Three-center

In the case of hydrogen molecule, the term (ri l/ r + R ri2), which involves three centers, does not show up in the calculation. We will not discuss this integral in the present work. 

The algorithm was applied to the MD simulations of a box of water molecules. The three-center water model was used [23]. The initial positions were at the equilibrium therefore all displacements were zero. The initial velocities were... 

Carbon can not only be involved in a single two-electron three-center bond formation but also in some carbodications simultaneously participate in two 2e-3c bonds. Diprotonated methane (CH/ ) and ethane... 

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... 

Fig. 5. Modes of M—H—B bonding where M—H—B represents a three-center hydrogen bridge bond for (a), (b), (c) tetrahydroborates and for (d), (e), (f)...

The valence theory (4) includes both types of three-center bonds shown as well as normal two-center, B—B and B—H, bonds. For example, one resonance stmcture of pentaborane(9) is given in projection in Figure 6. An octet of electrons about each boron atom is attained only if three-center bonds are used in addition to two-center bonds. In many cases involving boron hydrides the valence stmcture can be deduced. First, the total number of orbitals and valence electrons available for bonding are determined. Next, the B—H and B—H—B bonds are accounted for. Finally, the remaining orbitals and valence electrons are used in framework bonding. Alternative placements of hydrogen atoms require different valence stmctures. 

The electrophile in oxymercuration reactions, HgX or Hg " , is a soft acid and strongly polarizing. It polarizes the n electrons of an alkene to the extent that a three-center, two-... 

The methods outlined, of course, are readily applicable to a wide variety of substituted heterocycles like the carboxyl, hydroxy and mercapto derivatives of pyridines, pyridine 1-oxides, pyrroles, etc. The application to amines and to diaza compounds such as pyrimidine, where the two centers are basic, is obvious except that now 23 takes the role of the neutral compound, 21 and 22 the roles of the tautomeric first conjugate bases, and 20 the role of the second conjugate base. Extensions to molecules with more than two acidic or basic centers, such as aminonicotinic acid, pyrimidinecarboxylic acids, etc., are obvious although they tend to become algebraically cumbersome, involving (for three centers) three measurable Kg s, four Ay s, and fifteen ideal dissociation constants (A ), a total of twenty-two constants of which seven are independent. 

Fig. 8.7 The different transition-state shapes for the carbo-Diels-Alder reaction in the pressence of a strong Lewis acid (left) - a three center interaction - and a weak Lewis acid (right) [12]...

Photolytically generated carbene, as mentioned above, undergoes a variety of undiscriminated addition and insertion reactions and is therefore of limited synthetic utility. The discovery (3) of the generation of carbenes by the zinc-copper couple, however, makes carbene addition to double bonds synthetically useful. The iodo-methylzinc iodide complex is believed to function by electrophilic addition to the double bond in a three-center transition state giving essentially cis addition. Use of the... 

The boranes are electron-deficient compounds (Section 3.8) we cannot write valid Lewis structures for them, because too few electrons are available. For instance, there are 8 atoms in diborane, so we need at least 7 bonds however, there are only 12 valence electrons, and so we can form at most 6 electron-pair bonds. In molecular orbital theory, these electron pairs are regarded as delocalized over the entire molecule, and their bonding power is shared by several atoms. In diborane, for instance, a single electron pair is delocalized over a B—H—B unit. It binds all three atoms together with bond order of 4 for each of the B—H bridging bonds. The molecule has two such bridging three-center bonds (9). 

The carbonyl clusters provide an interesting set of models for the chemisorption of CO on nickel. It is very interesting that, for the Ni (CO) assignments, a plot of Pco versus 1/n for the three-center-bonded CO moieties extrapolates to 1950 cm for = oo (the "chemi-... 

In certain cases. X-ray crystallography has shown that a single H—A can form simultaneous hydrogen bonds with two B atoms bifurcated or three-center hydrogen bonds). An example is an adduct (1) formed from pentane-2,4-dione (in its... 

A simple one-step process involving a three-center cyclic transition state ... 

The Cd-borane interaction is assumed to be two electron, three centered. The only pentaborane derivative of mercury is represented as Hg(B5Hg)2. 

The selective reaction of K with the a-rh boron is explained by the metastable character of this variety at high T and by the existence in the structure of weak, three-center B—B bonds that correspond to particularly long B — B distances (2.03 X 10 pm a normal covalent B—B bond is 1.76 X 10 pm). 

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