Lowest unoccupied molecular orbital wave function

According to a modified intermediate neglect of differential overlap (MINDO)/3 calculation, the highest occupied molecular orbital (HOMO) of a dicyanoDHI 7 shows a wave function similar to the lowest unoccupied molecular orbital (LUMO). Thus a locally excited (LE) transition (n-Jt ) is most probably hidden under this band. The assignment of a second band of 7 is less clear. 

Table I shows that the band gap, the energy difference between HOMO (highest occupied molecular orbitals) and LUMO (lowest unoccupied molecular orbitals) levels, decreases monotonically with the increase in network dimension. This decrease is caused by the delocalization of skeleton a electrons, which form both band edges. As is well known, eigenvalues of delocalized wave functions confined to a potential well are determined by the well size and potential-barrier heights. When delocalized wave functions are confined to a smaller area, the HOMO level moves downward and the LUMO level moves upwards, which results in the increase in band gap energy. This quantum size effect is given by...

The VEH band structure computed for PTV is presented in Fig. 4, where all the crossings among k bands and among a bands are avoided due to the low symmetry of the unit cell. The HOMO (highest occupied molecular orbital) and LUMO (lowest unoccupied molecular orbital) bands are, as expected, n bands, and show the same atomic orbital composition patterns as those reported for PT. The HOMO band of PTV corresponds to wave functions delocalized over the carbon backbone,with essentially no contribution from... 

Figures 2 and 3 show the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) for the carbon monoxide molecule. In the figures, white colour is for the positive sign of the wave function, while black colour indicates the negative sign of the wave function.

The first term is the screened electrostatic interaction between the donor and acceptor charges Qi and Q2 - assumed to be point charges - at the equilibrium distance Rn in the adduct. The second term accounts for covalent effects. The factor of 2 indicates that two electrons are shared. The c coefficients are the molecular wave-function weights on atoms 1 and 2. The energies Em and E are equal, to a first approximation, to the frontier orbital energies the base HOMO (HOMO = highest occupied molecular orbital) and the acid LUMO (LUMO = lowest unoccupied molecular orbital), i.e. to the base first ionization potential and to the acid electron aflSnity. A typical frontier orbital diagram is shown in Fig. 6.1. 

The mechanisms of chemical reactions and the reactivity properties of the molecules involved started to be elucidated through the analysis of the wave functions defining the quantum state of molecular systems,5-7 for instance the Fukui s frontier molecular orbital (FMO) theory8,9 has been very successful in rationalizing organic reactions basically through the analysis of the in- and out-of-phase overlap between the highest occupied molecular orbital (HOMO) of the nucleophile and the lowest unoccupied molecular... 

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