Bond triangles

Figure 3.52 Leading hyperconjugative stabilizations in CFH2CH = CH2, showing the torsional dependence of n-o (solid lines) and a-n interactions (dotted lines) for the C—F (crosses) and two C—FI bonds (triangles, circles) of the—CFF12 group. The sum of all six interactions is shown as the heavy solid line (squares), which may be compared with the total barrier potential in Fig. 3.51.

F/g. 2 The bonding triangle, showing a selection of elements and compounds plotted against the Pauling electronegativities. 

The bonding triangle shows some elements plotted according to their Pauling electronegativity. 

Figure 15.12 Structure of an organic three-dimensional crystal. Seen are the covalent bonds S=0, hydrogen bonds (dotted lines) and charged bonds (triangles) (after [77]).

Bonding triangle applied as a classification scheme for the different types of crystalline solids. 

Figure 2-17. a) The redundanl bond malrix of ethanal with ihe zero values omitted, b) It can be compressed by reduction to the top right triangle, c) Omitting the hydrogen atoms provides the simplest non-redundant matrix representation. 

J. P. KiUus and G. Z. Whitten, A. Neiv Carbon Bond Mechanism for Air Quality Modeling, Report No. EPA 60013-82-041, U.S. Environmental Protection Agency, Research Triangle Park, N.C., 1982. 

Structure. The straiued configuration of ethylene oxide has been a subject for bonding and molecular orbital studies. Valence bond and early molecular orbital studies have been reviewed (28). Intermediate neglect of differential overlap (INDO) and localized molecular orbital (LMO) calculations have also been performed (29—31). The LMO bond density maps show that the bond density is strongly polarized toward the oxygen atom (30). Maximum bond density hes outside of the CCO triangle, as suggested by the bent bonds of valence—bond theory (32). The H-nmr spectmm of ethylene oxide is consistent with these calculations (33). 

The most important consequence of bound smoothing is the transfer of infonnation from those atoms for which NMR data are available to those that cannot be observed directly in NMR experiments. Within the original experimental bounds, the minimal distance intervals are identified for which all triangle inequalities can be satisfied. A distance chosen outside these intervals would violate at least one triangle inequality. Eor example, an NOE between protons pi and pj and the covalent bond between pj and carbon Cj imposes upper and lower bounds on the distance between pi and Cy, although this distance is not observable experimentally nor is it part of E hem-... 

The classification of amorphous carbon films according to carbon bond type and hydrogen content can be represented in a triangular diagram, Fig. 6 [e.g., 70]. The comers at the base of the triangle correspond to graphite (100% sp carbon) and diamond (100% sp carbon). The apex represents 100% H, but the upper limit for formation of solid films is defined by the tie line between the compositions of polyethene, -(CH2) -, and polyethyne, -(CH) -. 

N occupy an sp lone-pair in the plane of the ring (or the plane of the local PNP triangle) as in Fig. 12.26a. The situation at P is less clear mainly because of uncertainties concerning the d-orbital energies and the radial extent (size) of these orbitals in the bonding situation (as distinct from the free atom). In so far as symmetry is concerned, the sp lone-pair on each N can be involved in coordinate bonding in the jcy plane... 

The second type of trinuclear compounds containing (M302(02CR)(,(H20)3] and obtained by the reaction of M(CO)6 (M = Mo, W) with carboxylic acids, features a similar triangle of M-M bonded metal atoms but this time capped on both sides by hj-O atoms (Fig, 23.8d). Complexes m which either one or both of these capping atoms arc replaced by /iy-CR, alkylidene. 

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