds was 4.956 ± 0.016. As a result R0 values for the five- and six-coordinate compounds were recalculated separately. The R0 values for the five- and six-coordinate compounds were deter˚ , respectively. mined to be 1.870 ± 0.001 and 1.859 A The four Tc(IV) compounds used in the analysis are all six-coordinate. Using all four compounds resulted ˚ and an average in an initial R0 value of 1.845 ± 0.007 A back-calculated oxidation state of 4.001 ± 0.075. The
868
D.W. Wester, N.J. Hess / Inorganica Chimica Acta 358 (2005) 865–874
Table 2 Tc compounds in lower oxidation states used in the analysis Oxidation state
Compound
˚) R0 (A
BVS
References
(VI) (V) (V) (V) (V) (IV) (IV) (IV) (IV) (IV) (III)
Tris(3,5-di-tert-butylcatecholato)technetium Tetrabutylammonium bis(4-nitro-1,2-catecholato)oxotechnetium [(n-C4H9)4N][TcO(C6Cl4O2)2] Tetrabutylammonium bis(1,2-diolato)oxotechnetium [AsPh4]2[TcO(ox)2(Hox)] Æ 3H2O Tris(hydroxymethyl)(trimethylammonio)methanetechnetium Bis(tetraphenylarsonium) tris(oxalato)technetate Tc(IV)-diphosphonate complex K4[(C2O4)2Tc(l-O)2Tc(C2O4)2] Æ 3H2O (Tc1) K4[(C2O4)2Tc(l-O)2Tc(C2O4)2] Æ 3H2O (Tc2) Tris(acetylacetonato)technetium
1.955 1.870 1.870 1.870 1.859 1.845 1.845 1.845 1.845 1.845 1.768
6.005 4.990 5.014 4.984 5.000 3.994 4.060 4.092 3.932 3.926 2.997
[50] [51] [52] [53] [54] [55] [56] [57] [58] [58] [59]
excellent agreement between the BVS and the actual oxidation was unexpected due to the diverse extended Tc environments represented by the four compounds. The Tc in the tris(oxalate) [56] and tris(hydroxymethyl)(trimethylammonio)methane [55] complexes are monomeric whereas the methylenediphosphonate complex [57] is polymeric. Finally Tc is oxo-bridged in the oxalate dimer and has a strong Tc–Tc interaction [58]. This result may suggest that the BVS is insensitive to the extended Tc coordination environment. For Tc(III), the Tc(acac)3 complex [59] yields an R0 ˚ and a back-calculated oxidation state value of 1.768 A of 2.997 for this six-coordinate structure. Table 3 summarizes the R0 values calculated for Tc oxidation states (VII)–(III) for coordination environments consisting only of oxygen atoms. These values were used to calculate the Tc oxidation state in complex matrices based on coordination environments determined by EXAFS analysis in Section 3.3. It was surprising that the R0 values in Table 3 increase with increasing oxidation state, which is counter-intuitive to the trend expected, although similar to the linear trend calculated for Mo–O six-coordinate compounds assuming ˚ [60]. For this reason, we devised an alternab = 0.037 A tive method for determining the R0 values that is described in the following section. Also, the fact that the sample size for calculating these R0 values was extremely small, in some cases consisting of a single crystal structure, could also contribute to the unusual trend. For example, the single Tc(VI) complex used, the tris-catecholate, contains non-innocent ligands that can exist as Table 3 Summary of R0 values for Tc Tc oxidation state
No.
˚) R0(calc) (A
SD
(III) (six-coordinate) (IV) (six-coordinate) (V) (five-coordinate) (V) (six-coordinate) (VI) (six-coordinate) (VII) (four-coordinate)
1 3 3 1 1 15
1.768 1.841 1.870 1.859 1.955 1.909
n/a 0.005 0.001 n/a n/a 0.008
radical anions and can make the assignment of the oxidation state somewhat controversial. 3.2. Alternative method for estimating R0 As shown above, a search of the available crystallographic databases revealed that there are a limited number of Tc compounds, where oxygen is the only atom in the immediate coordination environment. Indeed, as shown in Table 3, for some Tc oxidation states the R0 values are based on a single crystal structure. Therefore an alternative method of estimating R0 was developed in order to calculate the R0 values of all oxidation states using R0 values for two well-characterized ones. These estimated R0 values could then be compared against those calculated from the available crystallographic data by the traditional approach used in Section 3.1. The method developed here essentially scales the difference between R0 and the average bond distance value for a given oxidation state by the ratio of the bond valences as shown in Eq. (5). Since the average bond valence sij is simply the oxidation state divided by the number of bonds, these values are readily calculated for both oxidation states. Thus, if the Rij values for both oxidation states are known, then the R0 value of the second oxidation state can be calculated by knowing the R0 value of the first oxidation state. We first tested this approach by using BVS data for several transition–metal–oxygen systems since, there is abundant BVS data and a rich variation in oxidation states and coordination environments available for comparison. Since the estimated R0 value will be dependent on the initial set of BVS parameters chosen, the R0 values were estimated twice using two independent sets of BVS parameters. Table 4 shows the data used for the Cr–O system [6]. Of the several possible starting points, we chose oxidation state (III) with coordination number six and oxidation state (VI) with coordination number four because of the large number of bond distances that were used to determine the experimental R0 values for these systems, 810 and 212, respectively. In addition, the average
D.W. Wester, N.J. Hess / Inorganica Chimica Acta 358 (2005) 865–874
869
Table 4 Calculated R0 values for Cr–O complexesa Oxidation state
CN
dav
˚) R0,exptl. (A
˚) R0,III/6 (calc) (A
˚) R0,VI/4 (calc) (A
Differenceb
(II) (II) (II) (II) (III) (III) (IV) (V) (V) (VI)
3 4 5 6 4 6 4 5 8 4
1.925 1.992 2.099 2.195 1.882 1.967 1.773 1.795 1.920 1.647
1.769(10) 1.735(23) 1.741(4) 1.735 n/a 1.708(7) 1.773 1.770(8) 1.738(14) 1.793(7)
1.773 1.733 1.757 1.784 1.775 [1.708] 1.773 1.795 1.744 1.799
1.779 1.742 1.769 1.799 1.778 1.717 1.773 1.795 1.751 [1.793]
0.007 0.003 0.022 0.057 n/a 0.009 0.000 0.025 0.010 0.006
a
The estimated standard deviation is given, where appropriate in parentheses after the value. The difference equals R0, exptl. (R0,III/6 + R0,VI/4)/2, except for the two systems used to calculate R0 values, i.e., oxidation state (III) with coordination number six and oxidation state (VI) with coordination number four, where the difference is simply R0, exptl. minus the single calculated value. b
bond distance values, dav in Table 4, are used for the Rij values in Eq. (5). The agreement of the calculated R0 values with the values measured experimentally was within three estimated standard deviations of the experimental R0 values except for complexes containing Cr(II) with coordination number five and Cr(V) with coordination number five. For Cr(II) with coordination number six, the agreement is also poor but there is no standard deviation for the experimental R0 because the value was calculated from only one structure. These larger discrepancies between the estimated and experimental R0 values may result from distortion of the Cr coordination polyhedra such that the average bond distance does not provide a representative basis for the calculation of a single R0 value. For example, for six-coordinate Cr(II) there is a tendency of ions with d4 electronic configuration to have distorted octahedral coordination environments known as Jahn–Teller distortions [61]. These octahedra are characterized by four ligands at one distance and two ligands at a different distance that is either closer or further away. As a result of this distortion, the calculated average bond distance may not accurately represent the contribution from the two ligands, especially when the difference is large. Examination of reference [6] reveals that R0 was calcu-
lated on the basis of one structure and that nearly 0.5 ˚ separated the minimum and maximum bond disA tances. Similarly, Cr(V) in penta-coordination has one short Cr–O double bond and four longer Cr–O bonds. In this case, the minimum and maximum bond distances ˚ . A similar range in miniare separated by nearly 0.4 A mum and maximum bond distances is reported for Cr(II) in penta-coordination. Table 5 shows data for the Mn–O system [7]. Unfortunately, the reported R0 values are listed only by coordination number and not by oxidation state, that is, no explicit oxidation state dependence is reported. However, oxidation-state-specific average bond lengths, dav, are reported. Therefore, the R0 values for the specific oxidation states were estimated using the reported average bond length, dav, for Rij in Eq. (5). Because the data for the seven- and eight-coordinate complexes must have come from only Mn(II) complexes, these were chosen as starting points for the calculations. Table 5 lists the results of the calculations starting with data from both the seven- and eight-coordinate complexes. It can be seen that the R0 values calculated reciprocally for the seven- and eight-coordinate complexes agree very well and are also in good general agreement with the five-coordinate complexes. The
Table 5 Calculated R0 values for Mn–O complexes Oxidation state
CN
dav
˚) R0 exptl.a (A
˚) R0,II/7 (calc) (A
˚) R0,II/8 (calc) (A
Differenceb
(II) (II) (II) (II) (III) (III) (IV)
5 6 7 8 5 6 6
2.121 2.176 2.242 2.286 1.959 2.015 1.899
1.762 1.753 1.766 1.761 1.762 1.753 1.753
1.773 1.759 [1.766] 1.759 1.765 1.752 1.745
1.774 1.760 1.767 [1.761] 1.765 1.752 1.745
0.012 0.007 0.001 0.002 0.003 0.001 0.008
a
The R0, exptl. values in the original article were reported only by coordination number as an average over all applicable oxidation states. The difference equals R0, exptl. (R0,II/7 + R0,II/8)/2, except for the two systems used to calculate R0 values, i.e., oxidation state (II) with coordination numbers seven and eight, where the difference is simply R0, exptl. minus the single calculated value. b
870
D.W. Wester, N.J. Hess / Inorganica Chimica Acta 358 (2005) 865–874
