Bond-centered electron density

In its treatment of ferroelectricity, the OOA introduces inaccuracies and may bring to wrong conclusions. One example is shown in Fig. 11. Applied to layered perovskite Pro.eoCao.aoMnOs, the OOA gives a bond-centered electron density distribution. The bonds are directed along axes of the primitive crystal lattice, from one metal site to another, over the distance of about 4 A (Fig. 11a). As every chemist knows, there are no true metal-to-metal 3d — 3d bonds that extend over a distance of 4 A. 

We shall assume implicitly that in two-center bonds the electron density is distributed symmetrically about the internuclear axis. In other words, we shall not explicitly consider the possibility of bent bonds. While this is unquestionably a good and useful approximation—doubtless a much better one than many others usually made in simple valence theory—it is well to remember that, except in special cases where symmetry considerations prohibit it, chemical bonds may well be, at least a little, bent. 

A diagonal element represents the atom-centered electron density associated with basis function Xn, while off-diagonal elements correspond to bond orders between pairs of basis functions. 

In this hypothetical compound, the boron atom would have an empty p orbital, and would therefore be an electrophilic center. The carbon atom of the C-Li bond withdraws electron density (via induction) from the lithium atom, rendering that carbon atom highly nucleophilic. 

We can consider the hydroboration step as though it involved borane (BH3) It sim phfies our mechanistic analysis and is at variance with reality only m matters of detail Borane is electrophilic it has a vacant 2p orbital and can accept a pair of electrons into that orbital The source of this electron pair is the rr bond of an alkene It is believed as shown m Figure 6 10 for the example of the hydroboration of 1 methylcyclopentene that the first step produces an unstable intermediate called a tt complex In this rr com plex boron and the two carbon atoms of the double bond are joined by a three center two electron bond by which we mean that three atoms share two electrons Three center two electron bonds are frequently encountered m boron chemistry The tt complex is formed by a transfer of electron density from the tt orbital of the alkene to the 2p orbital... 

For XH bonds, where X is any heavy atom, the hydrogen electron density is not thought to be centered at the position of the hydrogen nucleus but displaced along the bond somewhat, towards X. The MMh- force field reduces the XH bond length by a factor of 0.915 strictly for the purposes of calculating van der Waals interactions with hydrogen atoms. 

Both the oxygen and sulfur atoms have two lone pairs while the C/ carbon has ar unpaired electron, and in both cases the double bond shifts from the two carbor atoms to the carbon and the substituent. In acetyl radical, the electron density i centered primarily on the C2 carbon, and the spin density is drawn toward the lattei more than toward the former. In contrast, the density is more balanced between thf two terminal heavy atoms with the sulfur substituent (similar to that in allyl radical with a slight bias toward the sulfur atom. These trends can be easily related to th< varying electronegativity of the heavy atom in the substituent. 

In reaction with an alkene, initially a three-membered ring Lewis acid/Lewis base-complex 5 is formed, where the carbon-carbon double bond donates r-electron density into the empty p-orbital of the boron center. This step resembles the formation of a bromonium ion in the electrophilic addition of bromine to an alkene ... 

There is an interesting paradox in transition-metal chemistry which we have mentioned earlier - namely, that low and high oxidation state complexes both tend towards a covalency in the metal-ligand bonding. Low oxidation state complexes are stabilized by r-acceptor ligands which remove electron density from the electron rich metal center. High oxidation state complexes are stabilized by r-donor ligands which donate additional electron density towards the electron deficient metal centre. 

The double bond can also be pictured as consisting of two equivalent orbitals, where the centers of electron density point away from the C—C axis. This is the bent-bond or banana-bond picture. Support for this view is found in Pauling, L. Theoretical Organic Chemistry, The Kekule Symposium Butterworth London, 1959, p. 2 Palke, W.E. J, Am. Chem. Soc., 1986,108, 6543. However, most of the literature of organic chemistry is written in terms of the a-7t picture, and in this book we will use it. 

Dihydro-lH-l,5,2-azasilaboroles derive from the 2,5-dihydro-lH-l,2-aza-boroles ( 6.5.3.3) by substitution of the carbon neighboring N by a silicon atom. They may act as four-electron donors using electron density from the C=C double bond and the N atom. The B atom behaves as an acceptor center. Two pathways are known for complex synthesis reaction with a generated transition-metal complex fragment and reaction with metal atoms by the metal-vapor synthesis method. 

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