Electronic pair dimension

Eocalization in Practice-Computational Technique The Chemical Bonds of cr, n, S Symmetry Electron Pair Dimensions and the Eoundations of Chemistry Hybridization or Mixing One-Center AOs... 

Different electron pair dimensions originate from their different positions vs the OH or SH group. 

Dirac notation (p. 399) effectiveness of AOs mixing (p. 429) electron affinity (p. 466) electronic configuration (p. 451) electronic pair dimension (p. 475) electronic shells (p. 448) energy functional (p. 400) exchange integral (p. 419) exchange operator (p. 403) excitation energy (p. 458) external localization (p. 469)... 

If electron-pair, or covalent, bonding is periodic in two or three dimensions, crystals result. The most important case is the carbon-carbon bond. If it is extended periodically in two-dimensions the result is graphite in three-dimensions it is diamond. Other elements that form electron-pair bonds are Si, Ge, and a-Sn. Some binary compounds are A1P (isoelectronic with Si),... 

Note van der Waals radii describe the space-filling dimensions of atoms, When two atoms are joined covalently, the atomic radii at the point of bonding are less than the van der Waals radii, because the joined atoms are pulled together by the shared electron pair, The distance between nuclei in a van der Waals interaction or a covalent bond is about equal to the sum of the van der Waals or covalent radii, respectively, for the two atoms, Thus the length of a carbon-carbon single bond is about 0,077 nm + 0,077 nm = 0,154 nm,... 

Furthermore, the oxygen atom of the carbonyl group in the amide function has an electron pair oriented antiperiplanar to the polar C-N bond there is therefore an electronic delocalization caused by the overlap of that oxygen electron pair orbital with the antibonding orbital of the C-N sigma bond (o ) as shown in two dimensions by structure 5 and in three dimensions by structure . This additional n-o delocalization is referred to here as a secondary electronic delocalization. Thus, amides are similar to esters because they both have the primary electronic effect and one secondary electronic effect. This is in contrast with Z esters which have two secondary electronic effects besides the primary electronic effect. 

In amides, the nitrogen electron pair is n-r conjugated with the carbonyl group and this electronic delocalization is normally expressed by resonance structures 1, 2, and 3. As a result, the amide function is essentially planar and it is assumed that the three atoms (C, ii, and 0) of this function are sp hybridized. The amide function can be illustrated in three dimensions by structure 4. The electronic distribution can also be viewed as the result of the delocalization of two n electron pairs, one from the oxygen atom and one from the nitrogen atom (cf. 1 and 3 versus 2) and on that basis, it is referred to here as the primary electronic delocalization of the amide function. 

The arrangement in space of 3 atomic cores and 9 (or 8) electron-pairs that has the lowest (most negative) coulombic energy is shown schematically in Fig. 10. Large circles represent valence-shell electron-pairs smaller circles labelled A, B, C represent the kernels of the three heavy atoms. For convenience, Fig. 10 has been drawn to show the approximate b> solution for the problem in two dimensions. 

There is an arbitrariness in the choice of dimensions ttx of the geminal orbital subspaces. However, one can argue that for the valence geminals the proper choice is tix = 2 as in the GVB/PP scheme. In this case there is one orbital for each electron. One is then guaranteed a qualitatively correct picture of the disruption of an electron-pair bond. 

Step 4. Eight electrons are arranged as single bonds therefore we place 32 — 8 = 24 electrons arranged as lone pairs on the fluorine atoms. This satisfies the octet rule for all atoms. We note that there are four equivalents bonds from the central boron atom to each of the fluorine atoms. The geometric structure which permits four electron pairs to be equidistant from each other in three dimensions is the tetrahedron ... 

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