calculated R0 values for the five- and six-coordinate complexes decrease with increasing oxidation state as expected. The R0 value reported for five-coordinate ˚ ) is less than the calculated R0 values complexes (1.762 A for Mn(II) and Mn(III). The R0 value reported for six˚ ) falls near the middle coordinate complexes (1.753 A of the range of the R0 values calculated for six-coordinate complexes of Mn(II), -(III) and -(IV). For some oxidation-state–coordination-number pairs the agreement between experimental and calculated R0 values is actually better than would be expected based on comparison with the results for the Cr–O system. Specifically, Mn(III) has the same d4 electronic configuration as Cr(II) and the difference between the minimum and maximum reported Mn–O bond distances in this case ˚ [7], potentially indicating a tendency to form is 0.55 A distorted coordination polyhedra. Good agreement between experimental and calculated R0 values in this case may reflect the fact that the reported minimum, maximum, and average values are based on 42 distinct crystal structures [7] and the reported average value is also close to the average of the minimum and maximum values. This suggests that the experimental R0 value is in fact representative. Table 6 shows the results for Fe–O systems [8]. Like the Mn–O system, the reported R0 values are assumed to be independent of oxidation state; therefore, the experimental R0 values listed in Table 6 for a given coordination number are the same regardless of oxidation state. However, oxidation state specific average bond lengths are reported. The starting points for these calculations were the divalent three- and eight-coordinate systems. For four-coordinate complexes, the calculated R0 ˚ for Fe(II) and Fe(III), values were 1.735 and 1.741 A respectively, which is in good agreement with the R0 va˚ . The calculue for four-coordinate complexes, 1.740 A lated R0 values for the five- and six-coordinate complexes of Fe(II) and Fe(III) showed substantial differences from the observed values. For five-coordinate complexes, the calculated R0 values were 1.702 and ˚ for Fe(II) and Fe(III), respectively. The re1.754 A
˚, ported R0 for five-coordinate complexes is 1.739 A which is of intermediate value. Finally, the calculated R0 values for six-coordinate complexes were 1.685 and ˚ for Fe(II) and Fe(III), respectively, whereas 1.736 A ˚ . In this instance both the reported R0 value is 1.745 A calculated R0 values are less than the observed one. We can think of no satisfactory explanation for the ˚ ) between the experimental and large disparity (0.060 A estimated R0 values for Fe(II) in six-coordination. The experimental R0 is based on a large number of crystal structures (66) [8]. Furthermore, although there is moderate difference between the minimum and maximum ˚ , the reported average disFe–O bond distances, 0.40 A tance is also very close to the average of the minimum and maximum values, suggesting that on the average these are not severely distorted octahedral complexes. Table 7 shows data for Co–O complexes [9]. In this system as well, the R0 values were reported as independent of oxidation state but oxidation-state-specific average bond lengths are reported. The divalent five- and seven-coordinate complexes were chosen as starting points for the calculations. For Co(II), good agreement is seen for the lower coordination numbers (three, four, five and six). The agreement is not as good for the higher coordination numbers (seven and eight). Similarly, for Co(III), the calculated R0 value for the six-coordinate complexes is significantly less than the experimental value. A possible explanation for these discrepancies is that due to the large number of coordinating oxygen atoms they are unable to attain ideal Co–O bond lengths because of interatomic contacts. This concept was discussed by Pauling [29], who noted a correlation between cation–anion radius ratios and the relative stability of tetrahedral, octahedral and eight-coordinate structures. Goldschmidt [62] further described the lower limit of this relationship between radius ratio and structural stability as the ‘‘no rattle limit’’ or NRL. Essentially if the radius ratio is less than the NRL for a given structure type, then the cation will rattle in the void space created by anion–anion contacts. For six-
Table 6 Calculated R0 values for Fe–O complexes Oxidation state
CN
dav
˚) R0 exptl.a (A
˚) R0,II/3 (calc) (A
˚) R0,II/8 (calc) (A
Differenceb
(II) (II) (II) (II) (II) (III) (III) (III)
3 4 5 6 8 4 5 6
1.950 2.009 2.065 2.120 2.356 1.855 1.957 2.011
1.788 1.740 1.739 1.745 1.813 1.740 1.739 1.745
[1.788] 1.732 1.698 1.681 1.801 1.740 1.753 1.734
1.791 1.737 1.706 1.689 [1.813] 1.742 1.757 1.739
0.003 0.006 0.037 0.060 0.012 0.001 0.016 0.009
a
The R0 exptl., values in the original article were reported only by coordination number as an average over all applicable oxidation states. The difference equals R0, exptl. (R0,II/3 + R0,II/8)/2, except for the two systems used to calculate R0 values, i.e., oxidation state (II) with coordination numbers three and eight, where the difference is simply R0, exptl. minus the single calculated value. b
D.W. Wester, N.J. Hess / Inorganica Chimica Acta 358 (2005) 865–874
871
Table 7 Calculated R0 values for Co–O complexes Oxidation state
CN
dav
˚) R0 exptl.a (A
˚) R0,II/5 (calc) (A
˚) R0,II/7 (calc) (A
Differenceb
(II) (II) (II) (II) (II) (II) (III)
3 4 5 6 7 8 6
1.906 1.960 2.043 2.093 2.152 2.260 1.895
1.748 1.704 1.686 1.670 1.684 1.695 1.670
1.748 1.690 [1.686] 1.665 1.663 1.719 1.625
1.754 1.701 1.700 1.682 [1.683] 1.742 1.636
0.003 0.008 0.014 0.004 0.021 0.035 0.040
a
The R0 exptl., values in the original article were reported only by coordination number as an average over all applicable oxidation states. The difference equals R0, exptl. (R0,II/3 + R0,II/8)/2, except for the two systems used to calculate R0 values, i.e., oxidation state (II) with coordination numbers three and eight, where the difference is simply R0, exptl. minus the single calculated value. b
and eight-coordinate structures, the NRL is 0.41 and 0.73, respectively. Using the Shannon–Prewitt [61] ionic ˚ for low spin six-coradii values of 0.545, 0.90 and 1.40 A ordinate Co(III), eight-coordinate Co(II) and O2, respectively, ionic-radius ratios of 0.389 for the octahedral and 0.643 for the eight-coordinate configurations are calculated. Both of these values are less than the NRL for their structure types suggesting that anion–anion contacts would occur in the idealized structure. Analogous structural stability analyses based on ionicradii ratio are not available for seven-coordinate structure types. The polyhedra of Co(II) in five-, six- and eight-coor˚ differences between the minimum dination have 0.5 A and maximum Co–O bond distances and, for five- and six-coordination, the reported average bond distance is significantly different from the simple average of the minimum and maximum bond distance values. Thus, a second possible origin of the discrepancy between the experimental and estimated R0 values is the inability of a single R0 value to fully represent severely distorted coordination polyhedra as discussed earlier. Additionally, it should be noted that the experimental R0 value for Co(II) in eight-coordination is based on a single structure [9]. The above calculations for the Cr–O, Mn–O, Fe–O and Co–O systems demonstrate that this scaling method is a valid approach to estimating R0 and satisfactory agreement with experimental R0 values is obtained in
most cases. However, discrepancies between experimental and calculated R0 values are observed for ions typified by severe distortion of their coordination polyhedra or ions with small ionic radii and crowded coordination spheres resulting in interanionic contacts. We now apply the scaling approach to the Tc–O system to verify the experimental R0 values listed in Tables 1–3. We chose Tc(III) and Tc(IV) with octahedral coordination as starting points for our calculations. Table 8 lists the experimental and estimated R0 values for each Tc oxidation state and coordination number. The agreement is very good for Tc(VII), Tc(VI), Tc(IV) and Tc(III) oxidation states. However, the estimated R0 val˚ ues for five- and six-coordinate Tc(V) are 0.025–0.030 A greater than the experimental R0 values. A possible explanation is that the bonding environment for Tc(V), which contains a very short Tc@O double bond and four to five longer TcAO single bonds, is sufficiently distorted so that it is not adequately represented by a single average bond distance. As we have seen from our examination of the Cr–O, Mn–O, Fe–O and Co–O systems, it appears that as long as the coordination environment can be represented by a single bond distance that the scaling approach satisfactorily estimates R0. This argument is further strengthened by examining the results for Tc(VII), which formally contains three Tc@O double bonds and a single Tc–O bond. However, the XRD and EXAFS data for Tc(VII) both indicate the presence of four Tc–O bonds of nearly equivalent length
Table 8 Calculated R0 values for Tc–O complexes Oxidation state
CN
dav
˚) R0 exptl.a (A
˚) R0,III/6 (calc) (A
˚) R0,IV/6 (calc) (A
Differenceb
(III) (IV) (V) (V) (VI) (VII)
6 6 5 6 6 4
2.025 1.991 1.896 1.962 1.955 1.702
1.768 1.841(5) 1.870(1) 1.859 1.955 1.909(8)
[1.768] 1.841 1.896 1.894 1.955 1.910
1.769 [1.841] 1.896 1.895 1.955 1.909
0.001 0.000 0.026 0.035 0.000 0.001
a
The estimated standard deviation is given, where appropriate in parentheses after the value. The difference equals R0, exptl. (R0,III/6 + R0,IV/6)/2, except for the two systems used to calculate R0 values, i.e., oxidation states (III) and (IV) with coordination number six, where the difference is simply R0, exptl. minus the single calculated value. b
872
D.W. Wester, N.J. Hess / Inorganica Chimica Acta 358 (2005) 865–874
Table 9 Tc oxidation states calculated by BVS method using EXAFS data Compound
TcO4 ðaqÞ ð1Þ [PPh4][TcO4] (s) (2) TcO2 (cryst.) [thermal decomp. of NH4TcO4] (3) ‘‘Tc(IV)’’ (aq polymer) [electro-reduction] (4) ‘‘Tc(IV)’’ (aq polymer) [ electro-reduction] (5) TcO2 Æ xH2O (s) [hydrolysis of K2TcCl6] (6) TcO2 Æ xH2O (s) [radiolysis of TcO4 in Na2EDTA/NaOH] (7) TcO2 Æ xH2O (s) [hydrolysis of H2TcCl6] (8) Tc(IV) (aq dimer) [radiolysis of TcO4 in glyoxylate/NaOH] (9) Tc-MDP (aq) [HPLC purified] (10)
