Methylene orbitals

Our treatments of ethylene are all carried out with two methylene fragments that have the a la b parts of both of their configurations doubly occupied in all VB stmctures used. The 12 electrons involved can be placed in the core as described in Chapter 9, which means that there are only four electrons, those for the C—C a and 7t bonds, that are in the MCVB treatment. For simplicity we shall rename the other two methylene orbitals a, and tti, where / = 1,2 for the two ends of the molecule. The Weyl dimension formula tells us that there are 20 linearly independent tableaux from four electrons distributed in four orbitals. When we use D2h s mimetry, however, only 12 of them are involved in eight Ai functions. 

The carbon atoms form two orbits. The orbital on the central atom is in the center of the symmetry group and transforms as a 2. The three methylene orbitals are in C2 sites, transforming as the 2 urep of the site group, i.e., they are antisymmetric with respect to a and symmetric with respect to Ay. The induced representation is... 

Only one exception to the clean production of two monomer molecules from the pyrolysis of dimer has been noted. When a-hydroxydi-Zvxyljlene (9) is subjected to the Gorham process, no polymer is formed, and the 16-carbon aldehyde (10) is the principal product in its stead, isolated in greater than 90% yield. This transformation indicates that, at least in this case, the cleavage of dimer proceeds in stepwise fashion rather than by a concerted process in which both methylene—methylene bonds are broken at the same time. This is consistent with the predictions of Woodward and Hoffmann from orbital symmetry considerations for such [6 + 6] cycloreversion reactions in the ground state (5). 

The lowest energy molecular orbital of singlet methylene looks like a Is atomic orbital on carbon. The electrons occupying this orbital restrict their motion to the immediate region of the carbon nucleus and do not significantly affect bonding. Because of this restriction, and because the orbital s energy is very low (-11 au), this orbital is referred to as a core orbital and its electrons are referred to as core electrons. 

Singlet methylene also possesses unoccupied molecular orbitals. The unoccupied orbitals have higher (more positive) energies than the occupied orbitals, and these orbitals, because they are unoccupied, do not describe the electron distribution in singlet methylene. Nevertheless, the shapes of unoccupied orbitals, in particular, the few lowest energy unoccupied orbitals, are worth considering because they provide valuable insight into the methylene s chemical reactivity. 

For electron movement to occur, the donor and acceptor molecules must approach so that the donor HOMO and acceptor LUMO can interact. For example, the LUMO of singlet methylene is a 2p atomic orbital on carbon that is perpendicular to the molecular plane. Donors must approach methylene in a way that allows interaction of the donor HOMO with the 2p orbital. 

Draw a Lewis structure for singlet methylene, CH2 (all the electrons in singlet methylene are spin-paired). Ho many electrons remain after all bonds have been formei Where are the extra electrons located, in the plane the molecule or perpendicular to the plane Examine t highest-occupied molecular orbital (HOMO) of methyle to tell. 

Finally, display the highest-occupied molecular orbital (HOMO) of triphenylphosphinemethylidene. Is it primarily concentrated on the methylene carbon as would be expected of a fully-developed anion, or is it delocalized over both phosphorous and carbon Does this suggest that the molecule incorporates a n bond ... 

Examine electrostatic potential maps for dimethylsulfonium and dimethylsulfoxonium ylides. Which contains the more negatively-charged carbon Do either or both of the ylides incorporate a fully formed 7U bond Compare bond distances involving methylene and methyl carbons. Also examine the highest-occupied molecular orbital (HOMO) for evidence of 7U bonding. 

Examine the highest-occupied molecular orbital (HOMO) of singlet methylene. Where is the pair of electrons, inplane or perpendicular to the plane Next, examine the electrostatic potential map. Where is the molecule most electron rich, in the o or the 7t system Where is the most electron poor Next, display the corresponding map for triplet methylene. Which molecule would you expect to be the better nucleophile The better electrophile Explain. Experimentally, one state of methylene shows both electrophilic and nucleophilic chemistry, while the other state exhibits chemistry typical of radicals. Which state does which Elaborate. 

Divalent carbon species called carbenes are capable of fleeting existence. For example, methylene, CH2, is the simplest carbene. The two unshared electrons in methylene can be either spin-paired in a single orbital or unpaired in different orbitals. Predict the type of hybridization you expect carbon to adopt in singlet (spin-paired) methylene and triplet (spin-unpaired) methylene. Draw a picture of each, and identify the valence orbitals on carbon. 

The methylene group carries an empty p orbital. Howr will the methyl group interact w ith this empty orbital Clearly the 7r-type orbitals of the methyl group (ttu in E, tt. in B) have the appropriate symmetry to mix with the p orbital. A typical orbital interaction diagram (for E) is shown in Fig. 37. Several conclusions emerge immediately from this diagram ... 

The vinyl cation (Fig. 40 and III.13) in which the empty p orbital on the positive center is coplanar with the terminal methylene group, is clearly another candidate for hyperconjugative donation. The in-plane orbital readily overlaps with the odd p orbital, with formation of two delocalized orbitals and an energy gain... 

Methoxy radical 210 Methyl-de-diazoniation 253 Methylene, energy of triplet state 178 Molecular orbital method, applications to ArNj structure and to dediazoniations - ab initio 84ff., 177ff., 270, 280... 

FIGURE 2.5 The three bonding orbitals of 3-methylene-1,4-pentadiene (9). 

Given the zwitterionic natnre of single carbenes, the possibility exists for coordinating solvents such as ethers or aromatic compounds to associate weakly with the empty p-orbital of the carbene. Several experimental stndies have revealed dramatic effects of dioxane or aromatic solvents on prodnct distribntions of carbene reactions. Computational evidence has also been reported for carbene-benzene complexes. Indeed, picosecond optical grating calorimetry stndies have indicated that singlet methylene and benzene form a weak complex with a dissociation energy of 8.7kcal/mol. ... 

In the case of r)2-coordination of the exocyclic C=C bond, it becomes substantially elongated compared with the double bond of free alkenes, as a result of back donation from the metal to the 7t orbitals of the double bond. For instance, in complex 17b the coordinated bond length is 1.437 A (see Fig. 3.2).18 This is also reflected in the loss of planarity around the quaternary exocyclic carbon, the methylenic carbon being bent out of the ring plane by 10.78°.18 Similar structural features were also observed with other P2Pd conjugated olefin complexes.39... 

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