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Journal articles on the topic 'Bond length'

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Published: 4 June 2021

Last updated: 1 February 2022

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1

Jemmis, Eluvathingal D., Biswarup Pathak, R. Bruce King, and Henry F. Schaefer III. "Bond length and bond multiplicity: σ-bond prevents short π-bonds." Chem. Commun., no. 20 (2006): 2164–66. http://dx.doi.org/10.1039/b602116f.

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2

Ferraris, G., and G. Ivaldi. "Bond valence vs bond length in O...O hydrogen bonds." Acta Crystallographica Section B Structural Science 44, no. 4 (August 1, 1988): 341–44. http://dx.doi.org/10.1107/s0108768188001648.

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3

Bosi, Ferdinando. "Mean bond-length variation in crystal structures: a bond-valence approach." Acta Crystallographica Section B Structural Science, Crystal Engineering and Materials 70, no. 4 (July 31, 2014): 697–704. http://dx.doi.org/10.1107/s2052520614011470.

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The distortion theorem of the bond-valence theory predicts that the mean bond length 〈D〉 increases with increasing deviation of the individual bond lengths from their mean value according to the equation 〈D〉 = (D′ + ΔD), whereD′ is the length found in a polyhedron having equivalent bonds and ΔDis the bond distortion. For a given atom,D′ is expected to be similar from one structure to another, whereas 〈D〉 should vary as a function of ΔD. However, in several crystal structures 〈D〉 significantly varies without any relevant contribution from ΔD. In accordance with bond-valence theory, 〈D〉 variation is described here by a new equation: 〈D〉 = (DRU + ΔDtop + ΔDiso + ΔDaniso + ΔDelec), whereDRUis a constant related to the type of cation and coordination environment, ΔDtopis the topological distortion related to the way the atoms are linked, ΔDisois an isotropic effect of compression (or stretching) in the bonds produced by steric strain and represents the same increase (or decrease) in all the bond lengths in the coordination sphere, ΔDanisois the distortion produced by compression and stretching of bonds in the same coordination sphere, ΔDelecis the distortion produced by electronic effects. If present, ΔDeleccan be combined with ΔDanisobecause they lead to the same kind of distortions in line with the distortion theorem. EachD-index, in the new equation, corresponds to an algebraic expression containing experimental and theoretical bond valences. On the basis of this study, the ΔDindex defined in bond valence theory is a result of both the bond topology and the distortion theorem (ΔD= ΔDtop + ΔDaniso + ΔDelec), andD′ is a result of the compression, or stretching, of bonds (D′ =DRU + ΔDiso). The deficiencies present in the bond-valence theory in explaining mean bond-length variations can therefore be overcome, and the observed variations of 〈D〉 in crystal structures can be described by a self-consistent model.

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4

Paolini, John P. "The bond order?bond length relationship." Journal of Computational Chemistry 11, no. 10 (November 1990): 1160–63. http://dx.doi.org/10.1002/jcc.540111007.

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5

Mastryukov, Vladimir S., Mauricio Alcolea Palafox, and James E. Boggs. "Inverse bond length/bond angle relationships." Journal of Molecular Structure: THEOCHEM 304, no. 3 (February 1994): 261–67. http://dx.doi.org/10.1016/0166-1280(94)80023-5.

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6

Stenfors, Brock A., Richard J. Staples, Shannon M. Biros, and Felix N. Ngassa. "Crystal structure of 1-[(4-methylbenzene)sulfonyl]pyrrolidine." Acta Crystallographica Section E Crystallographic Communications 76, no. 3 (February 28, 2020): 452–55. http://dx.doi.org/10.1107/s205698902000208x.

