**Date Published:** February 01, 2018

**Publisher:** International Union of Crystallography

**Author(s):** Olivier Charles Gagné, Frank Christopher Hawthorne.

http://doi.org/10.1107/S2052520617017437

**Abstract**

**Bond-length distributions are examined for 33 configurations of the metalloid ions and 56 configurations of the post-transition metal ions bonded to oxygen. Lone-pair stereoactivity is discussed.**

**Partial Text**

This paper is the third in a series [Gagné & Hawthorne (2016a ▸, 2018 ▸); see also Gagné (2018 ▸) in this issue] on the bond-length distributions of ions bonded to oxygen in crystals, and will focus on the metalloid and post-transition metal ions. For a detailed introduction and rationale for this work and a description of the data-collection and data-filtering methods, see Gagné & Hawthorne (2016a ▸). In this series, we examine the distribution of bond lengths for 135 ions bonded to oxygen in 462 configurations using 180 331 bond lengths extracted from 9367 refined crystal structures; these data involve most ions of the periodic table and all coordination numbers in which they occur. Working with a large amount of data allows examination of subtle differences between the shapes of various distributions (e.g. bond-length distributions, mean bond-length distributions) which reflect differences in their structural and/or electronic behaviour. The factors that affect bond lengths are of general interest to all who work on crystal structures and their properties, and a comprehensive analysis of all the data should lead to increased understanding of those factors. Moreover, knowledge of possible variation in bond lengths is important in evaluating computational results on structural arrangements by setting expectations and limits as to what bond lengths may be observed between ion pairs, and are also useful in identifying unusual stereochemical features in new crystal structures.

Of the 135 ions for which we have gathered data in our bond-length dispersion analysis, we observe 14 cations with lone-pair electrons bonded to O2−, and 11 ions with stereoactive lone-pair electrons bonded to O2−. For the ions with stereoactive lone-pair electrons, seven ions are non-metals, three ions are metalloids and four ions are post-transition metals. For a thorough discussion of lone-pair stereoactivity and a general analysis for the 11 ions with stereoactive lone-pair electrons bonded to O2−, we refer the reader to the second paper of this series (Gagné & Hawthorne, 2018 ▸); here, we reiterate some important points, and give a more detailed discussion of lone-pair stereoactivity for the metalloids and post-transition metals later in text.

Whereas coordination number may be defined in simple terms, e.g. the number of counterions bonded to an ion, the decision to consider atom pairs as ‘bonded’ is not obvious in many situations. This is particularly true for ions with stereoactive lone-pair electrons, as their coordination polyhedra are prone to large distortions, can form secondary bonds (up to ∼4 Å in length), and may be observed in a wide spectrum of ‘intermediate states’ between stereoactivity and inactivity of the lone-pair electrons (Galy et al., 1975 ▸).

Dealing with a very large amount of data has allowed us to critically evaluate the reproducibility of our results as a function of sampling. We described the effects of sample size (e.g. the presence of outliers, non-random sampling) in the first paper of this series (Gagné & Hawthorne, 2016a ▸), as well as the effect of sample size on grand mean bond length (and its standard deviation), skewness, and kurtosis for [6]Na+ bonded to O2−. We reported the effect of sample size on these values for [4]S6+ and [6]I5+ bonded to O2− in the second paper of this series (Gagné & Hawthorne, 2018 ▸). Here, we do a similar analysis for [4]Si4+ and for [8]Bi3+. This analysis is done to sample bond strengths not covered by Gagné & Hawthorne (2016a ▸, 2018 ▸), as Gagné & Hawthorne (2018 ▸) showed dependence of grand mean bond length, skewness and kurtosis values on bond strength and multi-modality of the bond-length distribution. Here we sample similar but weaker bonds for Si—O (mean bond valence 1 v.u.) compared to [4]S6+—O2− (mean bond valence 1.5 v.u.), and for [8]Bi3+—O2− (0.375 v.u.) compared with [6]I5+—O2− (0.83 v.u.) for lone-pair stereoactive cations. We report the sample sizes as a function of the number of coordination polyhedra.

(1) We have examined the bond-length distributions for 33 configurations of the metalloid ions bonded to O2− using 5279 coordination polyhedra and 21 761 bond distances, and for 56 configurations of the post-transition metal ions bonded to O2− using 1821 coordination polyhedra and 10 723 bond distances.

Source:

http://doi.org/10.1107/S2052520617017437