Relationship between the lengths of covalent and intermolecular bonds in X -H... Y bridges
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TAL CHEMISTRY
Relationship between the Lengths of Covalent and Intermolecular Bonds in X–H···Y Bridges G. V. Yukhnevich Kurnakov Institute of General and Inorganic Chemistry, Russian Academy of Sciences, Leninskiі pr. 31, Moscow, 119991 Russia email: [email protected] Received July 2, 2009 XH YH Abstract—The formula exp(–ln2((rXH – r0X H )/(rsym – r0X H ))5/3) + exp(–ln2((rYH – r0Y H )/(rsym – r0Y H ))5/3) = 1 is proposed, which relates the lengths of both covalent and hydrogen bonds in homo and heterobridges. This formula is justified by the experimental data from the CSD bank, which was obtained by neutron diffraction for 108 O–H···N hydrogen bridges with bond angles exceeding 170°. DOI: 10.1134/S106377451003003X
INTRODUCTION The fundamental possibility of forming “hyperval ent” (or “fractional” in Il’insky’s terminology) bonds by atoms was stated more than 110 years ago based on the results of purely chemical studies [1, 2]. Ilinsky believed that each new weaker hypervalent bond is always formed due to the initial valent ones. Diffrac tion methods, IR spectroscopy, and quantum chemis try, which were developed in the 20th century, con firmed both these statements [3]. However, after the publication of [4], such a weak interaction between a hydrogen atom and any atom with a strong donor abil ity was referred to as a “hydrogen” bond. Much earlier, Pauling [5] had revealed that the changes in the bond length and bond multiplicity s are related by an inverse exponential dependence. On the assumption that, regardless of the proton position in an Х–Н···X bridge, the sum of multiplicities of hydrogen bonds (sXH and sH···X) is always unity, the lengths of these bonds, r1 and r2, are related as exp(–(r1 – r0)/b) + exp(–(r2 – r0)/b) = 1. (1) This equation was widely used by different research ers, and each found specific values of r0 and b for the chosen set of bridges by the leastsquares method [6, 7]. These values were significantly different, and this was always explained by the chemical specificity of the bridge set under consideration. The bond lengths in O–H···О bridges, as deter mined from the neutron diffraction data, were ana lyzed in [8]. The fundamental novelty of this consider ation was as follows: (i) all bridges were combined into one general set; (ii) r0 was the averaged bond length for a free molecule rather than a fitting parameter; and (iii) the dimension coefficient b was unambiguously determined in terms of r0 and rsym (1/2 of symmetric
O···H···О bridge length): b = (rsym – r0)/(ln2)1/h Å, which is why it also was not a fitting parameter. Thus, both fitting parameters, r0 and b, were excluded from relation (1) and a new parameter was introduced: the exponential factor h, which strongly affects the curve inflection. An analysis of bond lengths in 465 O–H···O bridges, which are implemented in more than 200 crystals, showed this exponent to be 5/3. Thus, it was established that the bond lengths in any О ⎯ Н···О bridge obeys the relation exp(–((r1 – r0)/b)5/3) + exp(–((r2 – r0)/b)5/3) = 1, (2
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