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The molecular structure of the title compound, C11H15NO2S, features a sulfonamide group with S=O bond lengths of 1.4357 (16) and 1.4349 (16) Å, an S—N bond length of 1.625 (2) Å, and an S—C bond length of 1.770 (2) Å. When viewing the molecule down the S—N bond, both N—C bonds of the pyrrolidine ring are oriented gauche to the S—C bond with torsion angles of −65.6 (2)° and 76.2 (2)°. The crystal structure features both intra- and intermolecular C—H...O hydrogen bonds, as well as intermolecular C—H...π and π–π interactions, leading to the formation of sheets parallel to the ac plane.

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7

Gagné, Olivier Charles, and Frank Christopher Hawthorne. "Bond-length distributions for ions bonded to oxygen: metalloids and post-transition metals." Acta Crystallographica Section B Structural Science, Crystal Engineering and Materials 74, no. 1 (January 12, 2018): 63–78. http://dx.doi.org/10.1107/s2052520617017437.

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Bond-length distributions have been examined for 33 configurations of the metalloid ions and 56 configurations of the post-transition metal ions bonded to oxygen, for 5279 coordination polyhedra and 21 761 bond distances for the metalloid ions, and 1821 coordination polyhedra and 10 723 bond distances for the post-transition metal ions. For the metalloid and post-transition elements with lone-pair electrons, the more common oxidation state between n versus n+2 is n for Sn, Te, Tl, Pb and Bi and n+2 for As and Sb. There is no correlation between bond-valence sum and coordination number for cations with stereoactive lone-pair electrons when including secondary bonds, and both intermediate states of lone-pair stereoactivity and inert lone pairs may occur for any coordination number > [4]. Variations in mean bond length are ∼0.06–0.09 Å for strongly bonded oxyanions of metalloid and post-transition metal ions, and ∼0.1–0.3 Å for ions showing lone-pair stereoactivity. Bond-length distortion is confirmed to be a leading cause of variation in mean bond lengths for ions with stereoactive lone-pair electrons. For strongly bonded cations (i.e. oxyanions), the causes of mean bond-length variation are unclear; the most plausible cause of mean bond-length variation for these ions is the effect of structure type, i.e. stress resulting from the inability of a structure to adopt its characteristic a priori bond lengths.

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8

Gagné, Olivier Charles, Patrick H. J. Mercier, and Frank Christopher Hawthorne. "A priori bond-valence and bond-length calculations in rock-forming minerals." Acta Crystallographica Section B Structural Science, Crystal Engineering and Materials 74, no. 6 (December 1, 2018): 470–82. http://dx.doi.org/10.1107/s2052520618010442.

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Within the framework of the bond-valence model, one may write equations describing the valence-sum rule and the loop rule in terms of the constituent bond valences. These are collectively called the network equations, and can be solved for a specific bond topology to calculate its a priori bond valences. A priori bond valences are the ideal values of bond strengths intrinsic to a given bond topology that depend strictly on the formal valences of the ion at each site in the structure, and the bond-topological characteristics of the structure (i.e. the ion connectivity). The a priori bond valences are calculated for selected rock-forming minerals, beginning with a simple example (magnesiochromite, = 1.379 bits per atom) and progressing through a series of gradually more complex minerals (grossular, diopside, forsterite, fluoro-phlogopite, phlogopite, fluoro-tremolite, tremolite, albite) to finish with epidote (= 4.187 bits per atom). The effects of weak bonds (hydrogen bonds, long Na+—O2− bonds) on the calculation of a priori bond valences and bond lengths are examined. For the selected set of minerals, a priori and observed bond valences and bond lengths scatter closely about the 1:1 line with an average deviation of 0.04 v.u. and 0.048 Å and maximum deviations of 0.16 v.u. and 0.620 Å. The scatter of the corresponding a priori and observed bond lengths is strongly a function of the Lewis acidity of the constituent cation. For cations of high Lewis acidity, the range of differences between the a priori and observed bond lengths is small, whereas for cations of low Lewis acidity, the range of differences between the a priori and observed bond lengths is large. These calculations allow assessment of the strain in a crystal structure and provide a way to examine the effect of bond topology on variation in observed bond lengths for the same ion-pair in different bond topologies.