despite the difference in electronic configuration. Therefore the Tc(VII) coordinate environment is well represented by a single average bond distance and our scaling method successfully estimates the experimental R0 value. 3.3. Calculation of BVS using EXAFS data Table 9 lists the chemical systems for which we used EXAFS data for the bond length and coordination number to calculate the Tc oxidation states by the BVS method. The (VII) and (IV) oxidation states were the only ones for which EXAFS data could be located for which the Tc coordination environment consisted entirely of oxygen atoms. The BVS sums were calculated using the published coordination-number values from EXAFS analysis although these values often departed from the ‘‘known’’ integral coordination numbers of four and six for the Tc(VII) and Tc(IV) oxidation states, respectively. It also should be mentioned that the analysis of the EXAFS data includes a scale factor that directly impacts the coordination number. Typical values range from 0.8 to 1.0 [63]. In the literature referenced in Table 9, this value varies from 0.75 [67] to 0.9 [64,68] or is not reported [65,66,69]. The range of scale-factor values used in EXAFS analysis presents a complication for BVS analysis since inspection of Eqs. (1) and (4) reveals that the coordination number will directly impact the calculated BVS value. Nonetheless, in most instances, the calculated oxidation state agrees well with the assumed oxidation state. For Tc(VII), both examples are of pertechnetate, although one is in solution (1) and the other is in a solid (2). For TcO4 in aqueous solution as the ammonium salt (1) [64], excellent agreement is found with a BVS of 7.114 calculated using the EXAFS data. The agreement is not quite as good for the solid [PPh4][TcO4] (6.776) (2), although it would appear from the data that the coordination number was assumed to be four and not actually fit to the EXAFS data [65]. EXAFS studies on Tc–O systems have been carried out on solids and solutions believed to contain Tc(IV). Tc(IV) solids were prepared by a variety of methods
Oxidation state
BVS
References
(VII) (VII) (IV) (IV) (IV) (IV) (IV) (IV) (IV) (IV)
7.114 6.776 4.121 3.750 4.114 4.013 3.788 2.679 4.266 3.944
[64] [65] [66] [67] [67] [67] [68] [68] [68] [69]
including thermal decomposition of TcO4 ð3Þ [66]; hydrolysis of K2[TcCl6] (6) [67] or H2[TcCl6] (8) [68]; and radiolysis of TcO4 in alkaline Na2EDTA solution (7) [68]. Only (3) is a crystalline TcO2 solid; (6), (7) and (8) are amorphous Tc(IV) solids believed to be TcO2 Æ xH2O. Polymeric Tc(IV) solution species were prepared by electrolysis of TcO4 in the presence of Cl and SO4 2 ð4Þ or SO4 2 only (5) [67] and by radiolysis of TcO4 in alkaline glyoxylate solution (9) [68]. Table 9 shows that the oxidation state calculated by the BVS method using EXAFS data agrees very well in several instances with the known oxidation state. This is particularly true for TcO2(3), TcO2 Æ xH2O prepared by hydrolysis of TcCl6 2 ð6Þ, and Tc(IV) solution species prepared by the electroreduction of pertechnetate in sulfate solutions (5). The calculated oxidation states of 4.121, 4.013 and 4.114, respectively, are well within the ±0.25 variance of the oxidation state that is acceptable. It is interesting to note that while the BVS calculated for the solution species (5) prepared by electrolysis of TcO4 in a solution with ½SO4 2 ¼ 0:1 M [34] is 4.114, that for the solution species prepared by electrolysis of TcO4 in a mixed electrolyte solution of [Cl] = 3 M and ½SO4 2 ¼ 0:1 M ð4Þ has a much lower value of 3.75. EXAFS analysis of the bond distances and coordination numbers for the two Tc polymers are very close, ˚ for the Tc–O(1) and differing by 0.06 and 0.02 A Tc–O(2) distances, respectively, and 0.06 for both the coordination numbers. EXAFS analysis of the Tc(IV) solution species produced by radiolysis of TcO4 in alkaline glyoxylate solution (9) do not yield results that can be easily interpreted by BVS. The distance of 2.008 ˚ is reasonable whereas the coordination number of 6.7 A is too large. Nevertheless, the BVS calculated using R0 = 1.841 for Tc(IV) gives a value of 4.266, which is just beyond the limit of acceptability. Analysis of EXAFS data for TcO2 Æ xH2O prepared by radiolysis of TcO4 in Na2[EDTA]/NaOH (7) [68] ˚ ) and a nearly integral gives a single distance (2.005 A coordination number (5.9). The BVS value calculated using the R0 value for Tc(IV) is 3.788, within the limit of acceptability. In this instance, the bond distance is slightly longer than would be expected for Tc(IV) and
D.W. Wester, N.J. Hess / Inorganica Chimica Acta 358 (2005) 865–874
the coordination number is slightly lower than that for six-coordinate Tc. These two factors combine to decrease the BVS so that the value for Tc(IV) falls below 4.0. The EXAFS data for TcO2 Æ xH2O produced by hydrolysis of TcCl6 2 ð8Þ do not yield results that can be easily interpreted by BVS. The distances and coordination numbers for the solid TcO2 Æ xH2O give BVS values that are in all instances well below the expected values. This indicates that either the distances are too long or the coordination numbers are too low or both. ˚ with In fact, the distances for 8 are 2.017 and 2.47 A coordination numbers of 3.9 and 1.4, respectively. The ˚ is much longer than any Tc–O bond distance of 2.47 A that has been encountered in this study. The sum of the coordination numbers, 5.3, is reasonable. Therefore, it would seem that these EXAFS data do not give a valid BVS because the distances are too long. Finally, excellent agreement is seen for the well characterized methylenediphosphonate complex of Tc(IV) (10) [69], where a BVS of 3.944 is calculated using the EXAFS data. These results clearly demonstrate the utility of using BVS to evaluate the model of the Tc coordination environment provided by EXAFS analysis even with the uncertainty in coordination numbers from EXAFS analysis. Slight discrepancies between the calculated BVS and the assumed oxidation state could also reflect the presence of multiple species since the EXAFS results represent an average of all species present. Where significant discrepancies exist, for example, TcO2 Æ xH2O, the EXAFS model may fail to describe fully or accurately the Tc coordination environment. In addition, highly distorted bonding environments may be more complex than those that can described by the BVS model.
Acknowledgements We thank Prof. Gus J. Palenik of the Department of Chemistry, University of Florida, for useful discussions. This work was supported by the Environmental Management Science Program of the US Department of Energy. Pacific Northwest National Laboratory is operated by Battelle for the US Department of Energy under Contract No. DE-AC06–76RL01830.
References [1] G.E. Brown Jr, G. Calas, G.A. Waychunas, J. Petiau, in: F.C. Hawthorne (Ed.), Reviews in Mineralogy, vol. 18, BookCrafters, Inc., Chelsea, MI, 1988, pp. 431–512. [2] D.B. Hunter, P.M. Bertsch, J. Radioanal. Nucl. Chem. 234 (1–2) (1988) 237. [3] D.E. Morris, P.G. Allen, J.M. Berg, C.J. Chisholm-Brause, S.D. Conradson, R.J. Donohoe, N.J. Hess, J.A. Musgrave, C.D. Tait, Environ. Sci. Technol. 30 (7) (1996) 2322.
873
[4] G.J. Palenik, Inorg. Chem. 36 (1997) 122. [5] G.J. Palenik, Inorg. Chem. 36 (1997) 3394. [6] R.W. Wood, K.A. Abboud, R.C. Palenik, G.J. Palenik, Inorg. Chem. 39 (2000) 2065. [7] G.J. Palenik, Inorg. Chem. 36 (1997) 4888. [8] S.M. Kanowitz, G.J. Palenik, Inorg. Chem. 37 (1998) 2086. [9] R.M. Wood, G.J. Palenik, Inorg. Chem. 37 (1998) 4149. [10] R.M. Wood, G.J. Palenik, Inorg. Chem. 38 (1999) 1031. [11] R.M. Wood, G.J. Palenik, Inorg. Chem. 38 (1999) 3926. [12] W.P. Jensen, G.J. Palenik, E.R.T. Tiekink, Polyhedron 20 (2001) 2137. [13] G.J. Palenik, Inorg. Chem. 42 (2003) 2725. [14] R.C. Scarrow, M.G. Trimitsis, C.P. Buck, G.M. Grove, R.A. Cowling, M.J. Nelson, Biochemistry 33 (1994) 15023. [15] M.J. Nelson, B.A. Brennan, D.B. Chase, R.A. Cowling, G.N. Grove, R.C. Scarrow, Biochemistry 34 (1995) 15219. [16] L. Shu, Y.-M. Chiou, A.M. Orville, M.A. Miller, J.D. Lipscomb, L. Que Jr., Biochemistry 34 (1995) 6649. [17] R.C. Scarrow, B.A. Brennan, J.G. Cummings, H. Jin, D.J. Duong, J.T. Kindt, M.J. Nelson, Biochemistry 35 (1996) 10078. [18] J. Bell, D.E. Ash, L.M. Snyder, R. Kulathila, N.J. Blackburn, D.J. Merkler, Biochemistry 36 (1997) 16239. [19] H.H. Thorp, Inorg. Chem. 37 (1998) 5690. [20] L. Janseen, L. Chandran, R. Block, J. Mol. Struct. 260 (1992) 81. [21] J.P. Naskar, S. Hati, D. Datta, Acta Crystallogr. Sect. B: Struct. Sci. 53 (1997) 885. [22] V.S. Urusov, Acta Crystallogr. Sect. B: Struct. Sci. 51 (1995) 641. [23] M. OKeeffe, Modern Perspectives in Inorganic Crystal Chemistry, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1991, pp. 163–175. [24] I.D. Brown, Structure and Bonding in Crystals, vol. II, Academic Press, New York, 1981, pp. 1–30. [25] I.D. Brown, The Chemical Bond in Inorganic Chemistry, Oxford University Press, Oxford, UK, 2002. [26] I.D. Brown, J. Chem. Educ. 77 (2000) 1070. [27] W.H. Zachariasen, J. Less Common Met. 62 (1978) 1. [28] M. OKeeffe, N.E. Brese, J. Am. Chem. Soc. 113 (1991) 3226. [29] L. Pauling, J. Am. Chem. Soc. 51 (1929) 1010. [30] L. Pauling, J. Am. Chem. Soc. 69 (1947) 542. [31] I.D. Brown, D. Altermatt, Acta Crystallogr. Sect. B: Struct. Sci. 41 (1985) 244. [32] N.E. Brese, M. OKeeffe, Acta Crystallogr. Sect. B: Struct. Sci. 47 (1991) 192. [33] I.D. Brown, K.K. Wu, Acta Crystallogr. Sect. B: Struct. Crystallogr. Cryst. Chem. 32 (1976) 1957. [34] I.D. Brown, J. Appl. Crystallogr. 29 (1996) 479. [35] A.M. Fedosseev, N.A. Budantseva, M.S. Grigoriev, K.E. Guerman, J.-C. Krupa, Radiochim. Acta 91 (2003) 147. [36] B. Eble, D. Berning, C.L. Barnes, K.V. Katti, S. Jurisson, J. Chem. Crystallogr. 29 (1) (1999) 39. [37] N.A. Baturin, M.S. Grigorev, S.V. Kryuchkov, V.G. Maksimov, Koord. Khim. 20 (9) (1994) 671. [38] N.A. Baturin, K.E. German, M.S. Grigorev, S.V. Kryuchkov, Koord. Khim. 17 (10) (1991) 1375. [39] V.P. Tarasov, G.A. Kirakosyan, K.E. German, M.S. Grigorev, Koord. Khim. 17 (12) (1991) 1643. [40] G. Meyer, R. Hoppe, Z. Anorg. Allg. Chem. 420 (1976) 40. [41] B. Kanellakopulos, K. Raptis, B. Nuber, M.L. Ziegler, Z. Naturforsch. B: Chem. Sci. 46 (1990) 15. [42] F.D. Rochon, P.C. Kong, R. Melanson, Acta Crystallogr. C 46 (1990) 8. [43] R. Faggiani, C.J.L. Lock, L.A. Epps, A.V. Kramer, D. Brune, Acta Crystallogr. C 44 (1988) 777. [44] V.I. Spitsyn, A.F. Kuzina, K.E. German, M.S. Grigorev, Dokl. Akad. Nauk SSSR 293 (1987) 101. [45] K.E. German, M.S. Grigorev, A.F. Kuzina, B.F. Gulev, V.I. Spitsyn, Dokl. Akad. Nauk SSSR, Ser. Khim. 287 (1986) 650.
