The three-dimensional structure of frequently occurring molecular fragments has been studied systematically. Molecular subunits which were examined include hydrogen bridges (O—HċO), triiodide anions (I−3), other linear triatomic fragments (Cl—SbċCl, S—SċS, Mo—OċMo), tetrahedral ions (SO2−4, PO3−4, AlCl−4) and related species (MSO3, etc.), molecules containing both keto- and amino-groups (mostly alkaloids), substituted annulenes and cycloheptatrienes, organic five-membered rings, and five-coordinated metal and nonmetal atoms. The bond distances and angles describing the structure of a giving fragment cover a range that is many times larger than the range of the experimental standard deviations. The changes of the various structural parameters of a fragment are correlated with each other. The observed mutual dependence (structural correlation) may be described by means of Pauling's equation relating bond length r to bond number n:r = r0 - clogn. The bond numbers n are expressed in terms of bond angles. The sum of bond numbers at a given atom is roughly constant and does not depend on the environment. “Standard bond lengths” of a fragment are determined by a least-squares procedure based on all available data. They are supplemented by curves that describe the observed distortions.
The shape of these correlation curves is reminiscent of the structural changes occurring along the pathways of chemical reactions, e.g. nucleophilic substitution at tetrahedrally coordinated atoms (SN1 and SN2), nucleophilic addition to carbonyl groups, electrocyclic ring closure of polyenes, pseudo-rotation of five-membered rings or Berry pseudo-rotation. For many of these reactions approximate energy hypersurfaces have been obtained from quantum mechanical calculations, model force fields and from spectroscopic information (IR, NMR). Comparison between reaction pathways determined from structural correlations with those obtained from models of the energy surfaces shows fair agreement.
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