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9

Gagné, Olivier Charles, and Frank Christopher Hawthorne. "Bond-length distributions for ions bonded to oxygen: results for the transition metals and quantification of the factors underlying bond-length variation in inorganic solids." IUCrJ 7, no. 4 (June 9, 2020): 581–629. http://dx.doi.org/10.1107/s2052252520005928.

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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, Δtopol and Δcryst, 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 Δtopol and Δcryst 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 Δtopol and Δcryst 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 π-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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10

Asher, R. L., D. Bellert, T. Buthelezi, Dan Lessen, and P. J. Brucat. "The bond length of ZrAr+." Chemical Physics Letters 234, no. 1-3 (March 1995): 119–22. http://dx.doi.org/10.1016/0009-2614(95)00006-p.

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11

Buthelezi, T., D. Bellert, V. Lewis, and P. J. Brucat. "The bond length of CoKr+." Chemical Physics Letters 242, no. 6 (September 1995): 627–31. http://dx.doi.org/10.1016/0009-2614(95)00789-7.

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12

Hayes, T., D. Bellert, T. Buthelezi, and P. J. Brucat. "The bond length of VAr+." Chemical Physics Letters 287, no. 1-2 (April 1998): 22–28. http://dx.doi.org/10.1016/s0009-2614(98)00129-8.

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13

Jones, Peter G., and Anthony J. Kirby. "Multiple bond length–reactivity correlations." J. Chem. Soc., Chem. Commun., no. 6 (1986): 444–45. http://dx.doi.org/10.1039/c39860000444.

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14

Aldrich, D. B., R. J. Nemanich, and D. E. Sayers. "Bond-length relaxation inSi1−xGexalloys." Physical Review B 50, no. 20 (November 15, 1994): 15026–33. http://dx.doi.org/10.1103/physrevb.50.15026.

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15

Demaison, J., M. Herman, and J. Lievin. "The equilibrium OH bond length." International Reviews in Physical Chemistry 26, no. 3 (July 2007): 391–420. http://dx.doi.org/10.1080/01442350701371919.

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16

Chiari, G., and G. Ferraris. "Bond valence VS bond length and Pauling's bond strength: The Ca – O bond." Zeitschrift für Kristallographie 191, no. 1-2 (January 1990): 39–43. http://dx.doi.org/10.1524/zkri.1990.191.1-2.39.

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17

La Macchia, Giovanni, Francesco Aquilante, Valera Veryazov, Björn O. Roos, and Laura Gagliardi. "Bond Length and Bond Order in One of the Shortest Cr−Cr Bonds." Inorganic Chemistry 47, no. 24 (December 15, 2008): 11455–57. http://dx.doi.org/10.1021/ic801537w.

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18

Bačík and Fridrichová. "The Site Occupancy Assessment in Beryl Based on Bond-Length Constraints." Minerals 9, no. 10 (October 18, 2019): 641. http://dx.doi.org/10.3390/min9100641.

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The site preference for each cation and site in beryl based on bond-length calculations was determined and compared with analytical data. Tetrahedral SiO4 six-membered rings normally have no substitutions which results from very compact Si4+–O bonds in tetrahedra. Any substitution except Be would require significant tetrahedral ring distortion. The Be tetrahedron should also be negligibly substituted based on the bond-valence calculation; the tetrahedral Li–O bond length is almost 20% larger than Be2+–O. Similar or smaller bond lengths were calculated for Cr3+, V3+, Fe3+, Fe2+, Mn3+, Mg2+, and Al3+, which can substitute for Be but also can occupy a neighboring tetrahedrally coordinated site which is completely vacant in the full Be occupancy. The octahedral site is also very compressed due to dominant Al with short bond lengths; any substitution results in octahedron expansion. There are two channel sites in beryl: the smaller 2b site can be occupied by Na+, Ca2+, Li+, and REE3+ (Rare Earth Elements); Fe2+ and Fe3+ are too small; K+, Cs+, Rb+, and Ba2+ are too large. The channel 2a-site average bond length is 3.38 Å which allows the presence of simple molecules such as H2O, CO2, or NH4 and the large-sized cations-preferring Cs+.

