Carbon molecular orbital model

Hiickel molecular orbitals in porphin were investigated by Longuet-Higgins et al. (68), and the extended Hiickel molecular orbital model was applied to metalloporphyrins in attempts by Pullman et al. (93), Ohno et al. (86), and Zerner et al. (120) to explain various experimental observations. Let us briefly consider a description of cyanoferriporphin. According to the Hiickel theory all but the -orbitals of each carbon and nitrogen atom of porphin are used up to form the relatively inert skeleton of single bonds. To describe the -bonding twenty-four molecular orbitals of porphin can then be formed as linear combinations of... 

Spherical-domain models of three-center bonds in localized-molecular-orbital models of a nonclassical carbonium ion, B4CI4, and TaeClfJ have been described 49,52) a drawing of a spherical-domain model of the methyl lithium tetramer, (LiCH, is shown in Fig. 31. Large, outer circles represent domains of electron-pairs of C—H bonds. Solid circles represent domains of Li+ ions. Shaded circles represent 4-center lithium-lithium-lithium-carbon bonds — i.e., electron-pair domains that touch, simultaneously, three lithium ions and the kernel of a carbon atom. The... 

M—has also been reported for olefins and acetylenes ir-bonded to rhodium and to platinum (6, 21, 46, 87). In the case of rhodium, iy(i°3Rh—is between 10 and 16 Hz for a 7r-bonded olefin (see Table XXVII), while for the cr-bonded carbon in [(C5H5)Rh(ff-C3Hs)-(w-CsHb)], 7( ° Rh—is 26 Hz. It was suggested the bonding of the olefin results from a 60% contribution from a dsp -vnet X orbital and sp -carbon orbital 21). For the olefins and acetylenes w-bonded to platinum 7( Pt—is between 18 and 195 Hz (see Table XXIX) compared to the range of 360 to 1000 Hz reported for carbon cr-bonded to platinum. It was found that 7( Pt— C) is less for a 7r-bonded acetylene than for a rr-bonded ethylene. This was considered as evidence for the Chatt-Dewar-Duncanson molecular orbital model 39, 63) of TT-bonding (XIV), rather than the formally equivalent valence-bond treatment, (XV) and (XVI) 46). However, no allowance appears to have been made for the effect on the hybridization at the carbon of the pseudo-... 

The molecular orbital model as a linear combination of atomic orbitals introduced in Chapter 4 was extended in Chapter 6 to diatomic molecules and in Chapter 7 to small polyatomic molecules where advantage was taken of symmetry considerations. At the end of Chapter 7, a brief outline was presented of how to proceed quantitatively to apply the theory to any molecule, based on the variational principle and the solution of a secular determinant. In Chapter 9, this basic procedure was applied to molecules whose geometries allow their classification as conjugated tt systems. We now proceed to three additional types of systems, briefly developing firm qualitative or semiquantitative conclusions, once more strongly related to geometric considerations. They are the recently discovered spheroidal carbon cluster molecule, Cgo (ref. 137), the octahedral complexes of transition metals, and the broad class of metals and semi-metals. 

The MO model of C2 predicts a doubly bonded molecule, with all electrons paired, but with both highest occupied molecular orhitals (HOMOs) having tt symmetry. C2 is unusual because it has two tt bonds and no cr bond. Although C2 is a rarely encountered allotrope of carbon (carbon is significantly more stable as diamond, graphite, fullerenes and other polyatomic forms described in Chapter 8), the acetylide ion, C2 , is well known, particularly in compounds with alkali metals, alkaline earths, and lanthanides. According to the molecular orbital model, 2 should have a bond order of 3 (configuration TT TT a-g ). This is supported by the similar C—C distances in acetylene and calcium carbide (acetylide) . ... 

An alternative, suggested by the molecular orbital model but needing further study, is that the em-dimethyl group should be considered, as a whole, to be a chromophore. If so, it should follow a sector rule centered on the central atom, here C(5) (90). The two methyl groups would lie in one plane (here, XY) and the other two carbon atoms (here, C(i) and C(5)) would lie in another (here, XZ). The YZ plane would not be needed in... 

The largest electron density in planar molecules like alkenes is not located between the two carbon atoms but rather above and below the molecular plane. Such distribution of electron density is rationalized by the molecular orbital model in which the double bond includes jc-orbitals as shown in the following figure. 

