Bonding three-center

Orbital interaction diagram for H2O using the bond orbital approach. 

Photoelectron spectrum of water. The inserts for the 2ai and 1i)2 levels have been magnified several times. The ionization potential for the 1ai molecular orbital is at 32.2 eV. 

Comparison of the valence ionization potentials for the group 16 H2A molecules. 

Determine the molecular orbitals for SH4 in a geometry, shown below, by interacting 

Consider the two geometries for an H4A3 molecule shown below. Interact the b orbitals on each H2A fragment with the two p AOs on the central A atom to form the ir bonds. Determine which structure is more stable when there are 2,4,6, and 8 electrons in the four resultant MOs. 

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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... 

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 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-... 

The many higher boranes such as B5H9 and BgH 2 are similarly electron deficient and cannot be described by a single Lewis structure. They can often be described in terms of a combination of two- and three-center bonds. Alternatively, their structures can be rationalized by electron-counting schemes such as those proposed by Wade. Analysis of the electron density of these molecules by the AIM method shows that there are bond paths between all adjacent pairs of atoms. So from the point of view of the AIM theory there are bonds between each adjacent pair of atoms, but these cannot all be regarded as Lewis two-center, two-electron bonds as is the case in B2H6. 

Isolated F-atom Molecular orbitals Isolated P-atom orbitals of three-center bond p orbitals... 

In each of the B-H-B bridges, only two electrons bond the three atoms together by having the orbitals on the boron atoms simultaneously overlap the hydrogen Is orbital. A bond of this type is known as a two-electron three-center bond. In terms of molecular orbitals, the bonding can be described as the combination of two boron orbitals and one hydrogen orbital to produce three molecular orbitals, of which only the one of lowest energy is populated ... 

FIGU RE 12.2 Orbital overlap leading to the formation of a two electron three center bond in [Li(CH3)4]. 

The structure of dimethylberyllium is similar to that of trimethylaluminum except for the fact that the beryllium compound forms chains, whereas the aluminum compound forms dimers. Dimethylberyllium has the structure shown in Figure 12.3. The bridges involve an orbital on the methyl groups overlapping an orbital (probably best regarded as sp3) on the beryllium atoms to give two-electron three-center bonds. Note, however, that the bond angle Be-C-Be is unusually small. Because beryllium is a Lewis acid, the polymeric [Be(CH3)2] is separated when a Lewis base is added and adducts form. For example, with phosphine the reaction is... 

The combination of boron and hydrogen orbitals in the three-center bond can be shown in a molecular orbital diagram as in Figure 13.2. Using this approach to bonding, the structures of some of the... 

Calculations of vibrational frequencies in a three-center bond as a function of Si—Si separation were performed by Zacher et al. (1986), using linear-combination-of-atomic-orbital/self-consistent field calculations on defect molecules (H3Si—H—SiH3). The value of Van de Walle et al. for H+ at a bond center in crystalline Si agrees well with the value predicted by Zacher et al. for a Si—H distance of 1.59 A. 

However, at first sight the ionic-resonance model would not seem applicable to I3- and related symmetric hypervalent species, because extreme I+I ionicity differences would not be expected between central and terminal atoms of intrinsically equal electronegativity. Nevertheless, we shall show that the complementary bidirectional resonance stabilization motif (3.188) can lead to effective three-center bonding even if central and terminal atoms are of equal electronegativity. 

The NBO picture of 3c/2e T-bonding may be developed along lines parallel to those for 3c/4e tu-bonding in Eqs. (3.194) et seq. Let us first consider the special case of a homopolar two-center bond aAc = 2-1/2(hA + hB) interacting with a vacant one-center orbital nB = hB to form a three-center bond tABc of the form... 

Figure 3.93 Three-center BHB orbitals (and occupancies) in diborane, showing (a) the three-center bond tBHb, (b) the three-center antibond tBhb(A), and (c) the three-center antibond tBhb(7i) -...

Figure 3.102 The residual ate NBO in H3BC2H4, showing the strong banana-bond shape of the NBO and the effective preparation for forming a second three-center bond (or agostic interaction) with an empty orbital approaching from the opposite face of the original ethylene moiety.

Table 3.40 displays the calculated 0b charges from natural population analysis (NPA) for all unique B atoms. This table also includes comparison of the NPA charges with corresponding zeroth-order (ZO) estimates given by Lipscomb, which are based essentially on the formal charges for conjectured three-center bond and. s /vx-code assignments for each species (to be discussed below). 

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