Date Published: February 01, 2018
Publisher: International Union of Crystallography
Author(s): Olivier Charles Gagné, Frank Christopher Hawthorne.
Bond-length distributions are examined for three configurations of the H+ ion, 16 configurations of the group 14–16 non-metal ions and seven configurations of the group 17 ions bonded to oxygen. Lone-pair stereoactivity for ions bonded to O2− is discussed, as well as the polymerization of the PO4 group.
A large number of inorganic crystal structures have been refined to relatively high degrees of accuracy and precision in the past few decades. A few studies have looked at the crystal-chemical behaviour of specific ions via the study of their bond-length distributions, and these were listed in the first paper of this series (Gagné & Hawthorne, 2016 ▸). However, a comprehensive examination of the variation in interatomic distances of ions has yet to be done for inorganic crystal structures, despite the pivotal influence that these kinds of studies have played in organic and organometallic chemistry (e.g. Allen et al., 1987 ▸; Mayer, 1988 ▸; Orpen et al., 1989 ▸). It is the goal of this series to lay the foundation for a comprehensive examination of variation of bond lengths and bond strengths for all ion configurations bonded to oxygen, and to provide easy access to the wealth of structural data that we have gathered. The examination of these distributions also serves to verify our understanding of bonding in inorganic crystal structures, and the various structural and electronic effects that manifest themselves via variations in bond lengths.
Of the 135 ions for which we have collected data, 11 ions have lone-pair electrons that are stereoactive. As this is the first paper in our series on bond-length distributions for cations bonded to oxygen that describes such ions, here we give a general discussion on lone-pair stereoactivity and discuss different models that attempt to rationalize lone-pair stereoactivity.
A contentious issue in the description of lone-pair stereoactive ions is that of coordination number. Whereas coordination number may be defined in simple terms, e.g. the number of counterions bonded to an ion, the decision of considering atom pairs as ‘bonded’ or not is less obvious in many situations. By-and-large, the determination of coordination number in ambiguous cases is a matter of judgement. This problem is accentuated with lone-pair stereoactive ions. For these ions, bonds are typically referred to as ‘primary’, i.e. short and strong, and ‘secondary’ (Alcock, 1972 ▸) or ‘tertiary’ (Preiser et al., 1999 ▸), i.e. long and weak. For example, Brown & Faggiani (1980 ▸) included all interatomic distances up to 3.5 Å in their description of 28 Tl+ structures, and gave 3.1 Å as the cut-off between primary and secondary. This problem is further complicated by ‘intermediate states’ of lone-pair stereoactivity, as described by Galy et al. (1975 ▸). Here, we adopt the terminology of Alcock (1972 ▸) without imposing a strict cut-off between primary and secondary bonds.
A critical issue involved in the calculation of the grand mean bond length, skewness and kurtosis values of bond-length distributions is whether the sample size is sufficiently large to ensure a representative distribution. In the first paper of this series (Gagné & Hawthorne, 2016 ▸), we described the effects of sampling (e.g. the presence of outliers, non-random sampling) and of sample size on grand mean bond length (and its standard deviation), skewness, and kurtosis for the alkali and alkaline earth metal ions bonded to O2−. As the current work deals with ions with dramatically different crystal chemistry, we report a similar analysis for S6+ and I5+.
Here, we give the bond-length distributions for 16 non-metals ions bonded to O2− observed in our bond-length dispersion analysis of inorganic structures, and give bond-length statistics for each ion as a function of coordination number. We noticed that the bond-length values at the tails of the distributions tend to involve a disproportionately large number of highly absorbing compounds (i.e. containing U, Pb, etc.). This behaviour (even more exaggerated) is characteristic of early structure determinations in the 1930s when no absorption corrections were done, and we suspect that the present disproportionate occurrence of very short and very long bond lengths in these compounds is due to either (1) inaccurate absorption corrections, or (2) total attenuation of the X-ray beam along the longer transmission paths through a crystal. Thus we examined heavily absorbing structures in the tails particularly carefully to check that the bond-valence sums were reasonable and that there were no anomalously large Ueq values for any of the constituent ions; structures that showed such anomalous values were discarded.
(1) We have examined the bond-length distributions for three configurations of the H+ ion, 16 configurations of the group 14–16 non-metal ions, and seven configurations of the group 17 ions bonded to O2−, for 223 coordination polyhedra and 452 bond lengths for the H+ ion, 5826 coordination polyhedra and 22 784 bond lengths for the group 14–16 non-metal ions, and 248 coordination polyhedra and 1394 bond lengths for the group 17 non-metal ions.