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19

Gagné, Olivier Charles, and Frank Christopher Hawthorne. "Mean bond-length variations in crystals for ions bonded to oxygen." Acta Crystallographica Section B Structural Science, Crystal Engineering and Materials 73, no. 6 (November 28, 2017): 1019–31. http://dx.doi.org/10.1107/s2052520617014548.

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Variations in mean bond length are examined in oxide and oxysalt crystals for 55 cation configurations bonded to O2−. Stepwise multiple regression analysis shows that mean bond length is correlated to bond-length distortion in 42 ion configurations at the 95% confidence level, with a mean coefficient of determination (〈R 2〉) of 0.35. Previously published correlations between mean bond length and mean coordination number of the bonded anions are found not to be of general applicability to inorganic oxide and oxysalt structures. For two of 11 ions tested for the 95% confidence level, mean bond lengths predicted using a fixed radius for O2− are significantly more accurate as those predicted using an O2− radius dependent on coordination number, and are statistically identical otherwise. As a result, the currently accepted ionic radii for O2− in different coordinations are not justified by experimental data. Previously reported correlation between mean bond length and the mean electronegativity of the cations bonded to the oxygen atoms of the coordination polyhedron is shown to be statistically insignificant; similar results are obtained with regard to ionization energy. It is shown that a priori bond lengths calculated for many ion configurations in a single structure-type leads to a high correlation between a priori and observed mean bond lengths, but a priori bond lengths calculated for a single ion configuration in many different structure-types leads to negligible correlation between a priori and observed mean bond lengths. This indicates that structure type has a major effect on mean bond length, the magnitude of which goes beyond that of the other variables analyzed here.

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20

Cruz-Cabeza, Aurora J., and Frank H. Allen. "Geometry and conformation of cyclopropane derivatives having σ-acceptor and σ-donor substituents: a theoretical and crystal structure database study." Acta Crystallographica Section B Structural Science 68, no. 2 (February 25, 2012): 182–88. http://dx.doi.org/10.1107/s0108768111054991.

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The structures of cyclopropane rings which carry σ-acceptor or σ-donor substituents have been studied using density-functional theory (DFT), and mean bond lengths and conformational parameters retrieved from the Cambridge Structural Database. It is confirmed that σ-acceptor substituents, e.g. halogens, generate positive ring bond-length asymmetry in which there is lengthening of the distal bond (opposite to the point of substitution), and shortening of the two vicinal bonds. This is due to withdrawal of electron density from the cyclopropane 1e′′ orbitals, which are bonding for the distal bond and antibonding for the vicinal bonds. For σ-donor substituents such as SiH3 or Si(CH3)3, the DFT and crystal structure data show negative ring bond-length asymmetry (distal bond shortened, vicinal bonds lengthened), owing to electron donation into the 4e′ ring orbital, which are also bonding for the distal bond and antibonding for the vicinal bonds. The results also show that —OH substituents induce weak positive asymmetry, but that the effects of methyl or amino substituents are either non-existent or extremely small, certainly too small to measure using crystal structure information.

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21

Thomas, Noel W. "Bond length based bond orders for borane cluster compounds." Polyhedron 5, no. 6 (January 1986): 1207–12. http://dx.doi.org/10.1016/s0277-5387(00)81393-5.

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22

Lendvay, G. "On the correlation of bond order and bond length." Journal of Molecular Structure: THEOCHEM 501-502 (April 2000): 389–93. http://dx.doi.org/10.1016/s0166-1280(99)00449-2.

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23

Shirley, William A., Roald Hoffmann, and Vladimir S. Mastryukov. "An Approach to Understanding Bond Length/Bond Angle Relationships." Journal of Physical Chemistry 99, no. 12 (March 1995): 4025–33. http://dx.doi.org/10.1021/j100012a024.

