HOMO-LUMO energy levels

Table 3.2 HOMO and LUMO energy levels, HOMO-LUMO energy gaps (Ee-l) of SiQDs with different surface passivations in their ground and first excited singlet states (unit eV). Note that HOMO and LUMO in excited state are actually two singly occupied orbitals [26]. Reprinted with permission from (Li QS, Zhang RQ, Lee ST, Niehaus TA, Frauenheim T (2008) Optimal surface functionalization of sihcon quantum dots, J Chem Phys 128 244714). Copyright (2008), American Institute of Physics...

In the field of optoelectronics, the development of pure-blue-to-deep-blue-emitting ionic phosphors is an ultimate challenge for full-color displays and white-light sources. Control of the frontier orbital energy level (HOMO-LUMO) is the sole method to achieve better blue phosphorescent iridium complexes by appropriate ligand selection and the introduction of adequate substituents. 

Selected structural and energetic parameters for the Cso, Sig Gc6o Sn ) and Pb6o compounds (HF/LanllDZ level). All distances are in angstroms energies and HOMO-LUMO gaps are in atomic umts... 

In summary, the position of the frontier electron energy levels (HOMO and LUMO) of porphyrins and phthalocyanines can be finely tuned by the appropriate combination of central metal and substituted ligand as detected in photoelectron spectroscopy or in the redox potentials. A rich redox chemistry in interplay with a number of reactants and counterions has been estabhshed. A systematic consideration of the electrochemical and photoelectrochemical characteristics of porphyrins and phthalocyanines as individual molecules in solution, as molecules adsorbed at surfaces, and as molecular thin films serving to mimic the characteristics of molecular aggregates is of much relevance to the choosing or designing of optimized porphyrin or phthalocyanine sensitizers for DSSCs. 

The particle-in-a-box wavefunction can also be applied to it electrons in conjugated hydrocarbon molecules such as butadiene. The wavelength of radiation that is absorbed when a it electron is promoted from the highest occupied energy level (HOMO) to the lowest unoccupied level (LUMO) has been calculated, and found to be reasonably close to the experimental value. 

For the calculation of energy levels homo( ) and lumo( ") of the NCs with a certain size and radius r, the following formulas developed by Brus [34], using the effective mass approximation and considering Coulomb interaction of the electron hole pair, have been applied ... 

Metals are distinguished by their opacity, reflectivity (metallic shine, metallic mirror), and conductivity. All of these properties are related. Reflectivity depends on high conductivity. Conductivity is high since there is no energy gap at the Fermi level (HOMO-LUMO gap), between the occupied and unoccupied levels. 

FIGURE 5.3 (a) The energy levels of LUMO, HOMO, and HOMO-1 for SWCNTs of different diameters, (b) The energy difference between LUMO and HOMO and the fitting curve. (Reprinted from Rrf. [22] with permission of AIP Publishing LLC. Copyright 2008.)... 

The results show an overall destabilization of the occupied and unoccupied energy levels. The LUMOs destabilization, however, offsets the HOMOs destabilization, leading to increased HOMO-LUMO gaps for the deprotonated species. As a matter of fact, the fully deprotonated N3 [104—106], which is found at pH > 11, exhibits its main spectral features in the visible and UV region at 2.48, 3.33, and 4.07 eV the bands in the visible are blue-shifted by ca. 0.2 eV going from pH <1.5 to pH 11. The related complex in which the NCS groups are replaced by Cl ligands complex has attracted considerable interest due to its red-shifted visible absorption bands (2.38, 3.25, and 4.03 eV) (see Fig. 4). 

It was previously pointed out that overlap factors cause the z component of I eg to rise in energy and 2eg to fall. This is also indicated in Figure 15.9. A low-spin 16-electron ML complex would then be stabilized by this distortion. At the octahedral geometry, all levels are doubly occupied up to t2g. For a 16-electron complex, there will be 4 electrons in t2g. The downward slope of I b overrules the one component of 16g that rises in energy. Notice also that since 2b2 goes up in energy a HOMO-LUMO gap is created for a distorted 16-electron complex. Notice also that this distortion will be stabilizing for a complex with only 12-electron (t2g is empty). We shall pursue the ramifications of this shortly. 

These absorptions are ascribed to n-n transitions, that is, transitions of an electron from the highest occupied n molecular orbital (HOMO) to the lowest unoccupied n molecular orbital (LUMO). One can decide which orbitals are the HOMO and LUMO by filling electrons into the molecular energy level diagram from the bottom up, two electrons to each molecular orbital. The number of electrons is the number of sp carbon atoms contributing to the n system of a neuhal polyalkene, two for each double bond. In ethylene, there is only one occupied MO and one unoccupied MO. The occupied orbital in ethylene is p below the energy level represented by ot, and the unoccupied orbital is p above it. The separation between the only possibilities for the HOMO and LUMO is 2.00p. 

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. 

Calculations for Ceo in the LDA approximation [62, 60] yield a narrow band (- 0.4 0.6 eV bandwidth) solid, with a HOMO-LUMO-derived direct band gap of - 1.5 eV at the X point of the fee Brillouin zone. The narrow energy bands and the molecular nature of the electronic structure of fullerenes are indicative of a highly correlated electron system. Since the HOMO and LUMO levels both have the same odd parity, electric dipole transitions between these levels are symmetry forbidden in the free Ceo moleeule. In the crystalline solid, transitions between the direct bandgap states at the T and X points in the cubic Brillouin zone arc also forbidden, but are allowed at the lower symmetry points in the Brillouin zone. The allowed electric dipole... 

The numerical value of hardness obtained by MNDO-level calculations correlates with the stability of aromatic compounds. The correlation can be extended to a wider range of compounds, including heterocyclic compounds, when hardness is determined experimentally on the basis of molar reffactivity. The relatively large HOMO-LUMO gap also indicates the absence of relatively high-energy, reactive electrons, in agreement with the reduced reactivity of aromatic compounds toward electrophilic reagents. 

Both the LUMO and LUMO + 1 energy levels of the nitronaphthyridines and the values of the coefficients at the carbon and ring nitrogen in the LUMO and LUMO -f 1 orbitals were determined. Using homo = -11.9 eV for ammonia, the values of the stabilization energy AE) for each position of the nitronaphthyridines were calculated. Tire results of the cal-... 

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