874
D.W. Wester, N.J. Hess / Inorganica Chimica Acta 358 (2005) 865–874
[46] R. Faggiani, C.J.L. Lock, J. Poce, Acta Crystallogr. B 36 (1980) 231. [47] B. Krebs, K.-D. Hasse, Acta Crystallogr. B 32 (1976) 1334. [48] B. Krebs, Z. Anorg. Allg. Chem. 380 (1971) 146. [49] I.D. Brown, Can. J. Phys. 73 (1995) 676. [50] L.A. DeLearie, R.C. Haltiwanger, C.G. Pierpont, J. Am. Chem. Soc. 111 (1989) 4324. [51] F.D. Rochon, R. Melanson, P.-C. Kong, Acta Crystallogr. C 48 (1992) 785. [52] M.J. Abrams, S.K. Larsen, J. Zubieta, Inorg. Chem. 30 (1991) 2031. [53] A. Davison, B.V. DePamphilis, A.G. Jones, K.J. Franklin, C.J.L. Lock, Inorg. Chim. Acta 128 (1987) 161. [54] J. Baldas, S.F. Colmanet, M.F. Mackay, J. Chem. Soc., Dalton Trans. (1988) 1725. [55] R. Alberto, A. Albinati, G. Anderegg, G. Huber, Inorg. Chem. 30 (1991) 3568. [56] S.F. Colmanet, G.A. Williams, M.F. Mackay, J. Chem. Soc., Dalton Trans. (1987) 2305. [57] K. Libson, E. Deutsch, B.L. Barnett, J. Am. Chem. Soc. 102 (7) (1980) 2476. [58] R. Alberto, G. Anderegg, A. Albinati, Inorg. Chim. Acta 178 (1990) 125.
[59] K. Hashimoto, C. Kabuto, T. Omori, K. Yoshihara, Chem. Lett. (1988) 1379. [60] M. Chem, Z. Zhou, S. Hu, Chin. Sci. Bull. 47 (12) (2002) 978. [61] R.D. Shannon, C.T. Prewitt, Acta Crystallogr. Sect. B: Struct. Crystallogr. Cryst. Chem. 25 (1969) 925. [62] V.M. Goldschmidt, J. Chem. Soc. (1937) 655. [63] J.J. Rehr, J. MustredeLeon, S.I. Zabinsky, R.C. Albers, J. Am. Chem. Soc. 113 (1991) 5135. [64] P.G. Allen, G.S. Siemering, D.K. Shuh, J.J. Bucher, N.M. Edelstein, C.A. Langton, S.B. Clark, T. Reich, M.A. Denecke, Radiochim. Acta 76 (1997) 77. [65] M.J. Wharton, B. Atkins, J.M. Charnock, F.R. Livens, R.A.D. Pattrick, D. Collison, Appl. Geochem. 15 (2000) 347. [66] I. Almahamid, J.C. Bryan, J.J. Bucher, A.K. Burrell, N.M. Edelstein, E.A. Hudson, N. Katsoyannis, W.W. Lukens, D.K. Shuh, H. Nitsche, T. Reich, Inorg. Chem. 34 (1995) 193. [67] L. Vichot, G. Ouvrard, G. Montavon, M. Fattahi, C. Musikas, B. Grambow, Radiochim. Acta 90 (2002) 575. [68] W.W. Lukens Jr, J.J. Bucher, N.M. Edelstein, D.K. Shuh, Environ. Sci. Technol. 36 (2002) 1124. [69] J.L. Martin, J. Yuan, C.E. Lunte, R.C. Elder, W.R. Heineman, E. Deutsch, Inorg. Chem. 28 (1989) 2899.
Bond-valence sums for Tc–O systems from EXAFS data Dennis W. Wester *, Nancy J. Hess Pacific Northwest National Laboratory, RSEG, P.O. Box 999, Richland, WA 99354, USA Received 21 April 2004; accepted 4 October 2004 Available online 22 October 2004
Abstract Literature data for structures containing exclusively Tc–O bonds were used to calculate unit-valence parameters R0 for Tc(VII), ˚ , respecTc(VI), Tc(V) (five-coordinate), Tc(V) (six-coordinate), Tc(IV) and Tc(III) as 1.909, 1.955, 1.870, 1.859, 1.841 and 1.768 A tively. A second method of estimating R0 was developed to validate the calculated values for these oxidation states because crystallographic data are limited. The method was first tested and shown to be valid using literature data for Cr, Mn, Fe and Co complexes. The validated R0 values for Tc were used to calculate bond-valence sums (BVS) for Tc solids and aqueous solutions using EXAFS data for the bond distances and coordination numbers. The calculated BVS showed good agreement with the expected values for the assumed Tc oxidation states. Ó 2004 Elsevier B.V. All rights reserved. Keywords: Bond-valence sums; R0 values; Tc–O systems; EXAFS
1. Introduction There has been increased interest in Tc environmental chemistry due to the presence of Tc in radioactive waste produced by nuclear weapons production facilities and the presence of Tc in commercial nuclear fuel. The fate of Tc in the environment is a major concern for licensing applications for nuclear waste repositories and for the closure of decommissioned US. Department of Energy (DOE) facilities because of the long half-life of 99Tc and the mobility of Tc under most environmental conditions. The fate of Tc in the environment is largely dependent on the local redox conditions. Although Tc can be present in oxidation states from (I) to (VII), most environmental conditions are sufficiently oxidizing that Tc is present in the Tc(VII) state and as the highly soluble anion, TcO4 . However, under anoxic condi*
Corresponding author. Tel.: +1 509 376 7195; fax: +1 509 375 1517. E-mail address: [email protected] (D.W. Wester). 0020-1693/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.ica.2004.10.002
tions the dominant oxidation state is Tc(IV) which forms poorly soluble amorphous solids. X-ray absorption spectroscopy (XAS) analysis has been an increasingly popular tool for the investigation of environmental samples [1–3]. It requires minimal sample preparation, preserves the essential chemistry, and can be used to examine the speciation of Tc in complicated liquid matrices and amorphous or crystalline solids. XAS provides element-specific oxidation-state determination from analysis of the X-ray absorption near-edge structure (XANES) and the identity of coordinating atoms and their atomic distances from analysis of the extended X-ray absorption fine structure (EXAFS). Even for ideal samples, analysis of the EXAFS can be highly model-dependent. Some EXAFS parameters, such as coordination number and disorder, are highly correlated. Since environmental samples are often dilute and/or inhomogeneous and are less than ideal XAS samples, we desired a tool to verify the coordination environment determined by modeling the EXAFS data.
866
D.W. Wester, N.J. Hess / Inorganica Chimica Acta 358 (2005) 865–874
With traditional use of the bond-valence sum (BVS), the oxidation state of a central atom can be determined if the R0 value and the lengths of the bonds from donor atoms to the central atom are known. The BVS method has been applied to a variety of metals mainly coordinated to a single type of donor atom, oxygen being the most common [4–13]. The bond lengths are typically determined from X-ray crystal structures, but EXAFS data could also be used. For example, the BVS method in combination with EXAFS has been used previously in studies of metal atoms in proteins [14–19]. For our application, the oxidation state can be determined from analysis of the XANES data so we sought to use the BVS method to verify, and perhaps aid in the construction of, coordination spheres based on EXAFS modeling. A review of the literature revealed that the R0 parameters for calculating BVS for Tc were not available, so our first task was to derive the R0 parameters from the existing X-ray crystal structures for Tc compounds where the Tc environment is composed only of oxygen atoms. The data were limited so we then developed a method of estimating R0 values by comparing the parameters for two oxidation states and tested this method against Cr, Mn, Fe and Co compounds for which there is abundant BVS data. We then used published EXAFS analyses of Tc compounds to compare the known or assumed oxidation state to that determined from BVS calculations. We first review the basics of the BVS approach below. 1.1. BVS method Several detailed discussions of the BVS method have appeared [20–28]; however, the BVS method can be traced back to Pauling [29]. Pauling first postulated the electrostatic valence principle for predominantly ionic crystals, according to which ‘‘the electric charge of each anion in a stable coordination structure tends to compensate the strength of the electrostatic valence bonds reaching to it from the cations at the centers of the polyhedra of which it forms a corner’’. From this, the mathematical expression X zj ¼ sij ; ð1Þ i
can be derived, where zj is the valence of cation j and sij is the valence of the individual bonds between the cation and surrounding anions, i. Later, Pauling [30] proposed for carbon compounds an empirical relation between the bond length Rij and the bond order nij Rij ¼ R b lnðnij Þ;
ð2Þ
where R is the length of a single bond (i.e., nij = 1) and ˚ . For inorganic compounds, the bond valence b = 0.31 A sij is a more accurate description than the strict bond or-
der. In addition, for inorganic compounds, including those of transition metals, the parameter b is commonly ˚ [31,32]. accepted [20–22,31–33] to have a value of 0.37 A Subsequent studies have shown this value to be generally accurate [20–22,32,33]. Eq. (2) is commonly rearranged and expressed as sij ¼ exp½ðR0 Rij Þ=b;
ð3Þ
where R0 depends upon the identity of the ij pair. By combining Eqs. (1) and (3), it can be seen that the valence of atom j can be calculated if the value of R0 and the lengths Rij of all bonds to an atom are known X zj ¼ exp½ðR0 Rij Þ=b: ð4Þ i
In fact, the R0 values for many common atom pairs are known [31–34]. Not surprisingly, R0 has been found to be dependent on both oxidation state and coordination number [8].