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24

Matthew, Daniel J., Sang Hoon Oh, Andrew Sevy, and Michael D. Morse. "The bond length and bond energy of gaseous CrW." Journal of Chemical Physics 144, no. 21 (June 7, 2016): 214306. http://dx.doi.org/10.1063/1.4952453.

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25

Gibbs, G. V., N. L. Ross, D. F. Cox, K. M. Rosso, B. B. Iversen, and M. A. Spackman. "Pauling bond strength, bond length and electron density distribution." Physics and Chemistry of Minerals 41, no. 1 (August 18, 2013): 17–25. http://dx.doi.org/10.1007/s00269-013-0619-z.

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26

Knop, Osvald, Russell J. Boyd, and S. C. Choi. "Sulfur-sulfur bond lengths, or can a bond length be estimated from a single parameter?" Journal of the American Chemical Society 110, no. 22 (October 1988): 7299–301. http://dx.doi.org/10.1021/ja00230a005.

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27

Sidey, Vasyl. "Universal `bond valenceversusbond length' correlation curve for manganese–oxygen bonds." Acta Crystallographica Section B Structural Science, Crystal Engineering and Materials 70, no. 3 (May 24, 2014): 608–11. http://dx.doi.org/10.1107/s2052520614004181.

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The oxidation-state independent `bond valence (s)versusbond length (r)' correlation curve for manganese–oxygen bonds has been closely approximated using the modified two-parameter Trömels=f(r) function [Trömel (1983).Acta Cryst.B39, 664–669],s= [(r0−l)/(r−l)]2, wherer0= 1.763 (2) Å andl= 1.148 (9) Å. Ther0andlrefinable parameters of the above function can be regarded as the alternative bond-valence parameters intended for use in the modern bond-valence model [Brown (2009).Chem. Rev.109, 6858–6919] in cases where the traditional bond-valence parameters (r0;n) and (r0;b) fail.

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28

Robinson, E. A. "The duodecet rule: Part 3. Fluoro species of the third period elements." Canadian Journal of Chemistry 70, no. 6 (June 1, 1992): 1696–705. http://dx.doi.org/10.1139/v92-213.

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On the basis of the suggested new value of 54 pm for the single bond covalent radius of fluorine, the previously established duodecetrule for period 3 elements in molecular species with highly electronegative ligands is extended to fluorides. It is shown, for species such as SiF4, (F3Si)2O, F3SiNH2, F3PO, and PF5, that the observed bond lengths are consistent with significant partial double bonding involving all the ligands, including fluorine, and with a total of six electron pairs in the valence shell of the central atom. Empirical rules based on d/d1, the ratio of an observed bond length to the corresponding single bond length calculated from the sum of covalent radii, are developed as a simple approximate guide to the extent of partial double bonding in bonds to third period elements. It is also shown that bond lengths in species such as Al2F5, AlO45−, and Al(NH2)4− are consistent with a duodecet rule.

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29

Harada, Jun, Mayuko Harakawa, and Keiichiro Ogawa. "Torsional vibration and central bond length of N-benzylideneanilines." Acta Crystallographica Section B Structural Science 60, no. 5 (September 15, 2004): 578–88. http://dx.doi.org/10.1107/s0108768104016532.

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The crystal structures of N-benzylideneaniline (1), N-benzylidene-4-carboxyaniline (2), N-(4-methylbenzylidene)-4-nitroaniline (3), N-(4-nitrobenzylidene)-4-methoxyaniline (4), N-(4-nitrobenzylidene)-4-methylaniline (5), N-(4-methoxybenzylidene)aniline (6) and N-(4-methoxybenzylidene)-4-methylaniline (7) were determined by X-ray diffraction analyses at various temperatures. In the crystal structures of all the compounds, an apparent shortening of the central C=N bond was observed at room temperature. As the temperature was lowered, the observed bond lengths increased to approximately 1.28 Å at 90 K, irrespective of substituents in the molecules. The shortening and the temperature dependence of the C=N bond length are interpreted in terms of an artifact caused by the torsional vibration of the C—Ph and N—Ph bonds in the crystals. In the crystal structures of (1) and (7), a static disorder around the C=N bond was observed, which is also responsible for the apparent shortening of the C=N bond.

