Hiickel molecular orbitals nonbonding

Two groups have studied the bonding in pentadienyl-metal-tricar-bonyl complexes (119, 238) and are agreed that effective overlap between the pentadienyl nonbonding orbital and an orbital of suitable symmetry on the metal (Fig. 17) makes a major contribution to the stability of these complexes. However, the two types of molecular orbital calculation [one an extended Hiickel (119) and the other a parameter-free approximate Hartree-Fock calculation (255)] disagree about the precise ordering of energy levels in this type of complex. 

Fig. 4.16 The n molecular orbitals and n energy levels for an acyclic three-p-orbital system in the simple Hiickel method. The MOs are composed of the basis functions (three p AOs) and the eigenvectors (the c s), while the energies of the MOs follow from the eigenvalues (Eq. 4.68). In the drawings of the MOs, the relative sizes of the AOs in each MO suggest the relative contribution of each AO to that MO. This diagram is for the propenyl radical. The paired arrows represent a pair of electrons of opposite spin, in the fully-occupied lowest MO, i/q, and the single arrow represents an unpaired electron in the nonbonding MO, 1j/2 the highest n MO, ij/3, is empty in the radical...

Molecular orbital calculations on reduced flavins, such as the extended Hiickel calculations of Pullman and Pullman (41) and the self-consistent field calculations of Fox et al. (42), suggest that the energy of the highest occupied molecular orbital (HOMO) varies only slightly with conformational changes about theN(5)-N(10) axis, and all of these calculations show the energy of the HOMO to be nonbonding to... 

The determinant of the —> a acency matrix A. It was observed that this determinant often equals zero and this is a necessary and sufficient condition for the presence of nonbonding molecular orbitals in Hiickel theory. The actual numerical value of det A is correlated to the thermodynamic stability of the molecule [Graovac and Gutman, 1978, 1979 Trinajstic, 1992 Gutman and Vidovic, 2002a]. 

Spin densities (p) are theoretical quantities, defined as the sum of the squared atomic orbital coefficients in the nonbonding semi-occupied molecular orbital (SOMO) of the radical species (Hiickel theory). For monoradical species, the spin density is connected to the experimental EPR hyperfine coupling constant a through the McConnell equation [38]. This relation provides the opportunity to test the spin density dependence of the D parameter [Eq. (8)] for the cyclopentane-1,3-diyl triplet diradicals 10 by comparing them with the known experimental hyperfine coupling constants (ap) of the corresponding substituted cumyl radicals 14 [39]. The good semiquadratic correlation (Fig. 9) between these two EPR spectral quantities demonstrates unequivocally that the localized triplet 1,3-diradicals 9-11 constitute an excellent model system to assess electronic substituent effects on the spin density in cumyl-type monoradicals. 

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