Gagné Olivier Charles, Hawthorne Frank Christopher
Geological Sciences, University of Manitoba, 125 Dysart Road, Winnipeg, Manitoba R3T 2N2, Canada.
Acta Crystallogr B Struct Sci Cryst Eng Mater. 2015 Oct;71(Pt 5):562-78. doi: 10.1107/S2052520615016297. Epub 2015 Sep 30.
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.
已通过128种阳离子的价和规则的均方根偏差（RMSD）对已发表的阳离子 - 氧键的两体键价参数进行了评估，使用了来自31489个配位多面体的180194个经过筛选的键长。RMSD值范围为0.033 - 2.451 v.u.（每单位电荷1.1 - 40.9%），加权平均值为0.174 v.u.（每单位电荷7.34%）。已为128种离子确定了一组最佳发表参数，并将其用作本文确定新键价参数的基准。已评估了两种推导键价参数的常用方法：（1）固定B并求解R(o)；（2）图解法。在90种在不止一种配位中观察到的离子的子集中，将B固定为0.37 Å时，加权平均RMSD为0.139 v.u.（每单位电荷6.7%），而图解推导得出的结果为0.161 v.u.（每单位电荷8.0%）。已考虑了这些（以及其他）推导方法的优缺点，得出结论：当前的键价参数推导方法并不令人满意。引入了一种新的推导方法，即广义简约梯度（GRG）方法，在相同的90种多配位离子样本上，该方法得出的加权平均RMSD为0.128 v.u.（每单位电荷6.1%）。对19个双参数方程和7个三参数方程进行评估以模拟键价 - 键长关系表明：（1）许多方程都能充分描述这种关系；（2）双参数方程的拟合已达到平稳状态；（3）Brown和Altermatt（1985）的方程足够好，无需使用所测试的任何其他方程。使用GRG方法和我们的完整数据集，针对Brown和Altermatt（1985）的方程，已为135种离子推导了改进的键价参数，涉及阳离子和阴离子键价和。
