Nonbonding molecular orbital NBMO

Figure 21-9 Energies and schematic representations of the it molecular orbitals of the 2-propenyl cation, 22. The calculated jr-electron energy of the cation is 2 a + 1.41/3) = 2a + 2.82/3. Orbitals with the energy a are neither bonding nor antibonding and are called nonbonding molecular orbitals (NBMO). The intermediate energy molecular orbital of the 2-propenyl cation is a NBMO because its component atomic orbitals, being on C1 and C3, are too far apart to be bonding or antibonding.

In any nonbonding molecular orbital (NBMO), the sum of the coefficients of the atoms s adjacent to a given atom r is zero. Hence the NBMO coefficients can be calculated very easily. The benzyl radical provides a nice example. All of the non-starred atoms have coefficients of zero. We give the para atom an arbitrary coefficient a. The sum of the coefficients of the atoms adjacent to the meta carbons must be zero, so the ortho coefficients are —a. For the sum of the coefficients around the ipso carbon to cancel, the benzylic carbon coefficient must be 2a. The value for a is given by the normalization condition ... 

Nonbonding molecular orbitals (NBMOs) are MOs with an energy sj = a, Xj = 0. The number of NBMOs is at least equal to the absolute value of the difference between the numbers of atoms in the two sets. Thus odd AHs (AHs with an odd number of atoms) have at least one NBMO. 

In NH, two valence MOs, corresponding to the N-H bond (2a) and lone pair on nitrogen (3a), are occupied by electron pairs. Two more valence electrons must be distributed between two degenerate, nonbonding molecular orbitals (NBMOs), Tlx, Ky, which consist of the 2px and 2py AOs on... 

Every odd alternant conjugated n system has a nonbonding molecular orbital, NBMO, with = a. The remaining MOs are arranged symmetrically above and below the NBMO. 

Number of NBMOs (NBMO = nonbonding molecular orbitals)... 

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