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30

Tiritiris, Ioannis, Stefan Saur, and Willi Kantlehner. "Crystal structure of (ethoxyethylidene)dimethylazanium ethyl sulfate." Acta Crystallographica Section E Crystallographic Communications 71, no. 12 (November 7, 2015): o916. http://dx.doi.org/10.1107/s2056989015020678.

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In the title salt, C6H14NO+·C2H5SO4−, the C—N bond lengths in the cation are 1.2981 (14), 1.4658 (14) and 1.4707 (15) Å, indicating double- and single-bond character, respectively. The C—O bond length of 1.3157 (13) Å shows double-bond character, indicating charge delocalization within the NCO plane of the iminium ion. In the crystal, C—H...O hydrogen bonds between H atoms of the cations and O atoms of neighbouring ethyl sulfate anions are present, generating a three-dimensional network.

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31

Demaison, J., L. Margulès, and James E. Boggs. "The equilibrium N–H bond length." Chemical Physics 260, no. 1-2 (October 2000): 65–81. http://dx.doi.org/10.1016/s0301-0104(00)00253-6.

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32

Lawrentz, U., W. Grahn, I. Dix, and P. G. Jones. "Bond-length alternation in rigidized merocyanines." Acta Crystallographica Section C Crystal Structure Communications 55, no. 3 (March 15, 1999): 446–50. http://dx.doi.org/10.1107/s0108270198013778.

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33

Shih, C. K., W. E. Spicer, W. A. Harrison, and Arden Sher. "Bond-length relaxation in pseudobinary alloys." Physical Review B 31, no. 2 (January 15, 1985): 1139–40. http://dx.doi.org/10.1103/physrevb.31.1139.

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34

Simard, Benoit, Peter A. Hackett, Andrew M. James, and Patrick R. R. Langridge-Smith. "The bond length of silver dimer." Chemical Physics Letters 186, no. 4-5 (November 1991): 415–22. http://dx.doi.org/10.1016/0009-2614(91)90201-j.

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35

Asher, R. L., D. Bellert, T. Buthelezi, and P. J. Brucat. "The bond length of Ni+2." Chemical Physics Letters 224, no. 5-6 (July 1994): 525–28. http://dx.doi.org/10.1016/0009-2614(94)00573-7.

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36

Franco, Annalisa, and Gianni Royer-Carfagni. "Effective bond length of FRP stiffeners." International Journal of Non-Linear Mechanics 60 (April 2014): 46–57. http://dx.doi.org/10.1016/j.ijnonlinmec.2013.12.003.

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37

Szczerba, Wojciech, Heinrich Riesemeier, and Andreas F. Thünemann. "Bond length contraction in gold nanoparticles." Analytical and Bioanalytical Chemistry 398, no. 5 (September 17, 2010): 1967–72. http://dx.doi.org/10.1007/s00216-010-4200-z.

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38

Goodenough, John B. "Bond-length mismatch in intergrowth structures." Journal of the Less Common Metals 116, no. 1 (February 1986): 83–93. http://dx.doi.org/10.1016/0022-5088(86)90219-5.

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39

Demaison, Jean, and Georges Wlodarczak. "The equilibrium C-H bond length." Structural Chemistry 5, no. 1 (February 1994): 57–66. http://dx.doi.org/10.1007/bf02278696.

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40

Kaupp, Martin, Bernhard Metz, and Hermann Stoll. "Breakdown of Bond Length-Bond Strength Correlation: A Case Study." Angewandte Chemie International Edition 39, no. 24 (December 15, 2000): 4607–9. http://dx.doi.org/10.1002/1521-3773(20001215)39:24<4607::aid-anie4607>3.0.co;2-l.