2. Experimental An examination of published parameters for performing BVS calculations revealed that the parameters for Tc have not appeared [31–34]. Thus, we surveyed the ICSD and Cambridge Structural databases for X-ray crystal structures of Tc compounds in which the Tc lies in an environment composed entirely of oxygen atoms. These compounds were sorted based on the reported oxidation state. Using the reported Tc–O bond distances, we calculated an R0 value for each compound by solving Eq. (4) for R0 after setting zTc equal to the re˚ . For some Tc oxiported integral valence and b = 0.37 A dation states, multiple compounds were identified and the calculated R0 values were averaged. The average R0 values were then used to back-calculate the oxidation state of the individual compounds. Compounds for which the calculated oxidation state differed significantly from the reported oxidation state were excluded from the data set and the average R0 was recalculated. For the Tc(VII) compounds, this process had to be carried out twice in order to produce an average R0 value for which all calculated oxidation states were acceptable. In addition, the Tc(V) compounds were also sorted by coordination number prior to determining R0 values. These calculations yielded the R0 values for Tc(VII)– Tc(III). The calculated R0 values were also estimated by a second method by comparing the R0 and Rij values for a pair of oxidation states, OX1 and OX2, and using Eq. (3). Specifically, Eq. (3) can be solved for b for each oxidation state. Since b is independent of oxidation state, the two equations are equal and the R0 value of one oxidation state can be estimated given the R0 value of the other oxidation state, the Rij values of both oxidation
D.W. Wester, N.J. Hess / Inorganica Chimica Acta 358 (2005) 865–874
states, and the average bond valence sij for both oxidation states, as shown in Eq. (5) below R0;OX2 ¼
lnðsij;OX2 Þ ðR0;OX1 Rij;OX1 Þ þ Rij;OX2 : lnðsij;OX1 Þ
ð5Þ
This method was also tested on transition metal–oxygen systems for which BVS data are currently available. We then tested whether the BVS approach could be used to verify the coordination environment determined by EXAFS analysis. To do this, we first surveyed the literature to extract EXAFS determinations of Tc compounds, where the coordination environment was composed solely of oxygen atoms. These compounds included both solid and solution samples. We used the calculated R0 values from XRD determinations and Eq. (4) to calculate the oxidation state using the EXAFS determinations for the bond lengths, Rij, and coordination numbers. We used the published coordination numbers in the BVS calculations although those determined by EXAFS analysis often have a non-integer value and, in some cases, are not in agreement with the accepted coordination number for the assumed oxidation state. The calculated oxidation state was then compared to the known or assumed oxidation state.
3. Results and discussion 3.1. Calculation of R0 values for Tc(VII)–Tc(III) Table 1 lists the bond distances, bond valences, and BVS for Tc(VII) compounds, which all contained pertechnetate anions with the exception of Tc2O7. The iniTable 1 Tc(VII) compounds used in the analysis Compound
BVSa
References
[NpO2]2[TcO4]4 Æ 3H2O [Tc(1)] [NpO2]2[TcO4]4 Æ 3H2O [Tc(2)] [NpO2]2[TcO4]4 Æ 3H2O [Tc(3)] [NpO2]2[TcO4]4 Æ 3H2O [Tc(4)] ½Ph3 P ¼ NHþ 2 ½TcO4 [(C5H5)2Fe]TcO4 (l-CH3CO2)4Tc2(TcO4)2 CsTcO4 CsTcO4 {(CH3)3SnOTcO3}n [(NH3)4Pt][TcO4]2 (3,6-Dimethyl-3,6-diazaoctan-1,8-dithiolateS1,N3,N6,S8)Tc(V)O(TcO4) [Bu4N][TcO4]b [Me4N][TcO4]b [NH4][TcO4] KTcO4 Tc2O7
7.026 7.011 7.009 6.929 7.105 7.272 7.171 7.062 6.787 7.179 6.878 7.159
[35] [35] [35] [35] [36] [37] [38] [39] [40] [41] [42] [43]
9.030 7.572 6.999 6.831 6.744
[44] [45] [46] [47] [48]
a b
Calculated using R0 = 1.909. Omitted from calculation of R0.
867
tial average R0 value calculated using all compounds in ˚ . The compounds [Bu4N]Table 1 was 1.901 ± 0.026 A [TcO4] and [Me4N][TcO4] were eventually omitted from subsequent rounds of calculations because the back-calculated oxidation states differed significantly from 7. ˚. The final R0 value was 1.909 ± 0.008 A The values in Table 1 show that the BVS calculation gives good agreement with the expected oxidation state for pertechnetate compounds containing both free and coordinated anions. The BVS values calculated for the two compounds that contain coordinated pertechnetate, (l-CH3CO2)4Tc2(TcO4)2 [38] and {(CH3)3SnOTcO3}n [41], are well within the acceptable range. An examination of (l-CH3CO2)4Tc2(TcO4)2 and {(CH3)3SnOTcO3}n found that these complexes contain loosely coordinated TcO4 for which the Tc–O distances are within the range typical of Tc–O double bonds (1.64– ˚ ). However, the bonds to the bridging oxygen 1.73 A atoms are on the longer end of this range whereas the bonds to the terminal oxygen atoms are on the shorter end of it. The BVS value calculated for Tc2O7, which contains TcO3 units linked by an oxygen bridge, was very near the lower end of the acceptable range. In this structure the bridging Tc–O bond is significantly longer ˚ ) than the others. Therefore, it would appear (1.840 A that the BVS for Tc2O7 falls near the lower end of the acceptable limits because the three terminal oxygen atoms are unable to approach Tc close enough to compensate for the lengthening of the bond to the bridging oxygen atom, as proposed by Brown [49], resulting in a distorted tetrahedral environment. Table 2 lists the R0 values for compounds with Tc in lower oxidation states. For Tc(VI), only one compound with all oxygen donors, tris(3,5-di-tert-butylatecholato)technetium(VI), was found in the literature [50]. The ˚ with a back-calculated calculated R0 value was 1.955 A oxidation state of 6.005 for this six-coordinate compound. For Tc(V), structures for a total of four complexes with all oxygen donors were found [51–54]. Although all have the oxotechnetium(V) core, three are five-coordinate and one is six-coordinate. Using all four compounds, the initial calculation of R0 gave a value ˚ . However, the back-calculated of 1.867 ± 0.006 A oxidation state of the six-coordinate [AsPh4]2[TcO(ox)2-(Hox)] Æ 3H2O compound was 4.533, whereas the average back-calculated oxidation state of the five-coordinate compounds was 4.956 ± 0.016. As a result R0 values for the five- and six-coordinate compounds were recalculated separately. The R0 values for the five- and six-coordinate compounds were deter˚ , respectively. mined to be 1.870 ± 0.001 and 1.859 A The four Tc(IV) compounds used in the analysis are all six-coordinate. Using all four compounds resulted ˚ and an average in an initial R0 value of 1.845 ± 0.007 A back-calculated oxidation state of 4.001 ± 0.075. The
868
D.W. Wester, N.J. Hess / Inorganica Chimica Acta 358 (2005) 865–874
Table 2 Tc compounds in lower oxidation states used in the analysis Oxidation state
Compound
˚) R0 (A
BVS
References
(VI) (V) (V) (V) (V) (IV) (IV) (IV) (IV) (IV) (III)
Tris(3,5-di-tert-butylcatecholato)technetium Tetrabutylammonium bis(4-nitro-1,2-catecholato)oxotechnetium [(n-C4H9)4N][TcO(C6Cl4O2)2] Tetrabutylammonium bis(1,2-diolato)oxotechnetium [AsPh4]2[TcO(ox)2(Hox)] Æ 3H2O Tris(hydroxymethyl)(trimethylammonio)methanetechnetium Bis(tetraphenylarsonium) tris(oxalato)technetate Tc(IV)-diphosphonate complex K4[(C2O4)2Tc(l-O)2Tc(C2O4)2] Æ 3H2O (Tc1) K4[(C2O4)2Tc(l-O)2Tc(C2O4)2] Æ 3H2O (Tc2) Tris(acetylacetonato)technetium
1.955 1.870 1.870 1.870 1.859 1.845 1.845 1.845 1.845 1.845 1.768
6.005 4.990 5.014 4.984 5.000 3.994 4.060 4.092 3.932 3.926 2.997
[50] [51] [52] [53] [54] [55] [56] [57] [58] [58] [59]
excellent agreement between the BVS and the actual oxidation was unexpected due to the diverse extended Tc environments represented by the four compounds. The Tc in the tris(oxalate) [56] and tris(hydroxymethyl)(trimethylammonio)methane [55] complexes are monomeric whereas the methylenediphosphonate complex [57] is polymeric. Finally Tc is oxo-bridged in the oxalate dimer and has a strong Tc–Tc interaction [58]. This result may suggest that the BVS is insensitive to the extended Tc coordination environment. For Tc(III), the Tc(acac)3 complex [59] yields an R0 ˚ and a back-calculated oxidation state value of 1.768 A of 2.997 for this six-coordinate structure. Table 3 summarizes the R0 values calculated for Tc oxidation states (VII)–(III) for coordination environments consisting only of oxygen atoms. These values were used to calculate the Tc oxidation state in complex matrices based on coordination environments determined by EXAFS analysis in Section 3.3. It was surprising that the R0 values in Table 3 increase with increasing oxidation state, which is counter-intuitive to the trend expected, although similar to the linear trend calculated for Mo–O six-coordinate compounds assuming ˚ [60]. For this reason, we devised an alternab = 0.037 A tive method for determining the R0 values that is described in the following section. Also, the fact that the sample size for calculating these R0 values was extremely small, in some cases consisting of a single crystal structure, could also contribute to the unusual trend. For example, the single Tc(VI) complex used, the tris-catecholate, contains non-innocent ligands that can exist as Table 3 Summary of R0 values for Tc Tc oxidation state
No.
