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Comprehensive derivation of bond-valence parameters for ion pairs involving oxygen.

Gagné OC, Hawthorne FC - Acta Crystallogr B Struct Sci Cryst Eng Mater (2015)

Bottom Line: Published two-body bond-valence parameters for cation-oxygen bonds have been evaluated via the root mean-square deviation (RMSD) from the valence-sum rule for 128 cations, using 180,194 filtered bond lengths from 31,489 coordination polyhedra.Values of the RMSD range from 0.033-2.451 v.u. (1.1-40.9% per unit of charge) with a weighted mean of 0.174 v.u. (7.34% per unit of charge).The evaluation of 19 two-parameter equations and 7 three-parameter equations to model the bond-valence-bond-length relation indicates that: (1) many equations can adequately describe the relation; (2) a plateau has been reached in the fit for two-parameter equations; (3) the equation of Brown & Altermatt (1985) is sufficiently good that use of any of the other equations tested is not warranted.

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Affiliation: Geological Sciences, University of Manitoba, 125 Dysart Road, Winnipeg, Manitoba R3T 2N2, Canada.

ABSTRACT
Published two-body bond-valence parameters for cation-oxygen bonds have been evaluated via the root mean-square deviation (RMSD) from the valence-sum rule for 128 cations, using 180,194 filtered bond lengths from 31,489 coordination polyhedra. Values of the RMSD range from 0.033-2.451 v.u. (1.1-40.9% per unit of charge) with a weighted mean of 0.174 v.u. (7.34% per unit of charge). The set of best published parameters has been determined for 128 ions and used as a benchmark for the determination of new bond-valence parameters in this paper. Two common methods for the derivation of bond-valence parameters have been evaluated: (1) fixing B and solving for R(o); (2) the graphical method. On a subset of 90 ions observed in more than one coordination, fixing B at 0.37 Å leads to a mean weighted-RMSD of 0.139 v.u. (6.7% per unit of charge), while graphical derivation gives 0.161 v.u. (8.0% per unit of charge). The advantages and disadvantages of these (and other) methods of derivation have been considered, leading to the conclusion that current methods of derivation of bond-valence parameters are not satisfactory. A new method of derivation is introduced, the GRG (generalized reduced gradient) method, which leads to a mean weighted-RMSD of 0.128 v.u. (6.1% per unit of charge) over the same sample of 90 multiple-coordination ions. The evaluation of 19 two-parameter equations and 7 three-parameter equations to model the bond-valence-bond-length relation indicates that: (1) many equations can adequately describe the relation; (2) a plateau has been reached in the fit for two-parameter equations; (3) the equation of Brown & Altermatt (1985) is sufficiently good that use of any of the other equations tested is not warranted. Improved bond-valence parameters have been derived for 135 ions for the equation of Brown & Altermatt (1985) in terms of both the cation and anion bond-valence sums using the GRG method and our complete data set.

No MeSH data available.


Relation between bond-valence parameter Ro divided by mean bond length and (a) oxidation state, (b) ionization energy and (c) Pauling electronegativity.
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fig4: Relation between bond-valence parameter Ro divided by mean bond length and (a) oxidation state, (b) ionization energy and (c) Pauling electronegativity.

Mentions: On the other hand, the ratio Ro/〈Rij〉 shows significant correlation with various cation properties: (1) oxidation state, Vi; (2) ionization energy, IE; and to a much lesser extent (3) Pauling electronegativity, These relations are shown in Fig. 4 ▸. We use the Pauling electronegativity scale (Pauling, 1960 ▸) as it gives a slightly better value for R2 (0.276) compared with the scales of Allen (Allen, 1989 ▸; 0.272) and Allred–Rochow (Allred & Rochow, 1958 ▸; 0.262). Similarly, Brese & O’Keeffe (1991 ▸) derived a correlation between Ro and a combination of (Allred–Rochow) electronegativity and an empirically derived ‘size parameter’. To evaluate the reliability of equations (22)–(24), we calculate the mean absolute deviation between the values of Ro predicted by these equations, and those derived by the GRG method for all usable ions. Equations (22)–(24) give mean deviations of 4.89, 4.21 and 9.00%, respectively. Even though the deviations calculated from equations (22) and (23) seem reasonable, one must be careful when using these equations to interpolate values for Ro. Thus, for equation (23) the experimental value of Ro falls within the range of its predicted value with error for only 61 of the 90 ions. Moreover, deviations on Ro have a much larger effect on the bond-valence sums than deviations on B. As a result, it is much safer to fix B to a reasonable value (such as the mean value of 0.399 Å) rather than fixing Ro, when dealing with uncommon cations observed in only one coordination.