Molecular orbital modeling of the reaction of organolithium compounds with carbonyl groups has examined the interaction of formaldehyde with the dimer of methyllithium. The reaction is predicted to proceed by initial complexation of the carbonyl group at lithium, followed by a rate-determining step involving formation of the new carbon-carbon bond. The cluster then reorganizes to incorporate the newly formed alkoxide ion. ... 

It is also useful to consider the bonding among the carbon atoms in diamond in terms of the molecular orbital model. Energy-level diagrams for diamond and a typical metal are given in Fig. 10.23. Recall that the conductivity of metals can be explained... 

We recall that the length of carbon-carbon O bonds depends on the hybridization of both carbon atoms. The bond length between the sp -hybridized methyl carbon atom and the sp -, sp -, and sp-hybridized central carbon atoms of propane, propene, and propyne, show this effect. The bond length for sp -sp bonded atoms, 151 pm, is 3 pm shorter than that of sp -sp bonded atoms. If there were no double bond character between C-2 and C-3 in butadiene, we might expect a bond length of 148 pm. However, the bond length of 1,3-butadiene is 146 pm. The molecular orbital model predicts a shorter bond length than would be expected from a Lewis structure because of the continuous overlap... 

The effecfs of boron addition were also calculated based on a semiempiri-cal molecular-orbital model. Results show that the introduction of boron is favorable for lithium intercalation. When a layer of BQ is coated onto the surface of natural graphite, the performance improves considerably. In contradiction, another theoretical study based also on a semiempirical molecular orbital method concludes that the substitution of the carbon by boron is not effective for lithium storage. This illustrates the complexity of the carbon structure. These results suggest that the exact bonding states of boron may markedly influence the properties of the carbon materials. 

The effects of nitrogen were also calculated based on semiempirical molecular orbital models, and the results could not definitely refute the favorable effects of nitrogen. Obviously there are limits in computational chemistry since the carbon structures are very complicated. Modeling has not yet arrived at a level completely reflechng especially the binding forms of heteroatoms and the various states and microstructures of carbons. Consequently, these kinds of computations are considerably speculahve. Recent results again showed this limit. What it does show, also, is that the bonding state of the heteroatoms must markedly influence the properties of the carbon materials. 

With strong nucleophiles such as methoxide, ring opening follows an Sn2 mechanism. Examine the next to lowest-unoccupied molecular orbital (LUMO+1) for propylene oxide. On which carbon is it most heavily concentrated Is this also the least crowded carbon (Examine a spacefilling model for propylene oxide.) What should be the product of Sn2 addition ... 

Another useful way to think about carbon electrophilicity is to compare the properties of the carbonyls lowest-unoccupied molecular orbital (LUMO). This is the orbital into which the nucleophile s pair of electrons will go. Examine each compound s LUMO. Which is most localized on the carbonyl group Most delocalized Next, examine the LUMOs while displaying the compounds as space-filling models. This allows you to judge the extent to which the LUMO is actually accessible to an approaching nucleophile. Which LUMO is most available Least available ... 

In addition to electrophilic attack on the pyrrole ring in indole, there is the possibility for additions to the fused benzene ring. First examine the highest-occupied molecular orbital (HOMO) of indole. Which atoms contribute the most What should be the favored position for electrophilic attack Next, compare the energies of the various protonated forms of indole (C protonated only). These serve as models for adducts formed upon electrophilic addition. Which carbon on the pyrrole ring (C2 or C3) is favored for protonation Is this the same as the preference in pyrrole itself (see Chapter 15, Problem 2)1 If not, try to explain why not. Which of the carbons on the benzene ring is most susceptible to protonation Rationalize your result based on what you know about the reactivity of substituted benzenes toward electrophiles. Are any of the benzene carbons as reactive as the most reactive pyrrole carbon Explain. 

To explain tlie stereodieniistiy of tlie allylic substitution reaction, a simple stereoelectronic model based on frontier molecular orbital considerations bas been proposed fl55. Fig. G.2). Organocopper reagents, unlike C-nudeopbiles, possess filled d-orbitals fd - configuration), wbidi can interact botli witli tlie 7t -fC=C) orbital at tlie y-carbon and to a minor extent witli tlie cr -fC X) orbital, as depicted... 

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