˚) R0(calc) (A
SD
(III) (six-coordinate) (IV) (six-coordinate) (V) (five-coordinate) (V) (six-coordinate) (VI) (six-coordinate) (VII) (four-coordinate)
1 3 3 1 1 15
1.768 1.841 1.870 1.859 1.955 1.909
n/a 0.005 0.001 n/a n/a 0.008
radical anions and can make the assignment of the oxidation state somewhat controversial. 3.2. Alternative method for estimating R0 As shown above, a search of the available crystallographic databases revealed that there are a limited number of Tc compounds, where oxygen is the only atom in the immediate coordination environment. Indeed, as shown in Table 3, for some Tc oxidation states the R0 values are based on a single crystal structure. Therefore an alternative method of estimating R0 was developed in order to calculate the R0 values of all oxidation states using R0 values for two well-characterized ones. These estimated R0 values could then be compared against those calculated from the available crystallographic data by the traditional approach used in Section 3.1. The method developed here essentially scales the difference between R0 and the average bond distance value for a given oxidation state by the ratio of the bond valences as shown in Eq. (5). Since the average bond valence sij is simply the oxidation state divided by the number of bonds, these values are readily calculated for both oxidation states. Thus, if the Rij values for both oxidation states are known, then the R0 value of the second oxidation state can be calculated by knowing the R0 value of the first oxidation state. We first tested this approach by using BVS data for several transition–metal–oxygen systems since, there is abundant BVS data and a rich variation in oxidation states and coordination environments available for comparison. Since the estimated R0 value will be dependent on the initial set of BVS parameters chosen, the R0 values were estimated twice using two independent sets of BVS parameters. Table 4 shows the data used for the Cr–O system [6]. Of the several possible starting points, we chose oxidation state (III) with coordination number six and oxidation state (VI) with coordination number four because of the large number of bond distances that were used to determine the experimental R0 values for these systems, 810 and 212, respectively. In addition, the average
D.W. Wester, N.J. Hess / Inorganica Chimica Acta 358 (2005) 865–874
869
Table 4 Calculated R0 values for Cr–O complexesa Oxidation state
CN
dav
˚) R0,exptl. (A
˚) R0,III/6 (calc) (A
˚) R0,VI/4 (calc) (A
Differenceb
(II) (II) (II) (II) (III) (III) (IV) (V) (V) (VI)
3 4 5 6 4 6 4 5 8 4
1.925 1.992 2.099 2.195 1.882 1.967 1.773 1.795 1.920 1.647
1.769(10) 1.735(23) 1.741(4) 1.735 n/a 1.708(7) 1.773 1.770(8) 1.738(14) 1.793(7)
1.773 1.733 1.757 1.784 1.775 [1.708] 1.773 1.795 1.744 1.799
1.779 1.742 1.769 1.799 1.778 1.717 1.773 1.795 1.751 [1.793]
0.007 0.003 0.022 0.057 n/a 0.009 0.000 0.025 0.010 0.006
a
The estimated standard deviation is given, where appropriate in parentheses after the value. The difference equals R0, exptl. (R0,III/6 + R0,VI/4)/2, except for the two systems used to calculate R0 values, i.e., oxidation state (III) with coordination number six and oxidation state (VI) with coordination number four, where the difference is simply R0, exptl. minus the single calculated value. b
bond distance values, dav in Table 4, are used for the Rij values in Eq. (5). The agreement of the calculated R0 values with the values measured experimentally was within three estimated standard deviations of the experimental R0 values except for complexes containing Cr(II) with coordination number five and Cr(V) with coordination number five. For Cr(II) with coordination number six, the agreement is also poor but there is no standard deviation for the experimental R0 because the value was calculated from only one structure. These larger discrepancies between the estimated and experimental R0 values may result from distortion of the Cr coordination polyhedra such that the average bond distance does not provide a representative basis for the calculation of a single R0 value. For example, for six-coordinate Cr(II) there is a tendency of ions with d4 electronic configuration to have distorted octahedral coordination environments known as Jahn–Teller distortions [61]. These octahedra are characterized by four ligands at one distance and two ligands at a different distance that is either closer or further away. As a result of this distortion, the calculated average bond distance may not accurately represent the contribution from the two ligands, especially when the difference is large. Examination of reference [6] reveals that R0 was calcu-
lated on the basis of one structure and that nearly 0.5 ˚ separated the minimum and maximum bond disA tances. Similarly, Cr(V) in penta-coordination has one short Cr–O double bond and four longer Cr–O bonds. In this case, the minimum and maximum bond distances ˚ . A similar range in miniare separated by nearly 0.4 A mum and maximum bond distances is reported for Cr(II) in penta-coordination. Table 5 shows data for the Mn–O system [7]. Unfortunately, the reported R0 values are listed only by coordination number and not by oxidation state, that is, no explicit oxidation state dependence is reported. However, oxidation-state-specific average bond lengths, dav, are reported. Therefore, the R0 values for the specific oxidation states were estimated using the reported average bond length, dav, for Rij in Eq. (5). Because the data for the seven- and eight-coordinate complexes must have come from only Mn(II) complexes, these were chosen as starting points for the calculations. Table 5 lists the results of the calculations starting with data from both the seven- and eight-coordinate complexes. It can be seen that the R0 values calculated reciprocally for the seven- and eight-coordinate complexes agree very well and are also in good general agreement with the five-coordinate complexes. The
Table 5 Calculated R0 values for Mn–O complexes Oxidation state
CN
dav
˚) R0 exptl.a (A
˚) R0,II/7 (calc) (A
˚) R0,II/8 (calc) (A
Differenceb
(II) (II) (II) (II) (III) (III) (IV)
5 6 7 8 5 6 6
2.121 2.176 2.242 2.286 1.959 2.015 1.899
1.762 1.753 1.766 1.761 1.762 1.753 1.753
1.773 1.759 [1.766] 1.759 1.765 1.752 1.745
1.774 1.760 1.767 [1.761] 1.765 1.752 1.745
0.012 0.007 0.001 0.002 0.003 0.001 0.008
a
The R0, exptl. values in the original article were reported only by coordination number as an average over all applicable oxidation states. The difference equals R0, exptl. (R0,II/7 + R0,II/8)/2, except for the two systems used to calculate R0 values, i.e., oxidation state (II) with coordination numbers seven and eight, where the difference is simply R0, exptl. minus the single calculated value. b
870
D.W. Wester, N.J. Hess / Inorganica Chimica Acta 358 (2005) 865–874
calculated R0 values for the five- and six-coordinate complexes decrease with increasing oxidation state as expected. The R0 value reported for five-coordinate ˚ ) is less than the calculated R0 values complexes (1.762 A for Mn(II) and Mn(III). The R0 value reported for six˚ ) falls near the middle coordinate complexes (1.753 A of the range of the R0 values calculated for six-coordinate complexes of Mn(II), -(III) and -(IV). For some oxidation-state–coordination-number pairs the agreement between experimental and calculated R0 values is actually better than would be expected based on comparison with the results for the Cr–O system. Specifically, Mn(III) has the same d4 electronic configuration as Cr(II) and the difference between the minimum and maximum reported Mn–O bond distances in this case ˚ [7], potentially indicating a tendency to form is 0.55 A distorted coordination polyhedra. Good agreement between experimental and calculated R0 values in this case may reflect the fact that the reported minimum, maximum, and average values are based on 42 distinct crystal structures [7] and the reported average value is also close to the average of the minimum and maximum values. This suggests that the experimental R0 value is in fact representative. Table 6 shows the results for Fe–O systems [8]. Like the Mn–O system, the reported R0 values are assumed to be independent of oxidation state; therefore, the experimental R0 values listed in Table 6 for a given coordination number are the same regardless of oxidation state. However, oxidation state specific average bond lengths are reported. The starting points for these calculations were the divalent three- and eight-coordinate systems. For four-coordinate complexes, the calculated R0 ˚ for Fe(II) and Fe(III), values were 1.735 and 1.741 A respectively, which is in good agreement with the R0 va˚ . The calculue for four-coordinate complexes, 1.740 A lated R0 values for the five- and six-coordinate complexes of Fe(II) and Fe(III) showed substantial differences from the observed values. For five-coordinate complexes, the calculated R0 values were 1.702 and ˚ for Fe(II) and Fe(III), respectively. The re1.754 A
˚, ported R0 for five-coordinate complexes is 1.739 A which is of intermediate value. Finally, the calculated R0 values for six-coordinate complexes were 1.685 and ˚ for Fe(II) and Fe(III), respectively, whereas 1.736 A ˚ . In this instance both the reported R0 value is 1.745 A calculated R0 values are less than the observed one. We can think of no satisfactory explanation for the ˚ ) between the experimental and large disparity (0.060 A estimated R0 values for Fe(II) in six-coordination. The experimental R0 is based on a large number of crystal structures (66) [8]. Furthermore, although there is moderate difference between the minimum and maximum ˚ , the reported average disFe–O bond distances, 0.40 A tance is also very close to the average of the minimum and maximum values, suggesting that on the average these are not severely distorted octahedral complexes. Table 7 shows data for Co–O complexes [9]. In this system as well, the R0 values were reported as independent of oxidation state but oxidation-state-specific average bond lengths are reported. The divalent five- and seven-coordinate complexes were chosen as starting points for the calculations. For Co(II), good agreement is seen for the lower coordination numbers (three, four, five and six). The agreement is not as good for the higher coordination numbers (seven and eight). Similarly, for Co(III), the calculated R0 value for the six-coordinate complexes is significantly less than the experimental value. A possible explanation for these discrepancies is that due to the large number of coordinating oxygen atoms they are unable to attain ideal Co–O bond lengths because of interatomic contacts. This concept was discussed by Pauling [29], who noted a correlation between cation–anion radius ratios and the relative stability of tetrahedral, octahedral and eight-coordinate structures. Goldschmidt [62] further described the lower limit of this relationship between radius ratio and structural stability as the ‘‘no rattle limit’’ or NRL. Essentially if the radius ratio is less than the NRL for a given structure type, then the cation will rattle in the void space created by anion–anion contacts. For six-
Table 6 Calculated R0 values for Fe–O complexes Oxidation state
CN
dav
˚) R0 exptl.a (A
˚) R0,II/3 (calc) (A
˚) R0,II/8 (calc) (A
Differenceb
(II) (II) (II) (II) (II) (III) (III) (III)
3 4 5 6 8 4 5 6
1.950 2.009 2.065 2.120 2.356 1.855 1.957 2.011
1.788 1.740 1.739 1.745 1.813 1.740 1.739 1.745
[1.788] 1.732 1.698 1.681 1.801 1.740 1.753 1.734
1.791 1.737 1.706 1.689 [1.813] 1.742 1.757 1.739
0.003 0.006 0.037 0.060 0.012 0.001 0.016 0.009
a