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41

Zio´ŀkowski, Jacek. "New relation between ionic radii, bond length, and bond strength." Journal of Solid State Chemistry 57, no. 3 (May 1985): 269–90. http://dx.doi.org/10.1016/0022-4596(85)90152-5.

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42

ZHANG, FANGFANG, and DONGFENG XUE. "CHEMICAL BONDING BEHAVIORS OF N—H⋯O HYDROGEN BONDS OF ${\rm{NH}}_4^ + \cdots {\rm{O}}$ SYSTEMS IN INORGANIC CRYSTALS." Modern Physics Letters B 23, no. 31n32 (December 30, 2009): 3943–50. http://dx.doi.org/10.1142/s0217984909022046.

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The original length d0 of N — H and H ⋯ O bonds in various inorganic [Formula: see text] systems was comprehensively studied from a chemical bond viewpoint. Two linear relationships between d0 and the average bond lengths of each [Formula: see text] system, d0, N - H , versus [Formula: see text] and d0, H ⋯ O versus [Formula: see text] were respectively established. It is indicated that d0 is affected by the crystalline environment evidently, therefore, the valence electron distribution of hydrogen atom which depends on the lengthening degree of the original bond length is strongly affected by the chemical environment of hydrogen atoms. The obtained valence electron distributions of hydrogen are in a good agreement with the bond valence sum rule, and their overall applicability to ammonium ion interactions was discussed.

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43

O'Brien, Sean E., and Paul LA Popelier. "Quantum molecular similarity. Part 2: The relation between properties in BCP space and bond length." Canadian Journal of Chemistry 77, no. 1 (January 1, 1999): 28–36. http://dx.doi.org/10.1139/v98-215.

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In previous work we introduced an abstract space of bond critical point properties, called BCP space, to measure the similarity between molecules. In this contribution we critically examine the dependence of properties in BCP space on equilibrium bond length, a topic which has been extensively investigated in the literature. For that purpose we have designed a data set of 57 molecules yielding 731 bond critical points. We confirm the existence of local linear relationships provided the bonds vary little in their chemical surroundings. Such relationships break down completely for larger subsets of bond critical points encompassing a wider variety of bonds. The patterns observed in the global picture show so little correlation that one may safely conclude that BCP properties cannot be trivially recovered or even predicted by knowledge of bond length alone.Key words: atoms in molecules, molecular similarity, bond critical points.

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44

Gagné, Olivier Charles, and Frank Christopher Hawthorne. "Bond-length distributions for ions bonded to oxygen: results for the non-metals and discussion of lone-pair stereoactivity and the polymerization of PO4." Acta Crystallographica Section B Structural Science, Crystal Engineering and Materials 74, no. 1 (January 13, 2018): 79–96. http://dx.doi.org/10.1107/s2052520617017541.

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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 (R 2 = 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 n versus n+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 O2−. Observed O—X—O bond angles indicate that the period 3 non-metal ions P3+, S4+, Cl3+ and Cl5+ are lone-pair seteroactive when bonded to O2−, 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, PO4 polymerizes via one or two bridging oxygen atoms, but not by three. Partitioning our PO4 dataset shows that multi-modality in the distribution of bond lengths is caused by the different bond-valence constraints that arise for Obr = 0, 1 and 2. For strongly bonded cations, i.e. oxyanions, the most probable cause of mean bond length variation is the effect of structure type, i.e. stress induced by the inability of a structure to follow its a priori bond lengths. For ions with stereoactive lone-pair electrons, the most probable cause of variation is bond-length distortion.

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45

Li, Hui, Hao Jie Xiao, Jiang Wang, Hai Xia Zhang, Hai Cheng Xuan, and Qing Liang Ma. "Size Dependent Bond Length of Metallic Clusters by Considering Bond Number." Materials Science Forum 850 (March 2016): 314–18. http://dx.doi.org/10.4028/www.scientific.net/msf.850.314.

