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Bond-length distributions for ions bonded to oxygen: results for the non-metals and discussion of lone-pair stereoactivity and the polymerization of PO.

ABSTRACT: 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, for 223 coordination polyhedra and 452 bond distances for the H ion, 5957 coordination polyhedra and 22 784 bond distances for the group 14–16 non-metal ions, and 248 coordination polyhedra and 1394 bond distances for the group 17 non-metal ions. H⋯O and O—H + H⋯O distances correlate with O⋯O distance ( = 0.94 and 0.96): H⋯O = 1.273 × O⋯O – 1.717 Å; O—H + H⋯O = 1.068 × O⋯O – 0.170 Å. These equations may be used to locate the hydrogen atom more accurately in a structure refined by X-ray diffraction. For non-metal elements that occur with lone-pair electrons, the most observed state between the +2 oxidation state is that of highest oxidation state for period 3 cations, and lowest oxidation state for period 4 and 5 cations when bonded to O. Observed O——O bond angles indicate that the period 3 non-metal ions P, S, Cl and Cl are lone-pair seteroactive when bonded to O, even though they do not form secondary bonds. There is no strong correlation between the degree of lone-pair stereoactivity and coordination number when including secondary bonds. There is no correlation between lone-pair stereoactivity and bond-valence sum at the central cation. In synthetic compounds, PO polymerizes one or two bridging oxygen atoms, but not by three. Partitioning our PO dataset shows that multi-modality in the distribution of bond lengths is caused by the different bond-valence constraints that arise for O = 0, 1 and 2. For strongly bonded cations, oxyanions, the most probable cause of mean bond length variation is the effect of structure type, stress induced by the inability of a structure to follow its bond lengths. For ions with stereoactive lone-pair electrons, the most probable cause of variation is bond-length distortion.

SUBMITTER: Gagne OC

PROVIDER: S-EPMC5798399 | biostudies-other | 2018 Feb

REPOSITORIES: biostudies-other

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Project description:Bond-length distributions have been examined for 55 configurations of alkali-metal ions and 29 configurations of alkaline-earth-metal ions bonded to oxygen, for 4859 coordination polyhedra and 38?594 bond distances (alkali metals), and for 3038 coordination polyhedra and 24?487 bond distances (alkaline-earth metals). Bond lengths generally show a positively skewed Gaussian distribution that originates from the variation in Born repulsion and Coulomb attraction as a function of interatomic distance. The skewness and kurtosis of these distributions generally decrease with increasing coordination number of the central cation, a result of decreasing Born repulsion with increasing coordination number. We confirm the following minimum coordination numbers: ([3])Li(+), ([3])Na(+), ([4])K(+), ([4])Rb(+), ([6])Cs(+), ([3])Be(2+), ([4])Mg(2+), ([6])Ca(2+), ([6])Sr(2+) and ([6])Ba(2+), but note that some reported examples are the result of extensive dynamic and/or positional short-range disorder and are not ordered arrangements. Some distributions of bond lengths are distinctly multi-modal. This is commonly due to the occurrence of large numbers of structure refinements of a particular structure type in which a particular cation is always present, leading to an over-representation of a specific range of bond lengths. Outliers in the distributions of mean bond lengths are often associated with anomalous values of atomic displacement of the constituent cations and/or anions. For a sample of ([6])Na(+), the ratio Ueq(Na)/Ueq(bonded anions) is partially correlated with ?([6])Na(+)-O(2-)? (R(2) = 0.57), suggesting that the mean bond length is correlated with vibrational/displacement characteristics of the constituent ions for a fixed coordination number. Mean bond lengths also show a weak correlation with bond-length distortion from the mean value in general, although some coordination numbers show the widest variation in mean bond length for zero distortion, e.g. Li(+) in [4]- and [6]-coordination, Na(+) in [4]- and [6]-coordination. For alkali-metal and alkaline-earth-metal ions, there is a positive correlation between cation coordination number and the grand mean incident bond-valence sum at the central cation, the values varying from 0.84?v.u. for ([5])K(+) to 1.06?v.u. for ([8])Li(+), and from 1.76?v.u. for ([7])Ba(2+) to 2.10?v.u. for ([12])Sr(2+). Bond-valence arguments suggest coordination numbers higher than [12] for K(+), Rb(+), Cs(+) and Ba(2+).

Project description:Bond-length distributions are examined for 63 transition metal ions bonded to O2- in 147 configurations, for 7522 coordination polyhedra and 41?488 bond distances, providing baseline statistical knowledge of bond lengths for transition metals bonded to O2-. A priori bond valences are calculated for 140 crystal structures containing 266 coordination polyhedra for 85 transition metal ion configurations with anomalous bond-length distributions. Two new indices, ?topol and ?cryst, are proposed to quantify bond-length variation arising from bond-topological and crystallographic effects in extended solids. Bond-topological mechanisms of bond-length variation are (1) non-local bond-topological asymmetry and (2) multiple-bond formation; crystallographic mechanisms are (3) electronic effects (with an inherent focus on coupled electronic vibrational degeneracy in this work) and (4) crystal-structure effects. The indices ?topol and ?cryst allow one to determine the primary cause(s) of bond-length variation for individual coordination polyhedra and ion configurations, quantify the distorting power of cations via electronic effects (by subtracting the bond-topological contribution to bond-length variation), set expectation limits regarding the extent to which functional properties linked to bond-length variation may be optimized in a given crystal structure (and inform how optimization may be achieved) and more. These indices further provide an equal footing for comparing bond-length variation and the distorting power of ions across ligand types, including resolution for heteroligand polyhedra. The observation of multiple bonds is found to be primarily driven by the bond-topological requirements of crystal structures in solids. However, sometimes multiple bonds are observed to form as a result of electronic effects (e.g. the pseudo Jahn-Teller effect, PJTE); resolution of the origins of multiple-bond formation follows calculation of the ?topol and ?cryst indices on a structure-by-structure basis. Non-local bond-topological asymmetry is the most common cause of bond-length variation in transition metal oxides and oxysalts, followed closely by the PJTE. Non-local bond-topological asymmetry is further suggested to be the most widespread cause of bond-length variation in the solid state, with no a priori limitations with regard to ion identity. Overall, bond-length variations resulting from the PJTE are slightly larger than those resulting from non-local bond-topological asymmetry, comparable with those resulting from the strong JTE, and less than those induced by ?-bond formation. From a comparison of a priori and observed bond valences for ?150 coordination polyhedra in which the strong JTE or the PJTE is the main reason underlying bond-length variation, the JTE is found not to have a cooperative relation with the bond-topological requirements of crystal structures. The magnitude of bond-length variation caused by the PJTE decreases in the following order for octahedrally coordinated d 0 transition metal oxyanions: Os8+ > Mo6+ > W6+ >> V5+ > Nb5+ > Ti4+ > Ta5+ > Hf4+ > Zr4+ > Re7+ >> Y3+ > Sc3+. Such ranking varies by coordination number; for [4] it is Re7+ > Ti4+ > V5+ > W6+ > Mo6+ > Cr6+ > Os8+ >> Mn7+; for [5] it is Os8+ > Re7+ > Mo6+ > Ti4+ > W6+ > V5+ > Nb5+. It is concluded that non-octahedral coordinations of d 0 ion configurations are likely to occur with bond-length variations that are similar in magnitude to their octahedral counterparts. However, smaller bond-length variations are expected from the PJTE for non-d 0 transition metal oxyanions.

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Bond-length distributions for ions bonded to oxygen: results for the non-metals and discussion of lone-pair stereoactivity and the polymerization of PO.

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