The R0 exptl., values in the original article were reported only by coordination number as an average over all applicable oxidation states. The difference equals R0, exptl. (R0,II/3 + R0,II/8)/2, except for the two systems used to calculate R0 values, i.e., oxidation state (II) with coordination numbers three and eight, where the difference is simply R0, exptl. minus the single calculated value. b
D.W. Wester, N.J. Hess / Inorganica Chimica Acta 358 (2005) 865–874
871
Table 7 Calculated R0 values for Co–O complexes Oxidation state
CN
dav
˚) R0 exptl.a (A
˚) R0,II/5 (calc) (A
˚) R0,II/7 (calc) (A
Differenceb
(II) (II) (II) (II) (II) (II) (III)
3 4 5 6 7 8 6
1.906 1.960 2.043 2.093 2.152 2.260 1.895
1.748 1.704 1.686 1.670 1.684 1.695 1.670
1.748 1.690 [1.686] 1.665 1.663 1.719 1.625
1.754 1.701 1.700 1.682 [1.683] 1.742 1.636
0.003 0.008 0.014 0.004 0.021 0.035 0.040
a
The R0 exptl., values in the original article were reported only by coordination number as an average over all applicable oxidation states. The difference equals R0, exptl. (R0,II/3 + R0,II/8)/2, except for the two systems used to calculate R0 values, i.e., oxidation state (II) with coordination numbers three and eight, where the difference is simply R0, exptl. minus the single calculated value. b
and eight-coordinate structures, the NRL is 0.41 and 0.73, respectively. Using the Shannon–Prewitt [61] ionic ˚ for low spin six-coradii values of 0.545, 0.90 and 1.40 A ordinate Co(III), eight-coordinate Co(II) and O2, respectively, ionic-radius ratios of 0.389 for the octahedral and 0.643 for the eight-coordinate configurations are calculated. Both of these values are less than the NRL for their structure types suggesting that anion–anion contacts would occur in the idealized structure. Analogous structural stability analyses based on ionicradii ratio are not available for seven-coordinate structure types. The polyhedra of Co(II) in five-, six- and eight-coor˚ differences between the minimum dination have 0.5 A and maximum Co–O bond distances and, for five- and six-coordination, the reported average bond distance is significantly different from the simple average of the minimum and maximum bond distance values. Thus, a second possible origin of the discrepancy between the experimental and estimated R0 values is the inability of a single R0 value to fully represent severely distorted coordination polyhedra as discussed earlier. Additionally, it should be noted that the experimental R0 value for Co(II) in eight-coordination is based on a single structure [9]. The above calculations for the Cr–O, Mn–O, Fe–O and Co–O systems demonstrate that this scaling method is a valid approach to estimating R0 and satisfactory agreement with experimental R0 values is obtained in
most cases. However, discrepancies between experimental and calculated R0 values are observed for ions typified by severe distortion of their coordination polyhedra or ions with small ionic radii and crowded coordination spheres resulting in interanionic contacts. We now apply the scaling approach to the Tc–O system to verify the experimental R0 values listed in Tables 1–3. We chose Tc(III) and Tc(IV) with octahedral coordination as starting points for our calculations. Table 8 lists the experimental and estimated R0 values for each Tc oxidation state and coordination number. The agreement is very good for Tc(VII), Tc(VI), Tc(IV) and Tc(III) oxidation states. However, the estimated R0 val˚ ues for five- and six-coordinate Tc(V) are 0.025–0.030 A greater than the experimental R0 values. A possible explanation is that the bonding environment for Tc(V), which contains a very short Tc@O double bond and four to five longer TcAO single bonds, is sufficiently distorted so that it is not adequately represented by a single average bond distance. As we have seen from our examination of the Cr–O, Mn–O, Fe–O and Co–O systems, it appears that as long as the coordination environment can be represented by a single bond distance that the scaling approach satisfactorily estimates R0. This argument is further strengthened by examining the results for Tc(VII), which formally contains three Tc@O double bonds and a single Tc–O bond. However, the XRD and EXAFS data for Tc(VII) both indicate the presence of four Tc–O bonds of nearly equivalent length
Table 8 Calculated R0 values for Tc–O complexes Oxidation state
CN
dav
˚) R0 exptl.a (A
˚) R0,III/6 (calc) (A
˚) R0,IV/6 (calc) (A
Differenceb
(III) (IV) (V) (V) (VI) (VII)
6 6 5 6 6 4
2.025 1.991 1.896 1.962 1.955 1.702
1.768 1.841(5) 1.870(1) 1.859 1.955 1.909(8)
[1.768] 1.841 1.896 1.894 1.955 1.910
1.769 [1.841] 1.896 1.895 1.955 1.909
0.001 0.000 0.026 0.035 0.000 0.001
a
The estimated standard deviation is given, where appropriate in parentheses after the value. The difference equals R0, exptl. (R0,III/6 + R0,IV/6)/2, except for the two systems used to calculate R0 values, i.e., oxidation states (III) and (IV) with coordination number six, where the difference is simply R0, exptl. minus the single calculated value. b
872
D.W. Wester, N.J. Hess / Inorganica Chimica Acta 358 (2005) 865–874
Table 9 Tc oxidation states calculated by BVS method using EXAFS data Compound
TcO4 ðaqÞ ð1Þ [PPh4][TcO4] (s) (2) TcO2 (cryst.) [thermal decomp. of NH4TcO4] (3) ‘‘Tc(IV)’’ (aq polymer) [electro-reduction] (4) ‘‘Tc(IV)’’ (aq polymer) [ electro-reduction] (5) TcO2 Æ xH2O (s) [hydrolysis of K2TcCl6] (6) TcO2 Æ xH2O (s) [radiolysis of TcO4 in Na2EDTA/NaOH] (7) TcO2 Æ xH2O (s) [hydrolysis of H2TcCl6] (8) Tc(IV) (aq dimer) [radiolysis of TcO4 in glyoxylate/NaOH] (9) Tc-MDP (aq) [HPLC purified] (10)
despite the difference in electronic configuration. Therefore the Tc(VII) coordinate environment is well represented by a single average bond distance and our scaling method successfully estimates the experimental R0 value. 3.3. Calculation of BVS using EXAFS data Table 9 lists the chemical systems for which we used EXAFS data for the bond length and coordination number to calculate the Tc oxidation states by the BVS method. The (VII) and (IV) oxidation states were the only ones for which EXAFS data could be located for which the Tc coordination environment consisted entirely of oxygen atoms. The BVS sums were calculated using the published coordination-number values from EXAFS analysis although these values often departed from the ‘‘known’’ integral coordination numbers of four and six for the Tc(VII) and Tc(IV) oxidation states, respectively. It also should be mentioned that the analysis of the EXAFS data includes a scale factor that directly impacts the coordination number. Typical values range from 0.8 to 1.0 [63]. In the literature referenced in Table 9, this value varies from 0.75 [67] to 0.9 [64,68] or is not reported [65,66,69]. The range of scale-factor values used in EXAFS analysis presents a complication for BVS analysis since inspection of Eqs. (1) and (4) reveals that the coordination number will directly impact the calculated BVS value. Nonetheless, in most instances, the calculated oxidation state agrees well with the assumed oxidation state. For Tc(VII), both examples are of pertechnetate, although one is in solution (1) and the other is in a solid (2). For TcO4 in aqueous solution as the ammonium salt (1) [64], excellent agreement is found with a BVS of 7.114 calculated using the EXAFS data. The agreement is not quite as good for the solid [PPh4][TcO4] (6.776) (2), although it would appear from the data that the coordination number was assumed to be four and not actually fit to the EXAFS data [65]. EXAFS studies on Tc–O systems have been carried out on solids and solutions believed to contain Tc(IV). Tc(IV) solids were prepared by a variety of methods
Oxidation state
BVS
References
(VII) (VII) (IV) (IV) (IV) (IV) (IV) (IV) (IV) (IV)
7.114 6.776 4.121 3.750 4.114 4.013 3.788 2.679 4.266 3.944
[64] [65] [66] [67] [67] [67] [68] [68] [68] [69]
including thermal decomposition of TcO4 ð3Þ [66]; hydrolysis of K2[TcCl6] (6) [67] or H2[TcCl6] (8) [68]; and radiolysis of TcO4 in alkaline Na2EDTA solution (7) [68]. Only (3) is a crystalline TcO2 solid; (6), (7) and (8) are amorphous Tc(IV) solids believed to be TcO2 Æ xH2O. Polymeric Tc(IV) solution species were prepared by electrolysis of TcO4 in the presence of Cl and SO4 2 ð4Þ or SO4 2 only (5) [67] and by radiolysis of TcO4 in alkaline glyoxylate solution (9) [68]. Table 9 shows that the oxidation state calculated by the BVS method using EXAFS data agrees very well in several instances with the known oxidation state. This is particularly true for TcO2(3), TcO2 Æ xH2O prepared by hydrolysis of TcCl6 2 ð6Þ, and Tc(IV) solution species prepared by the electroreduction of pertechnetate in sulfate solutions (5). The calculated oxidation states of 4.121, 4.013 and 4.114, respectively, are well within the ±0.25 variance of the oxidation state that is acceptable. It is interesting to note that while the BVS calculated for the solution species (5) prepared by electrolysis of TcO4 in a solution with ½SO4 2 ¼ 0:1 M [34] is 4.114, that for the solution species prepared by electrolysis of TcO4 in a mixed electrolyte solution of [Cl] = 3 M and ½SO4 2 ¼ 0:1 M ð4Þ has a much lower value of 3.75. EXAFS analysis of the bond distances and coordination numbers for the two Tc polymers are very close, ˚ for the Tc–O(1) and differing by 0.06 and 0.02 A Tc–O(2) distances, respectively, and 0.06 for both the coordination numbers. EXAFS analysis of the Tc(IV) solution species produced by radiolysis of TcO4 in alkaline glyoxylate solution (9) do not yield results that can be easily interpreted by BVS. The distance of 2.008 ˚ is reasonable whereas the coordination number of 6.7 A is too large. Nevertheless, the BVS calculated using R0 = 1.841 for Tc(IV) gives a value of 4.266, which is just beyond the limit of acceptability. Analysis of EXAFS data for TcO2 Æ xH2O prepared by radiolysis of TcO4 in Na2[EDTA]/NaOH (7) [68] ˚ ) and a nearly integral gives a single distance (2.005 A coordination number (5.9). The BVS value calculated using the R0 value for Tc(IV) is 3.788, within the limit of acceptability. In this instance, the bond distance is slightly longer than would be expected for Tc(IV) and
D.W. Wester, N.J. Hess / Inorganica Chimica Acta 358 (2005) 865–874
the coordination number is slightly lower than that for six-coordinate Tc. These two factors combine to decrease the BVS so that the value for Tc(IV) falls below 4.0. The EXAFS data for TcO2 Æ xH2O produced by hydrolysis of TcCl6 2 ð8Þ do not yield results that can be easily interpreted by BVS. The distances and coordination numbers for the solid TcO2 Æ xH2O give BVS values that are in all instances well below the expected values. This indicates that either the distances are too long or the coordination numbers are too low or both. ˚ with In fact, the distances for 8 are 2.017 and 2.47 A coordination numbers of 3.9 and 1.4, respectively. The ˚ is much longer than any Tc–O bond distance of 2.47 A that has been encountered in this study. The sum of the coordination numbers, 5.3, is reasonable. Therefore, it would seem that these EXAFS data do not give a valid BVS because the distances are too long. Finally, excellent agreement is seen for the well characterized methylenediphosphonate complex of Tc(IV) (10) [69], where a BVS of 3.944 is calculated using the EXAFS data. These results clearly demonstrate the utility of using BVS to evaluate the model of the Tc coordination environment provided by EXAFS analysis even with the uncertainty in coordination numbers from EXAFS analysis. Slight discrepancies between the calculated BVS and the assumed oxidation state could also reflect the presence of multiple species since the EXAFS results represent an average of all species present. Where significant discrepancies exist, for example, TcO2 Æ xH2O, the EXAFS model may fail to describe fully or accurately the Tc coordination environment. In addition, highly distorted bonding environments may be more complex than those that can described by the BVS model.