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In this study, size-dependent bond length of metallic clusters is established by introducing bond number. This model, free of any adjustable parameters, can be utilized to predict the change rule of bond length with size. If the atomic structure of a cluster is known, the size and shape-dependent bond number are obtained. The cubooctahedral structure is taken for simplicity to describe the shape and geometric characteristics of metallic clusters. It is found that the bond length decreases with the decreased size of metallic clusters, which is due to the structure relaxation and enhanced single bond energy. The theoretical predictions are consistent with the evidences of the simulations for Au and Ag clusters. This confirms the validity of taking cubooctahedron structure, even if the simulated Au and Ag clusters are not cuboctahedron ones. This can be expected to other metallic clusters even with other atomic structures.

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46

Li, Xiangzhu, and Josef Paldus. "Bond length alternation in cyclic polyenes. VII. Valence bond theory approach." International Journal of Quantum Chemistry 60, no. 1 (October 5, 1996): 513–27. http://dx.doi.org/10.1002/(sici)1097-461x(1996)60:1<513::aid-qua50>3.0.co;2-8.

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47

Laso, M., H. C. Öttinger, and U. W. Suter. "Bond‐length and bond‐angle distributions in coarse‐grained polymer chains." Journal of Chemical Physics 95, no. 3 (August 1991): 2178–82. http://dx.doi.org/10.1063/1.460965.

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48

Singh, Alaukik, Enrique del Rey Castillo, and Jason Ingham. "FRP-to-FRP bond characterization and force-based bond length model." Composite Structures 210 (February 2019): 724–34. http://dx.doi.org/10.1016/j.compstruct.2018.12.005.

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49

Lay, PA, GM Mclaughlin, and AM Sargeson. "Crystal and Molecular Structure of Tris(Ethane-1,2-Diamine)Osmium(III) Trifluoromethanesulfonate Monohydrate." Australian Journal of Chemistry 40, no. 7 (1987): 1267. http://dx.doi.org/10.1071/ch9871267.

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The crystal and molecular structure of racemic [Os(en)3] (CF3SO3)3.H2O has been determined. The [Os(en)3]3+ ion adopts a le ξob configuration and has approximate C2 symmetry with an Os-N(av.) bond length of 2.11 � and a bite angle for the chelate of - 82�. The previously recorded structure of the [Os(en-H)2(en)]2+ ion in which two deprotonated ethane-1,2-diamine ligands adoptoa cis configuration of the two amido donors, and in which the OsIV -N( amido ) bonds (1.90 �) are much shorter than the Os-N(amine) bonds, 2.11 ( cis ), 2.19 (trans), along with the present structure indicates a bond order > 1 for the osmiumo amido bond. The normal Os-N bond lengths fall into well defined ranges OS-NR3 (2.11-2.14 �), Os=NR2- (~1.90 �),Os=NR2 (- 1.70 �) and Os=N3-(- 1.58-1.63 �). These single bond lengths are more affected by trans effects than the formal oxidation state of the osmium centre.

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50

Gagné, Olivier Charles, and Frank Christopher Hawthorne. "Bond-length distributions for ions bonded to oxygen: alkali and alkaline-earth metals." Acta Crystallographica Section B Structural Science, Crystal Engineering and Materials 72, no. 4 (August 1, 2016): 602–25. http://dx.doi.org/10.1107/s2052520616008507.

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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]Be2+,[4]Mg2+,[6]Ca2+,[6]Sr2+and[6]Ba2+, 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 ratioUeq(Na)/Ueq(bonded anions)is partially correlated with 〈[6]Na+—O2−〉 (R2= 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]Ba2+to 2.10 v.u. for[12]Sr2+. Bond-valence arguments suggest coordination numbers higher than [12] for K+, Rb+, Cs+and Ba2+.

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