Lowest unoccupied molecular orbital levels

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...

Both newly generated HOMO (highest occupied molecular orbital) and LUMO (lowest unoccupied molecular orbital) levels of fluorinated compounds are lower than those of a hydrogen compound. These lower orbital energy levels of the fluorinated compound indicate a high reactivity toward the reductant (electron donor to the LUMO) and a low reactivity toward the oxidant (electron acceptor from the HOMO). Moreover, a lower HOMO suggests strongly that the valence electrons captured by the molecular nuclei in the fluorinated... 

We consider here the possibility that such conformational variations can affect the highest occupied and lowest unoccupied molecular orbital levels of the chromophores and thereby modulate their light-absorption properties. 

Similarly, for the eigen-energy of the lowest unoccupied molecular orbital level, the LUMO is analogous to level - the first level of CB in quantum solid, one will write for it, with n= NI2)+ in Eq. (3.151), the expression ... 

Ding L, Ylng H-Z, Zhou Y, Lei T, Pei J (2010) Polycyclic imide derivatives synthesis and effective tuning of lowest unoccupied molecular orbital levels through molecular engineering. Org Lett 12 5522-5525... 

The Diels-Alder reaction is believed to proceed m a single step A deeper level of understanding of the bonding changes m the transition state can be obtained by examining the nodal properties of the highest occupied molecular orbital (HOMO) of the diene and the lowest unoccupied molecular orbital (LUMO) of the dienophile... 

The most extensive calculations of the electronic structure of fullerenes so far have been done for Ceo- Representative results for the energy levels of the free Ceo molecule are shown in Fig. 5(a) [60]. Because of the molecular nature of solid C o, the electronic structure for the solid phase is expected to be closely related to that of the free molecule [61]. An LDA calculation for the crystalline phase is shown in Fig. 5(b) for the energy bands derived from the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) for Cgo, and the band gap between the LUMO and HOMO-derived energy bands is shown on the figure. The LDA calculations are one-electron treatments which tend to underestimate the actual bandgap. Nevertheless, such calculations are widely used in the fullerene literature to provide physical insights about many of the physical properties. 

The method involves the irradiation of a sample with polychromatic X-rays (synchrotron radiation) which inter alia promote electrons from the innermost Is level of the sulfur atom to the lowest unoccupied molecular orbitals. In the present case these are the S-S antibonding ct -MOs. The intensity of the absorption lines resulting from these electronic excitations are proportional to the number of such bonds in the molecule. Therefore, the spectra of sulfur compounds show significant differences in the positions and/or the relative intensities of the absorption lines [215, 220, 221]. In principle, solid, liquid and gaseous samples can be measured. 

Molecular engineering of ruthenium complexes that can act as panchromatic CT sensitizers for Ti02-based solar cells presents a challenging task as several requirements have to be fulfilled by the dye, which are very difficult to be met simultaneously. The lowest unoccupied molecular orbitals (LUMOs) and the highest occupied molecular orbitals (HOMOs) have to be maintained at levels where photo-induced electron transfer into the Ti02 conduction band and regeneration... 

Fig. 9 OMT bands for NiOEP, associated with transient reduction (1.78 V) and transient oxidation (—1.18 V). Data obtained from a single molecule in a UHV STM. The ultraviolet photoelectron spectrum is also shown, with the energy origin shifted (by the work function of the sample, as discussed in [25]) in order to allow direct comparison. The highest occupied molecular orbital, n, and the lowest unoccupied molecular orbital, %, are shown at their correct energy, relative to the Fermi level of the substrate. As in previous diagrams,

H2, N2, or CO dissociates on a surface, we need to take two orbitals of the molecule into account, the highest occupied and the lowest unoccupied molecular orbital (the HOMO and LUMO of the so-called frontier orbital concept). Let us take a simple case to start with the molecule A2 with occupied bonding level a and unoccupied anti-bonding level a. We use jellium as the substrate metal and discuss the chemisorption of A2 in the resonant level model. What happens is that the two levels broaden because of the rather weak interaction with the free electron cloud of the metal. 

Figure 1 shows the electron attachment energies (AE) and ionization potentials (IP) of silyl substituted 7t-systems and related compounds [4], AE can be correlated with the energy level of the LUMO (lowest unoccupied molecular orbital) and IP can be correlated with the energy level of the HOMO (highest occupied molecular orbital). For a-substituted 7t-systems, the introduction of a silyl group produces a decrease in the tc -(LUMO) level. This effect is attributed to the interaction between a low-lying silicon-based unoccupied orbital such as the empty d orbital of silicon and the it orbital (d -p interaction) as shown in Fig. 2. Recent investigations on these systems, however, indicate that d orbitals on silicon are not necessarily required for interpreting this effect a-effects of SiR3 can also be explained by the interaction between Si-R a orbitals and the 7r-system.

In the course of investigation of reactivity of the mesoionic compound 44 (Scheme 2) the question arose if this bicyclic system participates in Diels-Alder reactions as an electron-rich or an electron-poor component <1999T13703>. The energy level of the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) orbitals were calculated by PM3 method. Comparison of these values with those of two different dienophiles (dimethyl acetylenedicarboxylate (DMAD) and 1,1-diethylamino-l-propyne) suggested that a faster cycloaddition can be expected with the electron-rich ynamine, that is, the Diels-Alder reaction of inverse electron demand is preferred. The experimental results seemed to support this assumption. 

FIGURE 3.4 Molecular level alignment diagrams constructed using the HOMO and vacuum levels measured using UPS. The lowest unoccupied molecular orbital LUMO positions are inferred assuming a HOMO/LUMO gap equal to the onset of optical absorption. The chemical structure of CuPc is shown. (From Hill, I.G. and Kahn, A., J. Appl. Phys., 86, 2116, 1991. With permission.)... 

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