Acknowledgements We thank Prof. Gus J. Palenik of the Department of Chemistry, University of Florida, for useful discussions. This work was supported by the Environmental Management Science Program of the US Department of Energy. Pacific Northwest National Laboratory is operated by Battelle for the US Department of Energy under Contract No. DE-AC06–76RL01830.
References [1] G.E. Brown Jr, G. Calas, G.A. Waychunas, J. Petiau, in: F.C. Hawthorne (Ed.), Reviews in Mineralogy, vol. 18, BookCrafters, Inc., Chelsea, MI, 1988, pp. 431–512. [2] D.B. Hunter, P.M. Bertsch, J. Radioanal. Nucl. Chem. 234 (1–2) (1988) 237. [3] D.E. Morris, P.G. Allen, J.M. Berg, C.J. Chisholm-Brause, S.D. Conradson, R.J. Donohoe, N.J. Hess, J.A. Musgrave, C.D. Tait, Environ. Sci. Technol. 30 (7) (1996) 2322.
873
[4] G.J. Palenik, Inorg. Chem. 36 (1997) 122. [5] G.J. Palenik, Inorg. Chem. 36 (1997) 3394. [6] R.W. Wood, K.A. Abboud, R.C. Palenik, G.J. Palenik, Inorg. Chem. 39 (2000) 2065. [7] G.J. Palenik, Inorg. Chem. 36 (1997) 4888. [8] S.M. Kanowitz, G.J. Palenik, Inorg. Chem. 37 (1998) 2086. [9] R.M. Wood, G.J. Palenik, Inorg. Chem. 37 (1998) 4149. [10] R.M. Wood, G.J. Palenik, Inorg. Chem. 38 (1999) 1031. [11] R.M. Wood, G.J. Palenik, Inorg. Chem. 38 (1999) 3926. [12] W.P. Jensen, G.J. Palenik, E.R.T. Tiekink, Polyhedron 20 (2001) 2137. [13] G.J. Palenik, Inorg. Chem. 42 (2003) 2725. [14] R.C. Scarrow, M.G. Trimitsis, C.P. Buck, G.M. Grove, R.A. Cowling, M.J. Nelson, Biochemistry 33 (1994) 15023. [15] M.J. Nelson, B.A. Brennan, D.B. Chase, R.A. Cowling, G.N. Grove, R.C. Scarrow, Biochemistry 34 (1995) 15219. [16] L. Shu, Y.-M. Chiou, A.M. Orville, M.A. Miller, J.D. Lipscomb, L. Que Jr., Biochemistry 34 (1995) 6649. [17] R.C. Scarrow, B.A. Brennan, J.G. Cummings, H. Jin, D.J. Duong, J.T. Kindt, M.J. Nelson, Biochemistry 35 (1996) 10078. [18] J. Bell, D.E. Ash, L.M. Snyder, R. Kulathila, N.J. Blackburn, D.J. Merkler, Biochemistry 36 (1997) 16239. [19] H.H. Thorp, Inorg. Chem. 37 (1998) 5690. [20] L. Janseen, L. Chandran, R. Block, J. Mol. Struct. 260 (1992) 81. [21] J.P. Naskar, S. Hati, D. Datta, Acta Crystallogr. Sect. B: Struct. Sci. 53 (1997) 885. [22] V.S. Urusov, Acta Crystallogr. Sect. B: Struct. Sci. 51 (1995) 641. [23] M. OKeeffe, Modern Perspectives in Inorganic Crystal Chemistry, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1991, pp. 163–175. [24] I.D. Brown, Structure and Bonding in Crystals, vol. II, Academic Press, New York, 1981, pp. 1–30. [25] I.D. Brown, The Chemical Bond in Inorganic Chemistry, Oxford University Press, Oxford, UK, 2002. [26] I.D. Brown, J. Chem. Educ. 77 (2000) 1070. [27] W.H. Zachariasen, J. Less Common Met. 62 (1978) 1. [28] M. OKeeffe, N.E. Brese, J. Am. Chem. Soc. 113 (1991) 3226. [29] L. Pauling, J. Am. Chem. Soc. 51 (1929) 1010. [30] L. Pauling, J. Am. Chem. Soc. 69 (1947) 542. [31] I.D. Brown, D. Altermatt, Acta Crystallogr. Sect. B: Struct. Sci. 41 (1985) 244. [32] N.E. Brese, M. OKeeffe, Acta Crystallogr. Sect. B: Struct. Sci. 47 (1991) 192. [33] I.D. Brown, K.K. Wu, Acta Crystallogr. Sect. B: Struct. Crystallogr. Cryst. Chem. 32 (1976) 1957. [34] I.D. Brown, J. Appl. Crystallogr. 29 (1996) 479. [35] A.M. Fedosseev, N.A. Budantseva, M.S. Grigoriev, K.E. Guerman, J.-C. Krupa, Radiochim. Acta 91 (2003) 147. [36] B. Eble, D. Berning, C.L. Barnes, K.V. Katti, S. Jurisson, J. Chem. Crystallogr. 29 (1) (1999) 39. [37] N.A. Baturin, M.S. Grigorev, S.V. Kryuchkov, V.G. Maksimov, Koord. Khim. 20 (9) (1994) 671. [38] N.A. Baturin, K.E. German, M.S. Grigorev, S.V. Kryuchkov, Koord. Khim. 17 (10) (1991) 1375. [39] V.P. Tarasov, G.A. Kirakosyan, K.E. German, M.S. Grigorev, Koord. Khim. 17 (12) (1991) 1643. [40] G. Meyer, R. Hoppe, Z. Anorg. Allg. Chem. 420 (1976) 40. [41] B. Kanellakopulos, K. Raptis, B. Nuber, M.L. Ziegler, Z. Naturforsch. B: Chem. Sci. 46 (1990) 15. [42] F.D. Rochon, P.C. Kong, R. Melanson, Acta Crystallogr. C 46 (1990) 8. [43] R. Faggiani, C.J.L. Lock, L.A. Epps, A.V. Kramer, D. Brune, Acta Crystallogr. C 44 (1988) 777. [44] V.I. Spitsyn, A.F. Kuzina, K.E. German, M.S. Grigorev, Dokl. Akad. Nauk SSSR 293 (1987) 101. [45] K.E. German, M.S. Grigorev, A.F. Kuzina, B.F. Gulev, V.I. Spitsyn, Dokl. Akad. Nauk SSSR, Ser. Khim. 287 (1986) 650.
874
D.W. Wester, N.J. Hess / Inorganica Chimica Acta 358 (2005) 865–874
[46] R. Faggiani, C.J.L. Lock, J. Poce, Acta Crystallogr. B 36 (1980) 231. [47] B. Krebs, K.-D. Hasse, Acta Crystallogr. B 32 (1976) 1334. [48] B. Krebs, Z. Anorg. Allg. Chem. 380 (1971) 146. [49] I.D. Brown, Can. J. Phys. 73 (1995) 676. [50] L.A. DeLearie, R.C. Haltiwanger, C.G. Pierpont, J. Am. Chem. Soc. 111 (1989) 4324. [51] F.D. Rochon, R. Melanson, P.-C. Kong, Acta Crystallogr. C 48 (1992) 785. [52] M.J. Abrams, S.K. Larsen, J. Zubieta, Inorg. Chem. 30 (1991) 2031. [53] A. Davison, B.V. DePamphilis, A.G. Jones, K.J. Franklin, C.J.L. Lock, Inorg. Chim. Acta 128 (1987) 161. [54] J. Baldas, S.F. Colmanet, M.F. Mackay, J. Chem. Soc., Dalton Trans. (1988) 1725. [55] R. Alberto, A. Albinati, G. Anderegg, G. Huber, Inorg. Chem. 30 (1991) 3568. [56] S.F. Colmanet, G.A. Williams, M.F. Mackay, J. Chem. Soc., Dalton Trans. (1987) 2305. [57] K. Libson, E. Deutsch, B.L. Barnett, J. Am. Chem. Soc. 102 (7) (1980) 2476. [58] R. Alberto, G. Anderegg, A. Albinati, Inorg. Chim. Acta 178 (1990) 125.
[59] K. Hashimoto, C. Kabuto, T. Omori, K. Yoshihara, Chem. Lett. (1988) 1379. [60] M. Chem, Z. Zhou, S. Hu, Chin. Sci. Bull. 47 (12) (2002) 978. [61] R.D. Shannon, C.T. Prewitt, Acta Crystallogr. Sect. B: Struct. Crystallogr. Cryst. Chem. 25 (1969) 925. [62] V.M. Goldschmidt, J. Chem. Soc. (1937) 655. [63] J.J. Rehr, J. MustredeLeon, S.I. Zabinsky, R.C. Albers, J. Am. Chem. Soc. 113 (1991) 5135. [64] P.G. Allen, G.S. Siemering, D.K. Shuh, J.J. Bucher, N.M. Edelstein, C.A. Langton, S.B. Clark, T. Reich, M.A. Denecke, Radiochim. Acta 76 (1997) 77. [65] M.J. Wharton, B. Atkins, J.M. Charnock, F.R. Livens, R.A.D. Pattrick, D. Collison, Appl. Geochem. 15 (2000) 347. [66] I. Almahamid, J.C. Bryan, J.J. Bucher, A.K. Burrell, N.M. Edelstein, E.A. Hudson, N. Katsoyannis, W.W. Lukens, D.K. Shuh, H. Nitsche, T. Reich, Inorg. Chem. 34 (1995) 193. [67] L. Vichot, G. Ouvrard, G. Montavon, M. Fattahi, C. Musikas, B. Grambow, Radiochim. Acta 90 (2002) 575. [68] W.W. Lukens Jr, J.J. Bucher, N.M. Edelstein, D.K. Shuh, Environ. Sci. Technol. 36 (2002) 1124. [69] J.L. Martin, J. Yuan, C.E. Lunte, R.C. Elder, W.R. Heineman, E. Deutsch, Inorg. Chem. 28 (1989) 2899.