Highest occupied molecular orbital delocalized state

Fig. 12. The transition from a localized state (mean spacing 1.5, as indicated) to a delocalized state (mean speicing 1.1) for a cluster of 91 atoms with one-valence-electron each. Shown is the weight (logarithmic scale) of the highest occupied molecular orbital (HOMO) of the cluster on each one of the 91 atoms. The localized state decreases exponentially as one moves away from the atom on which it is centered. The delocalized state has, on the average, the same weight on all the atoms.

It is important to note that many metallic properties, such as the Knight shift and the Korringa relationship, are determined by the finite and quasiFermi level local density of states ( p-LDOS). In the approximation most familiar to chemists, what this means is that the highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO-LUMO) gap in metals is much smaller than the thermal energy kf,T, and the value of the / f-LDOS reflects the frontier orbital contributions in a metallic system [23]. The /ip-LDOS also represents a crucial metal sxudace attribute that can serve as an important conceptual bridge between the delocalized band structure (physics) picture and the localized chemical bonding (chemical) picture of metal-adsorbate interactions. 

In this equation, u denotes the irreducible representation spanned by uA and pB. From each pair of magnetic orbitals pA and uB localized on the A and B fragments respectively, one can construct two molecular orbitals delocalized on the whole molecule A - B. Each of these molecular orbitals is singly occupied in the pair state of highest spin multiplicity. We denote A,v the energy gap between these molecular orbitals for this state and Dw the energy gap between the two magnetic orbitals as shown below. 

The conjugation, that is, the resonance interaction between the n bonds, results in delocalized n electron states. In the case of PPV these states are occupied by the eight n electrons. There is a highest occupied molecular n orbital, and there is a gap by extending up to next level, the lowest unoccupied molecular n orbital. 

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