Comprehensive derivation of bond-valence parameters for ion pairs involving oxygen.

Gagné OC, Hawthorne FC - Acta Crystallogr B Struct Sci Cryst Eng Mater (2015)

Relation between bond-valence parameter Ro divided by mean bond length and (a) oxidation state, (b) ionization energy and (c) Pauling electronegativity.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4591556&req=5

fig4: Relation between bond-valence parameter Ro divided by mean bond length and (a) oxidation state, (b) ionization energy and (c) Pauling electronegativity.
Mentions: On the other hand, the ratio Ro/〈Rij〉 shows significant correlation with various cation properties: (1) oxidation state, Vi; (2) ionization energy, IE; and to a much lesser extent (3) Pauling electronegativity, These relations are shown in Fig. 4 ▸. We use the Pauling electronegativity scale (Pauling, 1960 ▸) as it gives a slightly better value for R2 (0.276) compared with the scales of Allen (Allen, 1989 ▸; 0.272) and Allred–Rochow (Allred & Rochow, 1958 ▸; 0.262). Similarly, Brese & O’Keeffe (1991 ▸) derived a correlation between Ro and a combination of (Allred–Rochow) electronegativity and an empirically derived ‘size parameter’. To evaluate the reliability of equations (22)–(24), we calculate the mean absolute deviation between the values of Ro predicted by these equations, and those derived by the GRG method for all usable ions. Equations (22)–(24) give mean deviations of 4.89, 4.21 and 9.00%, respectively. Even though the deviations calculated from equations (22) and (23) seem reasonable, one must be careful when using these equations to interpolate values for Ro. Thus, for equation (23) the experimental value of Ro falls within the range of its predicted value with error for only 61 of the 90 ions. Moreover, deviations on Ro have a much larger effect on the bond-valence sums than deviations on B. As a result, it is much safer to fix B to a reasonable value (such as the mean value of 0.399 Å) rather than fixing Ro, when dealing with uncommon cations observed in only one coordination.

Bottom Line: Published two-body bond-valence parameters for cation-oxygen bonds have been evaluated via the root mean-square deviation (RMSD) from the valence-sum rule for 128 cations, using 180,194 filtered bond lengths from 31,489 coordination polyhedra.Values of the RMSD range from 0.033-2.451 v.u. (1.1-40.9% per unit of charge) with a weighted mean of 0.174 v.u. (7.34% per unit of charge).The evaluation of 19 two-parameter equations and 7 three-parameter equations to model the bond-valence-bond-length relation indicates that: (1) many equations can adequately describe the relation; (2) a plateau has been reached in the fit for two-parameter equations; (3) the equation of Brown & Altermatt (1985) is sufficiently good that use of any of the other equations tested is not warranted.

View Article: PubMed Central - HTML - PubMed

Affiliation: Geological Sciences, University of Manitoba, 125 Dysart Road, Winnipeg, Manitoba R3T 2N2, Canada.

ABSTRACT
Published two-body bond-valence parameters for cation-oxygen bonds have been evaluated via the root mean-square deviation (RMSD) from the valence-sum rule for 128 cations, using 180,194 filtered bond lengths from 31,489 coordination polyhedra. Values of the RMSD range from 0.033-2.451 v.u. (1.1-40.9% per unit of charge) with a weighted mean of 0.174 v.u. (7.34% per unit of charge). The set of best published parameters has been determined for 128 ions and used as a benchmark for the determination of new bond-valence parameters in this paper. Two common methods for the derivation of bond-valence parameters have been evaluated: (1) fixing B and solving for R(o); (2) the graphical method. On a subset of 90 ions observed in more than one coordination, fixing B at 0.37 Å leads to a mean weighted-RMSD of 0.139 v.u. (6.7% per unit of charge), while graphical derivation gives 0.161 v.u. (8.0% per unit of charge). The advantages and disadvantages of these (and other) methods of derivation have been considered, leading to the conclusion that current methods of derivation of bond-valence parameters are not satisfactory. A new method of derivation is introduced, the GRG (generalized reduced gradient) method, which leads to a mean weighted-RMSD of 0.128 v.u. (6.1% per unit of charge) over the same sample of 90 multiple-coordination ions. The evaluation of 19 two-parameter equations and 7 three-parameter equations to model the bond-valence-bond-length relation indicates that: (1) many equations can adequately describe the relation; (2) a plateau has been reached in the fit for two-parameter equations; (3) the equation of Brown & Altermatt (1985) is sufficiently good that use of any of the other equations tested is not warranted. Improved bond-valence parameters have been derived for 135 ions for the equation of Brown & Altermatt (1985) in terms of both the cation and anion bond-valence sums using the GRG method and our complete data set.

No MeSH data available.