Degeneracy atomic orbitals

Gardner 45) has observed the spectrum of Cl atoms adsorbed on a silica-gel surface at 77°K. The experimental results indicate that the orbital degeneracy of the 3p atomic orbital has been removed as a result of the electrostatic interaction with the surface. From the occupancy of the atomic orbitals one would predict that gx >011 — 2.00 and indeed the experimental g values are = 2.012 with g = 2.003. The hyperfine coupling indicates that the impaired electron is highly localized in the 3p orbitals. 

The double degeneracy of NBMOs in m-[8] has nothing to do with the geometrical symmetry of the molecule, but, rather, with the connectivity of the two radical centres, or the phase relationship of the atomic orbitals in the conjugated system. Therefore, the term topological symmetry has been proposed to describe the connectivity of the carbon atoms carrying the n-electrons and the periodicity of the Jt-orbitals in this class of non-Kekule hydrocarbons. 

Fio. 8. Relative energy levels and degeneracies of the 13 bonding and 23 antibonding skeletal molecular orbitals (MO s) of the icosahedral anion BiaHia (148). (AO, atomic orbital.)... 

Herzberg (Nobel prize for Chemistry, 1971) commented on the two distinct photoionizations from methane that this observation illustrates the rather drastic nature of the approximation made in the valence bond treatment of CH4, in which the 2s and 2p electrons of the carbon atom are considered as degenerate and where this degeneracy is used to form tetrahedral orbitals representing mixtures of 2s and 2p atomic orbitals. The molecular orbital treatment does not have this difficulty". 

Fig. 3.25 Central atom orbital symmetries and degeneracies Tor Oh AB , ABS, and Cltl AB4 species.

The fact that these HOMOs and LUMOs have a two-fold degeneracy implies that there are four isoenergetic one-electron transitions to yield the first excited states this complication is however resolved by the interaction of these one-electron excitations, and this is known as configuration interaction. The concept of configuration interaction (Cl) is somewhat similar to that of the interaction of atomic orbitals to form molecular orbitals. An electron configuration defines the distribution of electrons in the available orbitals, and an actual state is a combination of any number of such electron configurations, the state wavefunction being... 

Write the determinantal wave functions for the ground state of the oxygen atom, assuming the unpaired electrons have a spin. What is the orbital degeneracy of the ground state What is the spin degeneracy ... 

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