Boron atom sets

Such cross-conjugation (where two of the vinyls are conjugated with each other through boron but not simultaneously with the third vinyl35) always lowers the total delocalization energy (DE) of the conjugated atomic set In simple Hiickel MO theory, for example, ( )-l,3,5-hexatriene (37) has a DE of 0.988/3, while 2-vinyl-1,3-butadiene (38) yields a DE of 0.900/3. 

Two other well defined carboranes 55g and 76 (vide infra, Section 3.2.7) are present in the reaction mixture containing 64c (vide infra, Scheme 3.2-35). Although pure 55g could not be isolated, its solution-state structure follows from a complete set of NMR spectra [71b], This unusual carborane is a spiro derivative without precedence and belongs to the family of 2,3,5-tricarba-mdo-hexaboranes(7). Ab initio MO calculations and NMR data indicate that the boron atom linked to the C3B3-framework by an endohedral C-B bond takes part in the cluster bonding [71b] (similar to an endohedral C-H bond in the other carboranes 55). 

On the supposition that the total number of unit cells keeps invariable and no aluminum atoms are lost during the boronation, the composition of unit cell and the population of vacancies can be estimated as listed in composition of unit cell (I) in Table 2. It can be seen that the vacancies occupy about 30-50% of total T sites after the boronation. However, it should be noted that the population of vacancies thus obtained by chemical analysis is only a bulk average result. The composition on the surface of crystallites is actually different from that in the bulk because the dissolution of silicon starts first from the outer surface, so that the vacancies on the surface are much more than those in the interior of crystallites. Such a large number of vacancies on the surface will result in corrosion and dissolution of the surface parts of crystal particles. Therefore, the number of unit cells in the sample after the boronation is actually less than that before the boronation, whereas boron atoms in each unit cell should be more than those shown in composition of unit cell (1) in Table 2. On the other hand, if all the 64 T sites are occupied by silicon and trivalent atoms, we can give another set of compositions as shown in composition of unit cell (II) in Table 2. The real composition of a unit cell should be between these two sets of compositions, that is, the 64 T sites are neither occupied completely nor vacated so severely that the collapse of the framework occurs. It can also be seen that the introduction of boron atoms is so limited that there are no more than 1.5 atoms per unit cell even though the repeated boronation is performed. 

The electronic structure of the boron atom is 1 s2 2s2 Ip1. It might be expected that boron would lose the outer electrons and be present in compounds as B3+ ions. This ionization, however, requires more than 6700 kJ mol-1, and this amount of energy precludes compounds that are strictly ionic. Polar covalent bonds are much more likely, and the hybridization can be pictured as follows. Promoting a 2s electron to one of the vacant 2p orbitals can be accomplished followed by the hybridization to produce a set of sp2 hybrid orbitals ... 

We can now go on to apply the same ideas to some other simple molecules. In boron trifluoride, for example, we start with the boron atom, which has three outer-shell electrons in its normal or ground state, and three fluorine atoms, each with seven outer electrons. As shown in the upper diagram, one of the three boron electrons is unpaired in the ground state. In order to explain the trivalent bonding of boron, we postulate that the atomic s- and p orbitals in the outer shell of boron mix to form three equivalent hybrid orbitals. These particular orbitals are called sp2 hybrids, meaning that this set of orbitals is derived from one s-orbital and two p-orbitals of the free atom. 

Since the boron atom has a ls22s22p configuration, we describe the B2 > molecule by considering how p atomic orbitals combine to form MOs. Recall that p orbitals have two lobes and that they occur in sets of three mutually j perpendicular orbitals [Fig. 14.35(a)]. When two B atoms approach each other, two pairs of p orbitals can overlap in a parallel manner [Figs. 14.35(b) and (c)] and one pair can overlap head-on [Fig. 14.35(d)],... 

C(C)4 have been found... 35 Two years later, Rasmussen and Radom30 designed the first stable ptC surrounded only by carbons, [ptC(C)4], the dimethanospiro[2,2]octaplane (Figure 3).30 Wang and Schleyer found a set of boron spiroalkanes with a ptC(C)4 through substitution of carbon by boron atoms.36,37 In 2003, a novel family of molecules based on a C( moiety was proposed by us, which constituted the simplest and smaller set of molecules containing a ptC(C)4, and more importantly, the first and, at that time, the only one stabilized purely by electronic factors.38... 

The B6H62 ion is a useful example a convenient set of coordinate axes for its boron atoms is shown in Figure 13-9. Each boron has four valence orbitals (s, ft, py, and pz), a total of 24 boron valence orbitals for the cluster. It is convenient to assign the z axis of each boron to point toward the center of the octahedron, with the x and y axes oriented as shown. 

Using the GIAO-MP2 method (tzp/dz basis set), Rasul et aU " calculated the B NMR chemical shifts of hypercoordinate boron atoms in selected boron compounds and NMR chemical shifts of the corresponding isoelectronic and isostructural carbocations for systems not yet observed under long-lived superacidic conditions B NMR and NMR chemical shift values for the methonium ion CH5+ (5) and the corresponding neutral boron analog BHs (15) were shown to reproduce well the experimental values. Calculations were also performed for the six-coordinate carbocation (diprotonated methane, 18) seven-coordinate carbocation (triprotonated methane, 27) the... 

Give a possible set of values of the four quantum numbers for all the electrons in a boron atom and a nitrogen atom if each is in the ground state. 

Consider the example of the boron atom and the making of comparisons of the Herman-Skillman numerical radial functions for 1 s, 2s and 2p with the Slater functions and possible Gaussian basis set approximations. 

Consider the molecule BH. Since the boron atom is four electrons short of a full octet, this should be a clear example of class A according to the Cremer-He criteria [13]. The MP series has been calculated [5,6] through about 15th order for several of the correlation-consistent basis sets [43] and all the Ei have the same sign. 

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