MO, Bonding

Figure 7-18. Schematic representation of the LCAO scheme in a, T-only calculation for ethylene, The AOs

The alkyl-bridged structures can also be described as comer-protonated cyclopropanes, since if the bridging C—C bonds are considered to be fully formed, there is an extra proton on the bridging carbon. In another possible type of structure, called edge-protonated cyclopropanes, the carbon-carbon bonds are depicted as fully formed, with the extra proton associated with one of the bent bonds. MO calculations, structural studies under stable-ion conditions, and product and mechanistic studies of reactions in solution have all been applied to understanding the nature of the intermediates involved in carbocation rearrangements. 

The pA of 1,3-dithiane is 36.5 (Cs" ion pair in THF). The value for 2-phenyl-1,3-dithiane is 30.5. There are several factors which can contribute to the anion-stabilizing effect of sulfur substituents. Bond dipole effects contribute but carmot be the dominant factor because oxygen substituents do not have a comparable stabilizing effect. Polarizability of sulfur can also stabilize the carbanion. Delocalization can be described as involving 3d orbitals on sulfur or hyperconjugation with the a orbital of the C—S bond. MO calculations favor the latter interpretation. An experimental study of the rates of deprotonation of phenylthionitromethane indicates that sulfur polarizability is a major factor. Whatever the structural basis is, there is no question that thio substituents enhance... 

Simple Hiickel calculations on benzene, in contrast, place all the n electrons in bonding MOs. The 7t-electron energy of benzene is calculated by summing the energies of the six 71 electrons, which is 6a -F 8/S, lower by 2/S than the value of 6a -F 6/S for three isolated double bonds. Thus, the HMO method predicts a special stabilization for benzene. 

The pattern of two half-filled degenerate levels persists for larger rings containing 4n 71 electrons. In contrast, all 4 -F 2 systems are predicted to have all electrons paired in bonding MOs with net stabilization relative to isolated double bonds. This pattern provides... 

As each B atom contributes 1 electron to its B-Ht bond and 2 electrons to the framework MOs, the (n + 1) framework bonding MOs are just filled by the 2n electrons from nB atoms and the 2 electrons from the anionic charge. Further, it is possible (conceptually) to remove a BHt group and replace it by 2 electrons to compensate for the 2 electrons contributed by the BHi group to the MOs. Electroneutrality can then be achieved by adding the appropriate number of protons this does not alter the number of electrons in the system and hence all bonding MOs remain just filled. 

Figure 6.22 Schematic indication of the p -p interaction between the vacant orbital on B and the 3 filled Pz orbitals on the 3 X atoms leading to a bonding MO of n symmetry.

Figure 17.2 Schematic molecular orbital energy diagram for diatomic halogen molecules. (For F2 the order of the upper and 7T bonding MOs is inverted.).

Consider the H2 molecule in a minimum basis consisting of one s-function on each centre, xa and xb- A RHF calculation will produce two MOs, and < 2, being the sum and difference of the two AOs. The sum of the two AOs is a bonding MO, with increased bability of finding the electrons between the two nuclei, while the difference is an antibonding MO, with decreased probability of finding the electrons between the two nuclei. 

The HF wave function will have two electrons in the lowest energy (bonding) MO. 

The dissociation problem can also be solved by using a wave function of the UHF type. Here the a and /) bonding MOs are allowed to localize , thereby reducing the MO symmetries to Coov... 

Figure 1.17 Molecular orbitals of H2- Combination of two hydrogen 1 s atomic orbitals leads to two H2 molecular orbitals. The lower-energy, bonding MO is filled, and the higher-energy, antibonding MO is unfilled.

Figure 1.18 A molecular orbital description of the C=C tt bond in ethylene. The lower-energy, tt bonding MO results from a combination of p orbital lobes with the same algebraic sign and is filled. The higher-energy, -tt antibonding MO results from a combination of p orbital lobes with the opposite algebraic signs and is unfilled.

The stability order of alkenes is due to a combination of two factors. One is a stabilizing interaction between the C=C tr bond and adjacent C-H a bonds on substituents. In valence-bond language, the interaction is called hyperconjugation. In a molecular orbital description, there is a bonding MO that extends over the four-atom C=C—< -H grouping, as shown in Figure 6.6. The more substituents that are present on the double bond, the more hyperconjugation there is and the more stable the alkene. 

Figure 30.2 The six n molecular orbitals of 1,3,5-hexatriene. In the ground state, the three bonding MOs are filled. In the excited state,

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